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PubMed1995

Comprehensive study on iterative algorithms of multiple sequence alignment.

Multiple sequence alignment is an important problem in the biosciences. To date, most multiple alignment systems have employed a tree-based algorithm, which combines the results of two-way dynamic programming in a tree-like order of sequence similarity. The alignment quality is not, however, high enough when the sequence similarity is low. Once an error occurs in the alignment process, that error can never be corrected. Recently, an effective new class of algorithms has been developed. These algorithms iteratively apply dynamic programming to partially aligned sequences to improve their alignment quality. The iteration corrects any errors that may have occurred in the alignment process. Such an iterative strategy requires heuristic search methods to solve practical alignment problems. Incorporating such methods yields various iterative algorithms. This paper reports our comprehensive comparison of iterative algorithms. We proved that performance improves remarkably when using a tree-based iterative method, which iteratively refines an alignment whenever two subalignments are merged in a tree-based way. We propose a tree-dependent, restricted partitioning technique to efficiently reduce the execution time of iterative algorithms.

Algorithms↗

PubMed2004

PROuST: a comparison method of three-dimensional structures of proteins using indexing techniques.

We present a new method for protein structure comparison that combines indexing and dynamic programming (DP). The method is based on simple geometric features of triplets of secondary structures of proteins. These features provide indexes to a hash table that allows fast retrieval of similarity information for a query protein. After the query protein is matched with all proteins in the hash table producing a list of putative similarities, the dynamic programming algorithm is used to align the query protein with each protein of this list. Since the pairwise comparison with DP is applied only to a small subset of proteins and, furthermore, DP re-uses information that is already computed and stored in the hash table, the approach is very fast even when searching the entire PDB. We have done extensive experimentation showing that our approach achieves results of quality comparable to that of other existing approaches but is generally faster.

Computational Biology↗

PubMed2003

Using guide trees to construct multiple-sequence evolutionary HMMs.

MOTIVATION: Score-based progressive alignment algorithms do dynamic programming on successive branches of a guide tree. The analogous probabilistic construct is an Evolutionary HMM. This is a multiple-sequence hidden Markov model (HMM) made by combining transducers (conditionally normalised Pair HMMs) on the branches of a phylogenetic tree. METHODS: We present general algorithms for constructing an Evolutionary HMM from any Pair HMM and for doing dynamic programming to any Multiple-sequence HMM. RESULTS: Our prototype implementation, Handel, is based on the Thorne-Kishino-Felsenstein evolutionary model and is benchmarked using structural reference alignments.

Algorithms↗

PubMed1993

Multiple sequence alignment by parallel simulated annealing.

We have developed simulated annealing algorithms to solve the problem of multiple sequence alignment. The algorithm was shown to give the optimal solution as confirmed by the rigorous dynamic programming algorithm for three-sequence alignment. To overcome long execution times for simulated annealing, we utilized a parallel computer. A sequential algorithm, a simple parallel algorithm and the temperature parallel algorithm were tested on a problem. The results were compared with the result obtained by a conventional tree-based algorithm where alignments were merged by two-way dynamic programming. Every annealing algorithm produced a better energy value than the conventional algorithm. The best energy value, which probably represents the optimal solution, was reached within a reasonable time by both of the parallel annealing algorithms. We consider the temperature parallel algorithm of simulated annealing to be the most suitable for finding the optimal multiple sequence alignment because the algorithm does not require any scheduling for optimization. The algorithm is also useful for refining multiple alignments obtained by other heuristic methods.

Algorithms↗

PubMed1995

An optimized parsing algorithm well suited to RNA folding.

The application of stochastic context-free grammars to the determination of RNA foldings allows a simple description of the sub-class of sought secondary structures, but it needs efficient parsing algorithms. The more classic thermodynamic model of folding, popularized by Zuker under the framework of dynamic programming algorithms, allows an easy computation of foldings but its use is delicate when constraints have to be introduced on sought secondary structures. We show here that S-attribute grammars unify these two models and we introduce a parsing algorithm whose efficiency enables us to handle problems until then too difficult or too large to deal with. As a matter of fact, our algorithm is as efficient as a standard dynamic programming one when applied to the thermodynamic model (yet it offers a greater flexibility for the expression of constraints) and it is faster and saves more space than other parsing algorithms used so far for stochastic grammars.

Algorithms↗

PubMed1991

A novel randomized iterative strategy for aligning multiple protein sequences.

The rigorous alignment of multiple protein sequences becomes impractical even with a modest number of sequences, since computer memory and time requirements increase as the product of the lengths of the sequences. We have devised a strategy to approach such an optimal alignment, which modifies the intensive computer storage and time requirements of dynamic programming. Our algorithm randomly divides a group of unaligned sequences into two subgroups, between which an optimal alignment is then obtained by a Needleman-Wunsch style of algorithm. Our algorithm uses a matrix with dimensions corresponding to the lengths of the two aligned sequence subgroups. The pairwise alignment process is repeated using different random divisions of the whole group into two subgroups. Compared with the rigorous approach of solving the n-dimensional lattice by dynamic programming, our iterative algorithm results in alignments that match or are close to the optimal solution, on a limited set of test problems. We have implemented this algorithm in a computer program that runs on the IBM PC class of machines, together with a user-friendly environment for interactively selecting sequences or groups of sequences to be aligned either simultaneously or progressively.

Amino Acid Sequence↗

PubMed2004

Detecting local structural similarity in proteins by maximizing number of equivalent residues.

A new algorithm for superimposing protein structures based on maximizing the number of spatially equivalent residues is introduced. The algorithm works in three distinct steps. First, the optimal residue map is calculated by structural alignment. By default, the double dynamic programming algorithm, as implemented in the program ASH, was used for the structure alignment step, but we also present results based on alignments imported from three other programs (Dali, CE, and VAST).Second, the structures are spatially superimposed such that the effective number of equivalent residues (NER)--aligned residue pairs that can be spatially overlapped--is maximized. The NER score is an analytic, differentiable similarity function that rewards spatially equivalent residues but ignores non-equivalent ones. Maximization of the NER score results in accurate superpositions in cases where root mean square deviation (RMSD) minimization fails. Third, the NER function is used in conjunction with traditional dynamic programming to realign the structures based on the proximity of residues in the superposition. Results are presented for a wide range of superposition problems and compared to results from Dali, CE, and VAST. In addition, several structure-structure pairs that show only partial similarity are discussed, and results are compared to those from the LGA, SARF2, and ThreeCa programs.

Algorithms↗

PubMed2000

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.

Algorithms↗

PubMed2005

Left ventricular volume estimation in cardiac three-dimensional ultrasound: a semiautomatic border detection approach.

RATIONALE AND OBJECTIVES: We propose a semiautomatic endocardial border detection method for three-dimensional (3D) time series of cardiac ultrasound (US) data based on pattern matching and dynamic programming, operating on two-dimensional (2D) slices of the 3D plus time data, for the estimation of full cycle left ventricular volume, with minimal user interaction. MATERIALS AND METHODS: The presented method is generally applicable to 3D US data and evaluated on data acquired with the Fast Rotating Ultrasound (FRU-) Transducer, developed by Erasmus Medical Center (Rotterdam, the Netherlands), a conventional phased-array transducer, rotating at very high speed around its image axis. The detection is based on endocardial edge pattern matching using dynamic programming, which is constrained by a 3D plus time shape model. It is applied to an automatically selected subset of 2D images of the original data set, for typically 10 equidistant rotation angles and 16 cardiac phases (160 images). Initialization requires the drawing of four contours per patient manually. We evaluated this method on 14 patients against MRI end-diastole and end-systole volumes. Initialization requires the drawing of four contours per patient manually. We evaluated this method on 14 patients against MRI end-diastolic (ED) and end-systolic (ES) volumes. RESULTS: The semiautomatic border detection approach shows good correlations with MRI ED/ES volumes (r = 0.938) and low interobserver variability (y = 1.005x - 16.7, r = 0.943) over full-cycle volume estimations. It shows a high consistency in tracking the user-defined initial borders over space and time. CONCLUSIONS: We show that the ease of the acquisition using the FRU-transducer and the semiautomatic endocardial border detection method together can provide a way to quickly estimate the left ventricular volume over the full cardiac cycle using little user interaction.

Algorithms↗

PubMed1998

Constructing phylogenies from quartets: elucidation of eutherian superordinal relationships.

In this work we present two new approaches for constructing phylogenetic trees. The input is a list of weighted quartets over n taxa. Each quartet is a subtree on four taxa, and its weight represents a confidence level for the specific topology. The goal is to construct a binary tree with n leaves such that the total weight of the satisfied quartets is maximized (an NP hard problem). The first approach we present is based on geometric ideas. Using semidefinite programming, we embed the n points on the n-dimensional unit sphere, while maximizing an objective function. This function depends on Euclidean distances between the four points and reflects the quartet topology. Given the embedding, we construct a binary tree by performing geometric clustering. This process is similar to the traditional neighbor joining, with the difference that the update phase retains geometric meaning: When two neighbors are joined together, their common ancestor is taken to be the center of mass of the original points. The geometric algorithm runs in poly(n) time, but there are no guarantees on the quality of its output. In contrast, our second algorithm is based on dynamic programming, and it is guaranteed to find the optimal tree (with respect to the given quartets). Its running time is a modest exponential, so it can be implemented for modest values of n. We have implemented both algorithms and ran them on real data for n = 15 taxa (14 mammalian orders and an outgroup taxon). The two resulting trees improve previously published trees and seem to be of biological relevance. On this dataset, the geometric algorithm produced a tree whose score is 98.2% of the optimal value on this input set (72.1% vs. 73.4%). This gives rise to the hope that the geometric approach will prove viable even for larger cases where the exponential, dynamic programming approach is no longer feasible.

Algorithms↗

PubMed2005

GATA: a graphic alignment tool for comparative sequence analysis.

BACKGROUND: Several problems exist with current methods used to align DNA sequences for comparative sequence analysis. Most dynamic programming algorithms assume that conserved sequence elements are collinear. This assumption appears valid when comparing orthologous protein coding sequences. Functional constraints on proteins provide strong selective pressure against sequence inversions, and minimize sequence duplications and feature shuffling. For non-coding sequences this collinearity assumption is often invalid. For example, enhancers contain clusters of transcription factor binding sites that change in number, orientation, and spacing during evolution yet the enhancer retains its activity. Dot plot analysis is often used to estimate non-coding sequence relatedness. Yet dot plots do not actually align sequences and thus cannot account well for base insertions or deletions. Moreover, they lack an adequate statistical framework for comparing sequence relatedness and are limited to pairwise comparisons. Lastly, dot plots and dynamic programming text outputs fail to provide an intuitive means for visualizing DNA alignments. RESULTS: To address some of these issues, we created a stand alone, platform independent, graphic alignment tool for comparative sequence analysis (GATA http://gata.sourceforge.net/). GATA uses the NCBI-BLASTN program and extensive post-processing to identify all small sub-alignments above a low cut-off score. These are graphed as two shaded boxes, one for each sequence, connected by a line using the coordinate system of their parent sequence. Shading and colour are used to indicate score and orientation. A variety of options exist for querying, modifying and retrieving conserved sequence elements. Extensive gene annotation can be added to both sequences using a standardized General Feature Format (GFF) file. CONCLUSIONS: GATA uses the NCBI-BLASTN program in conjunction with post-processing to exhaustively align two DNA sequences. It provides researchers with a fine-grained alignment and visualization tool aptly suited for non-coding, 0-200 kb, pairwise, sequence analysis. It functions independent of sequence feature ordering or orientation, and readily visualizes both large and small sequence inversions, duplications, and segment shuffling. Since the alignment is visual and does not contain gaps, gene annotation can be added to both sequences to create a thoroughly descriptive picture of DNA conservation that is well suited for comparative sequence analysis.

Algorithms↗

PubMed2004

Markov edit distance.

Edit distance was originally developed by Levenstein several decades ago to measure the distance between two strings. It was found that this distance can be computed by an elegant dynamic programming procedure. The edit distance has played important roles in a wide array of applications due to its representational efficacy and computational efficiency. To effect a more reasonable distance measure, the normalized edit distance was proposed. Many algorithms and studies have been dedicated along this line with impressive performances in recent years. There is, however, a fundamental problem with the original definition of edit distance that has remained elusive: its context-free nature. In determining the possible actions, i.e., insertion, deletion, and substitution, no systematic consideration was given to the local behaviors of the string/pattern in question that indeed encompass great amount of useful information regarding its content. In this paper, inspired by the success of the Markov Random Field theory, a new edit distance called Markov edit distance (MED) within the dynamic programming framework is proposed to take full advantage of the local statistical dependencies in the pattern in order to arrive at enhanced matching performance. Within this framework, two specialized distance measures are developed: The reshuffling MED to handle cases where a subpattern in the target pattern is the reshuffles of that in the source pattern, and the coherence MED which is able to incur local content based substitution, insertion, and deletion. The applications based on these two MEDs in string matching are then explored, whereof encouraging empirical results have been observed.

Algorithms↗

PubMed1992

Evolution of an automated ST-segment analysis program for dynamic real-time, noninvasive detection of coronary occlusion and reperfusion.

Patients in whom early and stable reperfusion through the infarct artery fails after thrombolytic treatment might benefit from further revascularization therapy. A reliable noninvasive technique able to detect both reperfusion and reocclusion would be useful to test this hypothesis. However, no such technique presently exists. ST-segment recovery analysis using continuous digital 12-lead ST monitoring has been shown to be an accurate predictor of infarct artery patency in real time. This method was dependent on a trained clinician's analysis of the recordings on a personal computer. For optimal bedside application, salient principles of this ST-segment recovery analysis were converted into algorithms and built into the ST monitor software. The essentials of these algorithms are described in this report.

Electrocardiography↗

PubMed1967