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PubMed2000

The practical use of the A* algorithm for exact multiple sequence alignment.

Multiple alignment is an important problem in computational biology. It is well known that it can be solved exactly by a dynamic programming algorithm which in turn can be interpreted as a shortest path computation in a directed acyclic graph. The A* algorithm (or goal-directed unidirectional search) is a technique that speeds up the computation of a shortest path by transforming the edge lengths without losing the optimality of the shortest path. We implemented the A* algorithm in a computer program similar to MSA (Gupta et al., 1995) and FMA (Shibuya and Imai, 1997). We incorporated in this program new bounding strategies for both lower and upper bounds and show that the A* algorithm, together with our improvements, can speed up computations considerably. Additionally, we show that the A* algorithm together with a standard bounding technique is superior to the well-known Carrillo-Lipman bounding since it excludes more nodes from consideration.

Algorithms↗
PubMed2001

On combinatorial DNA word design.

We consider the problem of designing DNA codes, namely sets of equi-length words over the alphabet [A, C, G, T] that satisfy certain combinatorial constraints. This problem is motivated by the task of reliably storing and retrieving information in synthetic DNA strands for use in DNA computing or as molecular bar codes in chemical libraries. The primary constraints that we consider, defined with respect to a parameter d, are as follows: for every pair of words w, x in a code, there are at least d mismatches between w and x if w not equal x and also between the reverse of w and the Watson-Crick complement of x. Extending classical results from coding theory, we present several upper and lower bounds on the maximum size of such DNA codes and give methods for constructing such codes. An additional constraint that is relevant to the design of DNA codes is that the free energies and enthalpies of the code words, and thus the melting temperatures, be similar. We describe dynamic programming algorithms that can (a) calculate the total number of words of length n whose free energy value, as approximated by a formula of Breslauer et al. (1986) falls in a given range, and (b) output a random such word. These algorithms are intended for use in heuristic algorithms for constructing DNA codes.

Algorithms↗
PubMed2002

Algorithms for phylogenetic footprinting.

Phylogenetic footprinting is a technique that identifies regulatory elements by finding unusually well conserved regions in a set of orthologous noncoding DNA sequences from multiple species. We introduce a new motif-finding problem, the Substring Parsimony Problem, which is a formalization of the ideas behind phylogenetic footprinting, and we present an exact dynamic programming algorithm to solve it. We then present a number of algorithmic optimizations that allow our program to run quickly on most biologically interesting datasets. We show how to handle data sets in which only an unknown subset of the sequences contains the regulatory element. Finally, we describe how to empirically assess the statistical significance of the motifs found. Each technique is implemented and successfully identifies a number of known binding sites, as well as several highly conserved but uncharacterized regions. The program is available at http://bio.cs.washington.edu/software.html.

Algorithms↗
PubMed2002

Super pairwise alignment (SPA): an efficient approach to global alignment for homologous sequences.

Sequence analysis is the basis of bioinformatics, while sequence alignment is a fundamental task for sequence analysis. The widely used alignment algorithm, Dynamic Programming, though generating optimal alignment, takes too much time due to its high computation complexity O(N(2)). In order to reduce computation complexity without sacrificing too much accuracy, we have developed a new approach to align two homologous sequences. The new approach presented here, adopting our novel algorithm which combines the methods of probabilistic and combinatorial analysis, reduces the computation complexity to as low as O(N). The computation speed by our program is at least 15 times faster than traditional pairwise alignment algorithms without a loss of much accuracy. We hence named the algorithm Super Pairwise Alignment (SPA). The pairwise alignment execution program based on SPA and the detailed results of the aligned sequences discussed in this article are available upon request.

Algorithms↗
PubMed2003

DNA library design for molecular computation.

A novel approach to designing a DNA library for molecular computation is presented. The method is employed for encoding binary information in DNA molecules. It aims to achieve a practical discrimination between perfectly matched DNA oligomers and those with mismatches in a large pool of different molecules. The approach takes into account the ability of DNA strands to hybridize in complex structures like hairpins, internal loops, or bulge loops and computes the stability of the hybrids formed based on thermodynamic data. A dynamic programming algorithm is applied to calculate the partition function for the ensemble of structures, which play a role in the hybridization reaction. The applicability of the method is demonstrated by the design of a twelve-bit DNA library. The library is constructed and experimentally tested using molecular biology tools. The results show a high level of specific hybridization achieved for all library words under identical conditions. The method is also applicable for the design of primers for PCR, DNA sequences for isothermal amplification reactions, and capture probes in DNA-chip arrays. The library could be applied for integrated DNA computing of twelve-bit instances of NP-complete combinatorial problems by multi-step DNA selection in microflow reactors.

Algorithms↗
PubMed2003

Natural selection and algorithmic design of mRNA.

Messenger RNA (mRNA) sequences serve as templates for proteins according to the triplet code, in which each of the 4(3) = 64 different codons (sequences of three consecutive nucleotide bases) in RNA either terminate transcription or map to one of the 20 different amino acids (or residues) which build up proteins. Because there are more codons than residues, there is inherent redundancy in the coding. Certain residues (e.g., tryptophan) have only a single corresponding codon, while other residues (e.g., arginine) have as many as six corresponding codons. This freedom implies that the number of possible RNA sequences coding for a given protein grows exponentially in the length of the protein. Thus nature has wide latitude to select among mRNA sequences which are informationally equivalent, but structurally and energetically divergent. In this paper, we explore how nature takes advantage of this freedom and how to algorithmically design structures more energetically favorable than have been built through natural selection. In particular: (1) Natural Selection--we perform the first large-scale computational experiment comparing the stability of mRNA sequences from a variety of organisms to random synonymous sequences which respect the codon preferences of the organism. This experiment was conducted on over 27,000 sequences from 34 microbial species with 36 genomic structures. We provide evidence that in all genomic structures highly stable sequences are disproportionately abundant, and in 19 of 36 cases highly unstable sequences are disproportionately abundant. This suggests that the stability of mRNA sequences is subject to natural selection. (2) Artificial Selection--motivated by these biological results, we examine the algorithmic problem of designing the most stable and unstable mRNA sequences which code for a target protein. We give a polynomial-time dynamic programming solution to the most stable sequence problem (MSSP), which is asymptotically no more complex than secondary structure prediction. We show that the corresponding least stable sequence problem (LSSP) is NP-complete, and develop two heuristics for the construction of such sequences. We have implemented these algorithms, and present experimental results placing the high/low stability sequences in context with both wildtype and random encodings. Our implementation has already been applied to the design of RNA "code-words" creating little or no secondary structure in RNA computing (Brenneman and Condon, 2001; Marathe et al., 2001), and we anticipate a variety of other applications of this work to sequence design problems (Skiena, 2001).

Algorithms↗
PubMed1994

Recent developments in linear-space alignment methods: a survey.

A dynamic-programming strategy for sequence alignment first proposed in 1975 by Dan Hirschberg can be adapted to yield a number of extremely space-efficient algorithms. Specifically, these algorithms align two sequences using only "linear space," i.e., an amount of computer memory that is proportional to the sum of the lengths of the two sequences being aligned. This paper begins by reviewing the basic idea, as it applies to the global (i.e., end-to-end) alignment of two DNA or protein sequences. Three of our recent extensions of the technique are then outlined. The first extension computes an optimal alignment subject to the constraint that each position, i, of the first sequence must be aligned somewhere between positions L[i] and U[i] of the second sequence, for given values of L and U. The second finds all aligned position pairs (i.e., potential columns of the alignment) that occur in an alignment whose score exceeds a given threshold. The third treats the case where each of the two sequences is allowed to be an alignment (e.g., a sequence of aligned pairs), using a sensitive scoring scheme. We also describe two linear-space methods for computing k best local (i.e., involving only a part of each sequence) alignments, where k > or = 1. One is a linear-space version of the algorithm of Waterman and Eggert (1987), and the other is based on the strategy proposed by Wilbur and Lipman (1983). Finally, we describe programs that implement various combinations of these techniques to provide a multisequence alignment method that is especially suited to handling a few very long sequences. The utility of these programs is illustrated by analysis of the locus control region of the beta-like globin gene cluster of several mammals.

Algorithms↗
PubMed1995

Algorithms for protein structural motif recognition.

The identification of protein sequences that fold into certain known three-dimensional (3D) structures, or motifs, is evaluated through a probabilistic analysis of their one-dimensional (1D) sequences. We present a correlation method that runs in linear time and incorporates pairwise dependencies between amino acid residues at multiple distances to assess the conditional probability that a given residue is part of a given 3D structure. This method is generalized to multiple motifs, where a dynamic programming approach leads to an efficient algorithm that runs in linear time for practical problems. By this approach, we were able to distinguish (2-stranded) coiled-coil from non-coiled-coil domains and globins from nonglobins. When tested on the Brookhaven X-ray crystal structure database, the method does not produce any false-positive or false-negative predictions of coiled coils.

Algorithms↗
PubMed1995

Constructing lattice models of protein chains with side groups.

An algorithm to construct lattice models of polymers with side chains is presented. A search for the global minimum of the error function for a given lattice-to-chain orientation is done by dynamic programming, making the search both fast and complete. Application of the algorithm is illustrated by constructing lattice models for 12 proteins of different sizes and structural types.

Algorithms↗
PubMed1996

Progressive multiple alignment with constraints.

A progressive alignment algorithm produces a multialignment of a set of sequences by repeatedly aligning pairs of sequences and/or previously generated alignments. We describe a method for guaranteeing that the alignment generated by a progressive alignment strategy satisfies a user-specified collection of constraints about where certain sequence positions should appear relative to others. Our main result is an algorithm to compute just the "prime" constraints that are implied by the user-given constraints; these are shown to be precisely the constraints that the alignment algorithm must obey. In practice, the time required to handle constraints is negligible and frequently much less than the time saved because the constraints permit searching a restricted region of the dynamic-programming grid. An alignment of the beta-like globin gene cluster of several mammals illustrates the practicality of the method.

Algorithms↗
PubMed1998

Transforming rooted agreement into unrooted agreement.

We give a simple technique that allows to transform dynamic programming type algorithms for the Maximum Agreement Subtree problem (MAST) for rooted trees into algorithms for the Maximum Agreement Subtree problem for unrooted trees (UMAST). Using this technique we obtain an O (n log n)-time algorithm for the UMAST problem for binary trees. This matches the complexity of the best known algorithm for the rooted case.

Algorithms↗
PubMed1998

Regression analysis of multiple protein structures.

A general framework is presented for analyzing multiple protein structures using statistical regression methods. The regression approach can superimpose protein structures rigidly or with shear. Also, this approach can superimpose multiple structures explicitly, without resorting to pairwise superpositions. The algorithm alternates between matching corresponding landmarks among the protein structures and superimposing these landmarks. Matching is performed using a robust dynamic programming technique that uses gap penalties that adapt to the given data. Superposition is performed using either orthogonal transformations, which impose the rigid-body assumption, or affine transformations, which allow shear. The resulting regression model of a protein family measures the amount of structural variability at each landmark. A variation of our algorithm permits a separate weight for each landmark, thereby allowing one to emphasize particular segments of a protein structure or to compensate for variances that differ at various positions in a structure. In addition, a method is introduced for finding an initial correspondence, by measuring the discrete curvature along each protein backbone. Discrete curvature also characterizes the secondary structure of a protein backbone, distinguishing among helical, strand, and loop regions. An example is presented involving a set of seven globin structures. Regression analysis, using both affine and orthogonal transformations, reveals that globins are most strongly conserved structurally in helical regions, particularly in the mid-regions of the E, F, and G helices.

Algorithms↗
PubMed1998

A decision tree system for finding genes in DNA.

MORGAN is an integrated system for finding genes in vertebrate DNA sequences. MORGAN uses a variety of techniques to accomplish this task, the most distinctive of which is a decision tree classifier. The decision tree system is combined with new methods for identifying start codons, donor sites, and acceptor sites, and these are brought together in a frame-sensitive dynamic programming algorithm that finds the optimal segmentation of a DNA sequence into coding and noncoding regions (exons and introns). The optimal segmentation is dependent on a separate scoring function that takes a subsequence and assigns to it a score reflecting the probability that the sequence is an exon. The scoring functions in MORGAN are sets of decision trees that are combined to give a probability estimate. Experimental results on a database of 570 vertebrate DNA sequences show that MORGAN has excellent performance by many different measures. On a separate test set, it achieves an overall accuracy of 95 %, with a correlation coefficient of 0.78, and a sensitivity and specificity for coding bases of 83 % and 79%. In addition, MORGAN identifies 58% of coding exons exactly; i.e., both the beginning and end of the coding regions are predicted correctly. This paper describes the MORGAN system, including its decision tree routines and the algorithms for site recognition, and its performance on a benchmark database of vertebrate DNA.

Algorithms↗
PubMed1999

Positional statistical significance in sequence alignment.

Beginning with the concept of near-optimal sequence alignments, we can assign a probability that each element in one sequence is paired in an alignment with each element in another sequence. This involves a sum over the set of all possible pairwise alignments. The method employs a designed hidden Markov model (HMM) and the rigorous forward and forward-backward algorithms of Rabiner. The approach can use any standard sequence-element-to-element probabilistic similarity measures and affine gap penalty functions. This allows the positional alignment statistical significance to be obtained as a function of such variables. A measure of the probabilistic relationship between any single sequence and a set of sequences can be directly obtained. In addition, the employed HMM with the Viterbi algorithm provides a simple link to the standard dynamic programming optimal alignment algorithms.

Adenylate Kinase↗
PubMed2005

The URMS-RMS hybrid algorithm for fast and sensitive local protein structure alignment.

We present an efficient and sensitive hybrid algorithm for local structure alignment of a pair of 3D protein structures. The hybrid algorithm employs both the URMS (unit-vector root mean squared) metric and the RMS metric. Our algorithm searches efficiently the transformation space using a fast screening protocol; initial transformations (rotations) are identified using the URMS algorithm. These rotations are then clustered and an RMS-based dynamic programming algorithm is invoked to find the maximal local similarities for representative rotations of the clusters. Statistical significance of the alignments is estimated using a model that accounts for both the score of the match and the RMS. We tested our algorithm over the SCOP classification of protein domains. Our algorithm performs very well; its main advantages are that (1) it combines the advantages of the RMS and the URMS metrics, (2) it searches extensively the transformation space, (3) it detects complex similarities and structural repeats, and (4) its results are symmetric. The software is available for download at biozon.org/ftp/software/urms/.

Algorithms↗
PubMed2005

A pairwise alignment algorithm which favors clusters of blocks.

Pairwise sequence alignments aim to decide whether two sequences are related and, if so, to exhibit their related domains. Recent works have pointed out that a significant number of true homologous sequences are missed when using classical comparison algorithms. This is the case when two homologous sequences share several little blocks of homology, too small to lead to a significant score. On the other hand, classical alignment algorithms, when detecting homologies, may fail to recognize all the significant biological signals. The aim of the paper is to give a solution to these two problems. We propose a new scoring method which tends to increase the score of an alignment when "blocks" are detected. This so-called Block-Scoring algorithm, which makes use of dynamic programming, is worth being used as a complementary tool to classical exact alignments methods. We validate our approach by applying it on a large set of biological data. Finally, we give a limit theorem for the score statistics of the algorithm.

Algorithms↗
PubMed2006

A hybrid micro-macroevolutionary approach to gene tree reconstruction.

Gene family evolution is determined by microevolutionary processes (e.g., point mutations) and macroevolutionary processes (e.g., gene duplication and loss), yet macroevolutionary considerations are rarely incorporated into gene phylogeny reconstruction methods. We present a dynamic program to find the most parsimonious gene family tree with respect to a macroevolutionary optimization criterion, the weighted sum of the number of gene duplications and losses. The existence of a polynomial delay algorithm for duplication/loss phylogeny reconstruction stands in contrast to most formulations of phylogeny reconstruction, which are NP-complete. We next extend this result to obtain a two-phase method for gene tree reconstruction that takes both micro- and macroevolution into account. In the first phase, a gene tree is constructed from sequence data, using any of the previously known algorithms for gene phylogeny construction. In the second phase, the tree is refined by rearranging regions of the tree that do not have strong support in the sequence data to minimize the duplication/lost cost. Components of the tree with strong support are left intact. This hybrid approach incorporates both micro- and macroevolutionary considerations, yet its computational requirements are modest in practice because the two-phase approach constrains the search space. Our hybrid algorithm can also be used to resolve nonbinary nodes in a multifurcating gene tree. We have implemented these algorithms in a software tool, NOTUNG 2.0, that can be used as a unified framework for gene tree reconstruction or as an exploratory analysis tool that can be applied post hoc to any rooted tree with bootstrap values. The NOTUNG 2.0 graphical user interface can be used to visualize alternate duplication/loss histories, root trees according to duplication and loss parsimony, manipulate and annotate gene trees, and estimate gene duplication times. It also offers a command line option that enables high-throughput analysis of a large number of trees.

ATP-Binding Cassette Transporters↗
PubMed2006

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.

Algorithms↗