O. Gotoh, An improved algorithm for matching biological sequences, J. Mol. Biol. 162 (1982), no. 3, 705-708.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of two sequences, S1 and S2, of lengths # n,inO(n ) time. The DPA can be made to calculate the longest common subsequence (LCS) the edit distance and other functions of two sequences by making suitable choices for z, c( f ( and g( The popular linear and piecewise linear gap costs [19] can also be included by storing extra state information in each entry, M[i, j and by making suitable choices of c( f ( and g( For given probabilities, P(match) P(mismatch) P(insert) and P(delete) which must sum to 1.0, the following instantiation of the dynamic programming algorithm ....

....by appropriate elaboration of the state information in M[i, j while the algorithm s complexity remains O(n ) but with a worse constant. Second order models are probably the upper limit in practice. Model class 2, below, is much more flexible in this regard. Linear gap costs etc. for indels [5, 19] could also be included in model class 1 by elaboration of the I 1and I 2 states. 4.2. Model class 2: averaging two sequences In this situation there are two real sequences, S1andS2, and we wish to know if and how they are directly related. They may have a common ancestor but this cannot be ....

Gotoh, O. (1982) An improved algorithm for matching biological sequences. J. Molec. Biol., 162, 705--708.

....D(i 1; j 1) i; j) D(i 1; j 1) c 3 ) 6) We use the term cost to denote the DNA level cost plus the protein level cost. A codon alignment of type 2 or type 3 describes a gap between codons. Since the combined gap cost function is ane we can use the technique introduced in [3] saying that a gap ending in (i; j) is either a continuation of an existing gap ending in (i 1; j) or (i; j 1) or the start of a new gap. i; j) minfD(i; j 1) D (i; j 1) g (7) i; j) minfD(i 1; j) D (i 1; j) g (8) 5.2 Codon alignments with one internal ....

O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705-708, 1981.

....Unit costs might not be the best choice when comparing biological sequences as some events are more likely than others. One can observe, however, that the recursion of equation 2.6 applies for arbitrary choices of costs for substitutions and single character indels as long as # is a metric. Gotoh [46] describes how to compute the distance between two sequences when the cost of an indel of k characters is an a#ne function of k. This method does not lead to an increase in time and space complexities compared to the simple algorithm sketched above, and works by introducing two new arrays for ....

....is used to formulate an algorithm requiring time O( a b ) for determining the distance between two sequences in the combined DNA and protein cost model. In chapter 5 we present an improved algorithm for this problem. The basic ideas of the algorithm are a vast extension of the ideas of [46] having numerous arrays for storing extendable distances between prefixes of the sequences, and The position in a codon should not be confused with the position in an alignment; a codon consists of three nucleotides that are said to be in the first, second and third position of the codon. 18 ....

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O. Gotoh. An improved algorithm for matching biological sequences.

....(insertions or deletions) are more common than shorter gaps, e.g. 55, 65, 23] To model this belief the gap cost should penalize shorter gaps and favor longer gaps. A commonly used way to do this is to use an a#ne gap cost function, i.e. a function of the form g(k) #k # for #, # 0. Gotoh in [67], and others in [61, 3] show how to compute an optimal alignment of two strings of lengths at most n using a#ne gap cost in time O(n ) A more general way is to use a concave gap cost function, i.e. a function g where g(k 1) g(k 1) as proposed by Waterman in [198] Both Miller and ....

....solved by a lot of bookkeeping in arrays that, so to say, keep track of all possible future situations in such a way that we can pick the best rightmost codon alignment in constant time when the future becomes the present. The idea of keeping track of future situations is vaguely inspired by Gotoh [67] who uses three arrays to keep track of future situations when computing an optimal alignment with a#ne gap cost. Our bookkeeping is albeit more complicated. By being careful we only have to keep approximately 400 arrays. This roughly implies that the constant factor of the O(n ) running time ....

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O. Gotoh. An improved algorithm for matching biological sequences.

....O(jsj . This is further improved to O(jsj log jsj) for convex free energy functions by Eppstein et.al. 1] Ane free energy functions (i.e. of the form a bn, where n is the size of the loop) allows for O(jsj ) computation time by borrowing a simple method used in sequence alignment [2]. Unfortunately the currently used free energy functions for internal loops are not convex, let al..one ane. Furthermore, the technique described in [1] hinges on the objective being to nd a structure of maximum stability, and thus does not translate to the calculation of the partition function of ....

O. Gotoh. An improved algorithm for matching biological sequences. J. Mol. Biol., 162:705-708, 1982.

....10 mcops, leading to a samba peak performance of 1280 mcops. In other words, the scan of a genomic data base can be done in a few dozens of seconds. For instance, the scan of a protein data base (swiss prot, release 34) with a query sequence of 1000 amino acids using an e#cient algorithm [11] [10] is performed in approximately 30 seconds. By comparison, the fastest sequential implementation (using the same algorithm) requires more than 15 minutes on a 167 MHz UltraSparc workstation [2] where the comparison routine has been tuned to exploit e#ciently the micro parallelism provided by the ....

O. Gotoh. An Improved Algorithm for Matching Biological Sequences. J. Mol. Biol., 162:705--708, 1982.

.... binary choices: sequence alignment and threading, global and local, with and without frequency profiles sequence alignment threading s t plain sequence frequency profile s f global local g l Optimal global sequence alignment with affine gap costs is done with a standard Gotoh algorithm (Gotoh 1982), local sequence alignment is performed using the Smith Waterman algorithm (Smith Waterman 1981) The alignment was performed using the Dayhoff PAM250 matrix, the algorithms were applied to plain sequences as well as to frequency profiles. The basic version of the 123D threading tool is ....

Gotoh, O. 1982. An improved algorithm for matching biological sequences. Journal of Molecular Biology 162:705--708.

....the same length in total. Since computationally cheap, so called ane gap costs are in common use. Here, the initiation of a gap is penalized by a high value gapinit , and each additional character of the gap is penalized by another, usually smaller value gapext . Based on ideas rst published by Gotoh (1982), Huang et al. 1990) show how to incorporate ane gap costs in local alignments without an overhead in computational complexity. The Jumping Alignments Algorithm We now extend the dynamic programming approach to jumping alignments where the scenario is the following. We are given a multiple ....

Gotoh, O. (1982) An improved algorithm for matching biological sequences. J. Mol. Biol., 162, 705{ 708.

....p (a i 1 a i 2 a i 3 ; b j 1 b j 2 b j 3 ) 6) 3 We use the term cost to denote the DNA level cost plus the protein level cost. A codon alignment of type 2 or type 3 describes a gap between codons. Since the combined gap cost function is ane we can use the technique introduced in [3] saying that a gap ending in (i; j) is either a continuation of an existing gap ending in (i 1; j) or (i; j 1) or the start of a new gap. D 2 (i; j) minfD(i; j 1) D 2 (i; j 1) g (7) D 3 (i; j) minfD(i 1; j) D 3 (i 1; j) g (8) 5.2 Codon alignments with one ....

O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705-708, 1981.

....3 ) 1 . This is further improved to O(jsj 2 log 2 jsj) for convex free energy functions by Eppstein et.al. 1] A ne free energy functions (i.e. of the form a bn, where n is the size of the loop) allows for O(jsj 2 ) computation time by borrowing a simple method used in sequence alignment [2]. Unfortunately the currently used free energy functions for internal loops are not convex, let al..one a ne. Furthermore, the technique described in [1] hinges on the objective being to nd a structure of maximum stability, and thus does not translate to the calculation of the partition function ....

O. Gotoh. An improved algorithm for matching biological sequences. J. Mol. Biol., 162:705708, 1982.

....wider class of functions, the linear or a#ne gap cost functions. These functions satisfy equation 4, with g(j i) c (j i) for some constant c. A simple modification of the solution to the original sequence alignment problem also solves the linear sequence alignment problem in time O(mn) [21]. The gap sequence alignment problem can again be solved by a simple dynamic programming algorithm [65] The algorithm is similar to that for the original sequence alignment problem; however where in recurrence 3 we needed only consider insertions and deletions of the final position of each ....

O. Gotoh, An Improved Algorithm for Matching Biological Sequences, J. Mol. Biol. 162, 1982, pp. 705--708.

....execute their instructions independently. In this paper, we only present and evaluate methods using MIMD systems. 2. Comparison Algorithms and Parallel Computational Methods To obtain maximum sensitivity, we use the dynamic programming algorithm of Smith and Waterman [12] as modified by Gotoh [4], for comparing two biological sequences. The Gotoh algorithm was also used by the other MIMD system developers [3,5,8,10,11] we reviewed in our work. Since Deshpande et al. and Miller 232 et al. used the same master worker method that was first applied to sequence database searching by Sittig et ....

Gotoh, O. (1982) An Improved Algorithm for Matching Biological Sequences. J. Mol. Biol., 162, 705-708.

....cost of the remaining alignment. D 1 (i; j) D(i Gamma 1; j Gamma 1) c p (a i 1 a i 2 a i 3 ; b j 1 b j 2 b j 3 ) 6) A codon alignment of type 2 or type 3 describes a gap between codons. Since the combined gap cost function is affine we can use the technique introduced in [2] saying that a gap ending in (i; j) is either a continuation of an existing gap ending in (i Gamma 1; j) or (i; j Gamma 1) or a start of a new gap. D 2 (i; j) minfD(i; j Gamma 1) ff fi; D 2 (i; j Gamma 1) fig (7) D 3 (3i; 3j) minfD(i Gamma 1; j) ff fi; D 3 (i Gamma ....

Gotoh, O. An improved algorithm for matching biological sequences. Journal of Molecular Biology 162 (1981), 705--708.

....the same length in total. Since computationally cheap, so called ane gap costs are in common use. Here, the initiation of a gap is penalized by a high value gapinit , and each additional character of the gap is penalized by another, usually smaller value gapext . Based on ideas rst published by Gotoh (1982), Huang, Hardison, Miller (1990) show how to incorporate ane gap costs in local alignments without an overhead in computational complexity. The Jumping Alignment Algorithm We now extend the dynamic programming approach to jumping alignments where the scenario is the following. We are given a ....

Gotoh, O. 1982. An improved algorithm for matching biological sequences. J. Mol. Biol. 162:705-708.

....alignment can be computed in time O(js 1 jjs 2 j) by dynamic programming, and the corresponding alignment can be found by backtracking the computation. Several improvements of this algorithm has later been proposed, e.g. in [25] the space complexity of the algorithm is reduced to O(js 1 j) and in [19] the algorithm is extended to handle aOEne gap costs 12 . A problem with alignments is that the score matrix is chosen somewhat subjectively. This has been treated in [49] where a statistical alignment 13 is used. The great advantage of this approach is that the parameters maximising the ....

....1 j Gamma 2l c Gamma1 Delta (4l Gammac)j Sigmaj c (N Gammajs 1 j) O(cN js 1 jl c j Sigmaj c )2 c , which is not at all impressing compared with the suOEx method. The big improvement is in the space complexity which is reduced to O(cl) e.g. by the methods described in [25] and [19]. 3.4 Extension to probe selection A related problem often occurring in disease detection is the probe selection problem. Here we are given a set of positives and a set of negatives. The problem now is to nd a DNA sequence, called the DNA probe, that is close to the positives and far away ....

O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705708, 1981.

....1 . This is further improved to O(n 2 log 2 n) for convex free energy functions in (Eppstein et al. 1988) Ane free energy functions (i.e. of the form a bN , where N is the size of the loop) allows for O(n 2 ) computation time by borrowing a simple method used in sequence alignment by (Gotoh, 1982). Unfortunately the currently used free energy functions for internal loops are not convex, let al..one ane. Furthermore the technique described in (Eppstein et al. 1988) hinges on the objective being to nd a structure of maximum stability, and thus does not translate to the calculation of the ....

Gotoh, O. (1982). An improved algorithm for matching biological sequences. J. Mol. Biol. 162, 705-708.

....instead of edge labels. Given two networks N 1 and N 2 representing sequence sets I 1 and I 2 , their algorithm calculates d(I 1 ; I 2 ) for linear gap penalty functions g(k) b Delta k. Hein [13] has rephrased this approach for sequence graphs, in combination with the reasoning of Gotoh [10] in order to handle affine linear gap penalty functions g(k) a b Delta k and represent all sequences on any shortest path between I 1 and I 2 in a new sequence graph. For the purpose of exposition, we present the alignment algorithm for the simpler case of a linear gap penalty function g(k) b ....

O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology 162:705--708, 1982.

.... a certain residue in the target sequence to a certain location in the template fold (Sippl, 1993; Flockner et al. 1995) The alignment engine contains a global (Needleman Wunsch, 1970) and a local (Smith Waterman, 1981) alignment algorithm and a fast version of both variants as suggested by Gotoh (Gotoh, 1982). Structure based alignments usually have a substantial fraction of unpaired residues and algorithms that allow double gaps seem to be most appropriate. Alexandrov and Luethy (Alexandrov Luethy, 1998) suggest a modification of the Gotoh algorithm to handle double gaps and they also report ....

Gotoh, O. (1982). An improved algorithm for matching biological sequences. J. Mol. Biol. 162, 705--708.

....fik for an indel of k letters. The first letter costs ff fi and each succeeding letter costs fi. Three recursions are required: E; F and H . Set E 0;0 = F 0;0 = 0; H i;j = 0 if i Delta j = 0, E i;0 = F i;0 = Gammaff Gamma fii and E 0;j = F 0;j = Gammaff Gamma fij. Then the recursion due to Gotoh (1982) is E i;j = maxfH i;j Gamma1 Gamma (ff fi) E i;j Gamma1 Gamma fi; 0g; F i;j = maxfH i Gamma1;j Gamma (ff fi) F i Gamma1;j Gamma fi; 0g; and H i;j = maxfH i Gamma1;j Gamma1 s(x i ; y j ) E i;j ; F i;j ; 0g: For declumping all three matrices must be recomputed, stopping in a row or ....

GOTOH, O. (1982). An improved algorithm for matching biological sequences.

....1 is a hardware accelerator designed for speeding up the algorithms involved in biological sequence comparison. Computations which require several hours on standard workstations are performed in a few tens of seconds on Samba. Samba implements a parameterized Smith and Waterman algorithm [14] [7]. By setting differently a few parameters, local or global comparisons can be performed, with or without gap penalty. Thus, a variety of software, such as blast [1] fasta [12] or ssearch [13] may be implemented on that accelerator. The complete Samba system comprises a workstation, a systolic ....

....two sequences. This is probably the most useful algorithm for current research, since two biological sequences which present a little overall similarity may share surprising relationships on short segments. Setting delta to 0 in equation (1) leads directly to the Smith and Waterman equation [14] [7]. Parameters must be set to: ffl delta = 0 ffl alpha = ff ffl beta = fi ffl hi(i) vi(i) 0 The similarity matrix H contains local maxima which may be interpreted as areas where similarities appear between two sequences. Multiple gap costs are taken into consideration as follows: ff) is ....

O. Gotoh. An Improved Algorithm for Matching Biological Sequences. J. Mol. Biol., 162:705--708, 1982.

....the i th amino acid and M ij is the probability that an amino acid i mutates into an amino acid j at one PAM distance [5] The function PAM(s1, s2) is the PAM distance of two sequences s i , s 2 that maximizes the score. Usually the optimal score is determined via standard dynamic programming [29, 16]. An a#ne gap cost is used according to the formula a l b, where a is a fixed gap cost, l is the length of the gap and b is the incremental cost [2] Definition 1.5 A Tree scoring function is a function F : T # IR. Definition 1.6 Let T be the set of all possible trees that can be ....

O. Gotoh. An improved algorithm for matching biological sequences. J. Mol. Biol., 162:705--708, 1982.

....VNRLQQSIVSLRDAFNDGTKLLEELDHRVLNYKPQANPFGNGPIFMVTAIVPGLHLLPI The gaps arise from insertions (or their counterpart deletions) during divergent evolution. The alignment is normally done by a dynamic programming (DP) algorithm using Dayho# matrices (Gotoh, 1982; Smith and Waterman, 1981; Needleman and Wunsch, 1970; Altschul, 1991) which finds the alignment that maximizes the probability that the two sequences evolved from an ancestral sequence as opposed to being random sequences. An a#ne gap cost is used according to the formula a l b, where a is a ....

Gotoh, O. (1982). An improved algorithm for matching biological sequences. J. Mol. Biol., 162:705--708.

....in an imperative programming language like FORTRAN or C. But we have already done all the algorithm design work, the rest is merely straightforward formula manipulation. Gotoh first specified the recurrences for computing the optimal global alignment under the affine cost model in quadratic time (Gotoh, 1982; Waterman, 1995) Readers familiar with this work will rightfully expect that our tabulated parsers ali , exIns , and exDel correspond to the three tables D, F , and E used in (Waterman, 1995) Substituting the definition of the affine cost algebra and the parser combinators, we can ....

Gotoh, O. (1982). An improved algorithm for matching biological sequences, J. Mol. Biol. 162: 705--708.

....This type of gap penalty function is used in computing most pairwise alignments. With linear gap penalties, we can still nd a solution in time O(mn) the idea is to use three (m 1) n 1) arrays that keep track of what kind of gap we have and where it comes from (either in s or t) See [2] or the Setubal and Meidanis textbook [3] for details. Multiple Sequence Alignments (MSA) So far, we have concentrated on comparisons between a pair of sequences. However, we often are given several sequences that we have to align simultaneously. Motivation: Multiple sequence alignments (or ....

Gotoh, O. (1982) An improved algorithm for matching biological sequences. J. Mol. Biol. 162:705-708.

....by the evolutionary tree on the right. VNRLQQNIVSL EVDHKVANYKP VNRLQQSIVSLRDAFNDGTKLLEELDHRVLNYKP The gaps arise from insertions (or their counterpart deletions) during divergent evolution. The alignment is normally done by a dynamic programming (DP) algorithm using Dayhoff matrices [12, 32, 28, 1], which finds the alignment that maximizes the probability that the two sequences evolved from an ancestral sequence as opposed to being random sequences. An affine gap cost is used according to the formula a l b, where a is a fixed gap cost, l is the length of the gap and b is the incremental ....

O. Gotoh. An improved algorithm for matching biological sequences. J. Mol. Biol., 162:705--708, 1982.

.... alignments, of course) 85 count alg: Algebra a Int count alg = fE, fR, fD, fI, fL, fS, choice) where fE = 1 fR x = x fD x = x fI x = x fL x = x fS x = x choice [ choice xs = sum xs] The following scoring algebra implements a model with affine gap scores [6]. Such a model is used e.g. by CLUSTALW, a popular sequence alignment tool [12] We have extended this algebra by scores for recombinant insertions and deletions. We have given a clear advantage to recombinant indels over regular ones by dividing their penalties by the length of the observed ....

O. Gotoh. An Improved Algorithm for Matching Biological Sequences. J. Mol. Biol., 162:705--708, 1982.

....functions, the linear or a#ne gap cost functions. For these functions, the cost g(x) of a gap of length x is k 1 k 2 x for some constants k 1 and k 2 . A simple modification of the solution to the original sequence alignment problem also solves the linear sequence alignment problem in time O(mn) [19]. For general functions, the gap sequence alignment problem can be solved in time O(mn 2 ) by a simple dynamic programming algorithm [51] The algorithm is similar to that for the original sequence alignment problem, but the computation of each entry in the dynamic programming matrix depends ....

O. Gotoh, An Improved Algorithm for Matching Biological Sequences, J. Mol. Biol. 162, 1982, pp. 705--708.

....labels instead of edge labels. Given two networks N 1 and N 2 representing sequence sets I 1 and I 2 , their algorithm calculates d(I 1 ; I 2 ) for linear gap penalty functions g(k) b Delta k. Hein [4] has rephrased this approach for sequence graphs, in combination with the reasoning of Gotoh [3] in order to handle affine linear gap penalty functions g(k) a b Delta k and represent all sequences on any shortest path between I 1 and I 2 in a new sequence graph. For the purpose of exposition, we present the alignment algorithm for the simpler case of a linear gap penalty function g(k) ....

O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology 162:705--708, 1982.

....labels instead of edge labels. Given two networks N 1 and N 2 representing sequence sets I 1 and I 2 , their algorithm calculates d(I 1 ; I 2 ) for linear gap penalty functions g(k) b Delta k. Hein (1989a) has rephrased this approach for sequence graphs, in combination with the reasoning of Gotoh (1982) in order to handle affine linear gap penalty functions g(k) a b Delta k and represent all sequences on any shortest path between I 1 and I 2 in a new sequence graph. Assuming that V(G 1 ) f1; mg and V(G 2 ) f1; ng, the following Algorithm Align calculates d(G 1 ; G 2 ) ....

Gotoh, O. 1982. An improved algorithm for matching biological sequences. Journal of Molecular Biology 162, 705--708.

....labels instead of edge labels. Given two networks N 1 and N 2 representing sequence sets I 1 and I 2 , their algorithm calculates d(I 1 ; I 2 ) for linear gap penalty functions g(k) b Delta k. Hein [13] has rephrased this approach for sequence graphs, in combination with the reasoning of Gotoh [10] in order to handle affine linear gap penalty functions g(k) a b Delta k and represent all sequences on any shortest path between I 1 and I 2 in a new sequence graph. For the purpose of exposition, we present the alignment algorithm for the simpler case of a linear gap penalty function g(k) ....

O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology 162:705--708, 1982.

.... cost matrix (cf. 10] with appropriately chosen gap penalties 1 d(a; Gamma) for all a 2 A) For each pair of rows 1 More sophisticated gap penalty functions are in use, e.g. the so called affine gap penalty function, which works for pairwise as well as for multiple sequence alignment [1] [17]. 18 m p ; m q in an alignment M 2 M S , define wmp ;mq : N X i=1 d(m pi ; m qi ) and denote by w opt (s p ; s q ) the minimum of wmp ;mq , taken over all alignments M . The weighted sum of pairs score for an alignment M 2 M S relative to a given family of (generally non negative) ....

O. Gotoh. An Improved Algorithm for Matching Biological Sequences. J. Mol. Biol. 162, pages 705--708, 1981.

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O. Gotoh, An improved algorithm for matching biological sequences, J. Mol. Biol. 162 (1982), no. 3, 705-708.

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Gotoh, O. (1982). An improved algorithm for matching biological sequences. J. Mol. Biol. 162 (3), 705-708.

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Gotoh. 1982. An improved algorithm for matching biological sequences. In Journal of Molecular Biology, number 162, pages 705--708.

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Gotoh, O.: An improved algorithm for matching biological sequences. Journal of Molecular Biology 162 (1982) 708--708

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Gotoh, O.: An improved algorithm for matching biological sequences. Journal of Molecular Biology 162 (1982) 708--708

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Gotoh, O.: An improved algorithm for matching biological sequences. J. Mol. Biol. 162 (1982) 705--708

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O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162, 1982.

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O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705-708, 1982.

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Gotoh O. An improved algorithm for matching biological sequences. J Mol Biol 1982;162:705--708.

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O. Gotoh, "An improved algorithm for matching biological sequences," Jornal of Molecular Biology, vol. 162, pp. 705--708, 1982.

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Gotoh, O. An Improved Algorithm for Matching Biological Sequences. Journal of Molecular Biology. 162:705-708, 1981.

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O. Gotoh. An improved algorithm for matching biological sequences. J. Mol. Biol., 162:705-708 (1982).

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sc O. Gotoh, An improved algorithm for matching biological sequences, J. Mol. Biol., 162(1982), pp: 705--708.

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O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705-708, 1982.

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Osamu Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705#708, 1982.

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Gotoh, O. [1982]. "An improved algorithm for matching biological sequences," Jour. Mol. Biol. 162, 705-708.

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Osamu Gotoh. 1982. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705--708.

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O. Gotoh. An Improved Algorithm for Matching Biological Sequences. J. Mol. Biol., 162, pages 705--708, 1982.

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O. Gotoh [1982] An improved algorithm for matching biological sequences, J. Mol. Biol. 162, 705--708.

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