Sequence Comparison.pdf

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Chapter 4 Homology Search Tools The alignment methods introduced in Chapter 3 are good for comparing two sequences accurately. However, they are not adequate for homology search against a large biological database such as GenBank. As of February 2008, there are approximately 85,759,586,764 bases in 82,853,685 sequence records in the traditional GenBank divisions. To search such kind of huge databases, faster methods are required for identifying the homology between the query sequence and the database sequence in a timely manner. One common feature of homology search programs is the filtration idea, which uses exact matches or approximate matches between the query sequence and the database sequence as a basis to judge if the homology between the two sequences passes the desired threshold. This chapter is divided into six sections. Section 4.1 describes how to implement the filtration idea for finding exact word matches between two sequences by using efficient data structures such as hash tables, suffix trees, and suffix arrays. FASTA was the first popular homology search tool, and its file format is still widely used. Section 4.2 briefly describes a multi-step approach used by FASTA for finding local alignments. BLAST is the most popular homology search tool now. Section 4.3 reviews the first version of BLAST, Ungapped BLAST, which generates ungapped alignments. It then reviews two major products of BLAST 2.0: Gapped BLAST and Position- Specific Iterated BLAST (PSI-BLAST). Gapped BLAST produces gapped alignments, yet it is able to run faster than the original one. PSI-BLAST can be used to find distant relatives of a protein based on the profiles derived from the multiple alignments of the highest scoring database sequence segments with the query segment in iterative Gapped BLAST searches. Section 4.4 describes BLAT, short for “BLAST-like alignment tool.” It is often used to search for the database sequences that are closely related to the query sequences such as producing mRNA/DNA alignments and comparing vertebrate sequences. PatternHunter, introduced in Section 4.5, is more sensitive than BLAST when a hit contains the same number of matches. A novel idea in PatternHunter is the 63
64 4 Homology Search Tools use of an optimized spaced seed. Furthermore, it has been demonstrated that using optimized multiple spaced seed will speed up the computation even more. Finally, we conclude the chapter with the bibliographic notes in Section 4.6. 4.1 Finding Exact Word Matches An exact word match is a run of identities between two sequences. In the following, we discuss how to find all short exact word matches, sometimes referred to as hits, between two sequences using efficient data structures such as hash tables, suffix trees, and suffix arrays. Given two sequences A = a 1 a 2 ...a m , and B = b 1 b 2 ...b n , and a positive integer k, theexact word match problem is to find all occurrences of exact word matches of length k, referred to as k-mers between A and B. This is a classic algorithmic problem that has been investigated for decades. Here we describe three approaches for this problem. 4.1.1 Hash Tables A hash table associates keys with numbers. It uses a hash function to transform a given key into a number, called hash, which is used as an index to look up or store the corresponding data. A method that uses a hash table for finding all exact word matches of length w between two DNA sequences A and B is described as follows. Since a DNA sequence is a sequence of four letters A, C, G, and T, there are 4 w possible DNA w-mers. The following encoding scheme maps a DNA w-mer to an integer between 0 and 4 w − 1. Let C = c 1 c 2 ...c w be a w-mer. The hash value of C is written V (C) and its value is V (C)=x 1 × 4 w−1 + x 2 × 4 w−2 + ···+ x w × 4 0 , where x i = 0,1,2,3ifc i = A, C, G, T, respectively. For example, if C=GTCAT, then V (C)=2 × 4 4 + 3 × 4 3 + 1 × 4 2 + 0 × 4 1 + 3 × 4 0 = 732. In fact, we can use two bits to represent each nucleotide: A(00), C(01), G(10), and T(11). In this way, a DNA segment is transformed into a binary string by compressing four nucleotides into one byte. For C=GTCAT given above, we have V (C)=732 = 1011010011 2 . Initially, a hash table H of size 4 w is created. To find all exact word matches of length w between two sequences A and B, the following steps are executed. The first step is to hash sequence A into a table. All possible w-mers in A are calculated by
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Computational Biology Editors-in-Ch
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Kun-Mao Chao·Louxin Zhang Sequence
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KMC: To Daddy, Mommy, Pei-Pei and L
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viii Foreword I invite you to study
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x Preface Chapters 2 to 5 form the
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Acknowledgments We are extremely gr
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Contents Foreword .................
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Contents xix Part II. Theory ......
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Chapter 1 Introduction 1.1 Biologic
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1.2 Alignment: A Model for Sequence
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1.2 Alignment: A Model for Sequence
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1.3 Scoring Alignment 7 ( ) k m a k
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1.4 Computing Sequence Alignment 9
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Page 30 and 31: 1.8 Bibliographic Notes and Further
Page 32 and 33: PART I. ALGORITHMS AND TECHNIQUES 1
Page 34 and 35: 18 2 Basic Algorithmic Techniques 2
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Page 48 and 49: 32 2 Basic Algorithmic Techniques O
Page 50 and 51: Chapter 3 Pairwise Sequence Alignme
Page 52 and 53: 3.3 Global Alignment 37 3.2 Dot Mat
Page 54 and 55: 3.3 Global Alignment 39 ⎧ ⎨ S[i
Page 56 and 57: 3.3 Global Alignment 41 ( ai b j )
Page 58 and 59: 3.4 Local Alignment 43 ⎧ 0, ⎪
Page 60 and 61: 3.4 Local Alignment 45 Algorithm LO
Page 62 and 63: 3.5 Various Scoring Schemes 47 Fig.
Page 64 and 65: 3.6 Space-Saving Strategies 49 Fig.
Page 66 and 67: 3.6 Space-Saving Strategies 51 Algo
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Page 70 and 71: 3.7 Other Advanced Topics 55 ning,
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Page 74 and 75: 3.7 Other Advanced Topics 59 3.7.4
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Page 84 and 85: 4.3 BLAST 69 SALSDLHAHKLRVDPVNFKLLS
Page 86 and 87: 4.3 BLAST 71 length w, whereas for
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Page 90 and 91: 4.5 PatternHunter 75 BLAT identifie
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Page 96 and 97: 82 5 Multiple Sequence Alignment S
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Page 100 and 101: 86 5 Multiple Sequence Alignment Fi
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Page 104 and 105: Chapter 6 Anatomy of Spaced Seeds B
Page 106 and 107: 6.2 Basic Formulas on Hit Probabili
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Page 124 and 125: 6.5 Spaced Seed Selection 111 Count
Page 126 and 127: 6.6 Generalizations of Spaced Seeds
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6.7 Bibliographic Notes and Further
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120 7 Local Alignment Statistics tr
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122 7 Local Alignment Statistics Fi
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124 7 Local Alignment Statistics Le
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126 7 Local Alignment Statistics Be
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128 7 Local Alignment Statistics we
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130 7 Local Alignment Statistics A
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132 7 Local Alignment Statistics pr
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134 7 Local Alignment Statistics wh
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136 7 Local Alignment Statistics Ta
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138 7 Local Alignment Statistics Be
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140 7 Local Alignment Statistics 7.
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Chapter 8 Scoring Matrices With the
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8.1 The PAM Scoring Matrices 151 AB
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8.2 The BLOSUM Scoring Matrices 153
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8.3 General Form of the Scoring Mat
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8.4 How to Select a Scoring Matrix?
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8.5 Compositional Adjustment of Sco
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8.6 DNA Scoring Matrices 161 This i
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8.7 Gap Cost in Gapped Alignments 1
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Appendix A Basic Concepts in Molecu
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A.4 The Genomes 175 ondary structur
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Appendix B Elementary Probability T
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B.3 Major Discrete Distributions 17
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B.3 Major Discrete Distributions 18
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B.5 Mean, Variance, and Moments 183
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B.5 Mean, Variance, and Moments 185
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B.6 Relative Entropy of Probability
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B.7 Discrete-time Finite Markov Cha
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B.8 Recurrent Events and the Renewa
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B.8 Recurrent Events and the Renewa
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196 C Software Packages for Sequenc
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198 References 19. Bafna, V. and Pe
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200 References 71. Fitch, W.M. and
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202 References 122. Letunic, I., Co
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204 References 173. Robinson, A.B.
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Index O-notation, 18 P-value, 139 a
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Index 209 heuristic, 85 progressive
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