Index O-notation, 18 P-value, 139 affine gap penalty, 8, 46, 163 algorithm, 17, 18 Huffman’s, 20 mergesort, 22 Needleman-Wunsch, 9, 60 Smith-Waterman, 10, 61, 71 alignment, 2, 37 gapped, 3, 72 global, 9, 38, 39, 41, 42, 50 graph, 3, 38, 86 local, 10, 42, 52 multiple, 11, 73, 81, 196 number of, 5 optimal, 9, 38, 41 pairwise, 11, 35, 195 score, 8, 37, 83, 121 ungapped, 3, 69 amino acid, 174 background frequency, 121, 123, 134 backtracking procedure, 24, 41, 45 band alignment, 54, 68 binary search, 28 BLAST, 69, 91, 130, 132, 139, 141 BLASTN, 92 BLASTP, 115, 142 BLASTX, 141 BLASTZ, 62, 79, 112 BLAT, 74 block, 153 BLOSUM45, 141, 158, 171 BLOSUM62, 135, 138, 141, 158, 170 BLOSUM80, 141, 158, 172 central dogma of molecular biology, 175 Chebyshev’s inequality, 185 Chen-Stein method, 135 ClustalW, 87 consecutive seed, 92, 94, 95, 100–104, 112 consensus alignment, 87 constant gap penalty, 48 deletion, 3 distribution background frequency, 121, 123 Bernoulli, 179 binomial, 180 divergence, 187 exponential, 163, 182 extreme value, 120, 121, 134–136 location and scale parameters, 120 mean and variance, 120 function, 179 geometric, 180 geometric-like, 128, 137, 180 normal, 183 optimal local alignment scores, 121, 134 λ, K, 121 λ, K estimation, 136 gapped, 134 ungapped, 121, 132, 138 Poisson, 180 relative entropy, 187 uniform, 182 divide-and-conquer, 21 DNA, 173 dot matrix, 37 dynamic programming, 23 E-value or Expect value, 128, 139, 141, 144 edge effect, 130, 133 207
208 Index effective size of search space, 140, 141 event, 177 certain, 177 complementary, 177 disjoint, 177 impossible, 177 independent, 178 intersection, 177 rare, 120, 181 recurrent, 191 union, 177 evolutionary model Markov chain, 150, 161 exact word match problem, 64 extreme value distribution, 120, 121, 134–136 location and scale parameters, 120 mean and variance, 120 FASTA, 68 Fibonacci number, 25 first hit probability, 94 function density, 179 distribution, 179 moment-generating, 186 probability generating, 181 gap, 8 extension, 72 generalized, 163 penalty, 136 effect, 134 logarithmic region, 135 penalty model, 8, 46 affine, 163 constant, 48 Gapped BLAST, 72 GenBank, 36, 63 gene, 175 generalized gap, 163 genome, 175 global alignment, 9, 38, 39, 41, 42, 50 greedy method, 18 greedy-choice property, 19 hash table, 64 Hedera, 110, 113 hidden Markov model, 62 Hirschberg’s linear space approach, 50, 55, 59 hit, 70, 74 non-overlapping, 72, 100, 103 overlapping, 76 probability, 94 homology, 1 search, 10, 63, 195 HSP, 70, 75, 78 Huffman coding, 19 insertion, 3 Karlin-Altschul sum statistic, 131, 138, 140 length adjustment, 140, 142, 143 linear space, 50, 55 local alignment, 10, 42, 52 longest common subsequence, 9, 30 longest increasing subsequence, 27 Mandala, 111, 113 Markov chain absorbing state, 189 aperiodic, irreducible, 189 evolutionary model, 150, 161 high-order, 191 memoryless, time homogeneity, 188 stationary distribution, 189 matrix BLOSUM, 153 BLOSUM45, 141, 158, 171 BLOSUM62, 135, 138, 141, 158, 170 BLOSUM80, 141, 158, 172 PAM, 150 PAM120, 158, 169 PAM250, 138, 158, 166 PAM30, 141, 158, 167 PAM70, 141, 158, 168 scoring, 7, 37 valid, 156 substitution, 8 maximal word match, 67 maximal-scoring segment, 123, 130 pair, MSP, 70, 71, 132 maximum segment score, 123, 128, 132 maximum-sum segment, 26, 70 mergesort, 22 model gap penalty, 8, 46 Markov chain, 188 absorbing state, 189 aperiodic, irreducible, 189 high-order, 191 memoryless, time homogeneity, 188 stationary distribution, 189 sequence Bernoulli, 12 Markov chain, 12 MSP, 70, 71, 132 multiple alignment, 11, 73, 81, 196
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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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1.5 Multiple Alignment 11 1.5 Multi
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1.8 Bibliographic Notes and Further
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PART I. ALGORITHMS AND TECHNIQUES 1
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18 2 Basic Algorithmic Techniques 2
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20 2 Basic Algorithmic Techniques F
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22 2 Basic Algorithmic Techniques s
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24 2 Basic Algorithmic Techniques F
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26 2 Basic Algorithmic Techniques F
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28 2 Basic Algorithmic Techniques P
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32 2 Basic Algorithmic Techniques O
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Chapter 3 Pairwise Sequence Alignme
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3.3 Global Alignment 37 3.2 Dot Mat
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3.3 Global Alignment 39 ⎧ ⎨ S[i
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3.3 Global Alignment 41 ( ai b j )
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3.4 Local Alignment 43 ⎧ 0, ⎪
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3.4 Local Alignment 45 Algorithm LO
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3.5 Various Scoring Schemes 47 Fig.
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3.6 Space-Saving Strategies 49 Fig.
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3.6 Space-Saving Strategies 51 Algo
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3.6 Space-Saving Strategies 53 scor
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3.7 Other Advanced Topics 55 ning,
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3.7 Other Advanced Topics 57 (0,0).
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3.7 Other Advanced Topics 59 3.7.4
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3.8 Bibliographic Notes and Further
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Chapter 4 Homology Search Tools The
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4.1 Finding Exact Word Matches 65 F
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4.1 Finding Exact Word Matches 67 F
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4.3 BLAST 69 SALSDLHAHKLRVDPVNFKLLS
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4.3 BLAST 71 length w, whereas for
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4.3 BLAST 73 Fig. 4.9 A scenario of
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4.5 PatternHunter 75 BLAT identifie
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4.5 PatternHunter 77 can develop an
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4.6 Bibliographic Notes and Further
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82 5 Multiple Sequence Alignment S
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84 5 Multiple Sequence Alignment S
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86 5 Multiple Sequence Alignment Fi
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Chapter 6 Anatomy of Spaced Seeds B
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6.2 Basic Formulas on Hit Probabili
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6.2 Basic Formulas on Hit Probabili
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6.2 Basic Formulas on Hit Probabili
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6.3 Distance between Non-Overlappin
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6.3 Distance between Non-Overlappin
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6.3 Distance between Non-Overlappin
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6.4 Asymptotic Analysis of Hit Prob
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6.4 Asymptotic Analysis of Hit Prob
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6.4 Asymptotic Analysis of Hit Prob
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6.5 Spaced Seed Selection 111 Count
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6.6 Generalizations of Spaced Seeds
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6.7 Bibliographic Notes and Further
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6.7 Bibliographic Notes and Further
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120 7 Local Alignment Statistics tr
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128 7 Local Alignment Statistics we
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130 7 Local Alignment Statistics A
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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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142 7 Local Alignment Statistics 7.
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144 7 Local Alignment Statistics al
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146 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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