Contents
Preface page ix
1 Introduction 1
1.1 Sequence similarity, homology, and alignment 2
1.2 Overview of the book 2
1.3 Probabilities and probabilistic models 4
1.4 Further reading 10
2 Pairwise alignment 12
2.1 Introduction 12
2.2 The scoring model 13
2.3 Alignment algorithms 18
2.4 Dynamic programming with more complex models 29
2.5 Heuristic alignment algorithms 33
2.6 Linear space alignments 35
2.7 Significance of scores 36
2.8 Deriving score parameters from alignment data 42
2.9 Further reading 45
3 Markov chains and hidden Markov models 47
3.1 Markov chains 48
3.2 Hidden Markov models 52
3.3 Parameter estimation for HMMs 62
3.4 HMM model structure 69
3.5 More complex Markov chains 73
3.6 Numerical stability of HMM algorithms 78
3.7 Further reading 80
4 Pairwise alignment using HMMs 81
4.1 Pair HMMs 82
4.2 The full probability of x and y, summing over all paths 88
4.3 Suboptimal alignment 90
4.4 The posterior probability that x
i
is aligned to y
j
92
96
v
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