生物信息学中的数学方法引论 : 第2版

Part I Sequence Analysis

1 Introduction: Biological Sequences

2 Sequence Alignment

2.1 Sequence Similarity

2.2 Dynamic Programming: Global Alignment

2.3 Dynamic Programming: Local Alignment

2.4 Alignment with Affine Gap Model

2.5 Heuristic Alignment Algorithms

2.5.1 FASTA

2.5.2 BLAST

2.6 Significance of Scores

2.7 Multiple Alignment

2.7.1 MSA

2.7.2 Progressive Alignment

Exercises

3 Markov Chains and Hidden Markov Models

3.1 Markov Chains

3.2 Hidden Markov Models

3.3 The Viterbi Algorithm

3.4 The Forward Algorithm

3.5 The Backward Algorithm and Posterior Decoding

3.6 Parameter Estimation for HMMs

3.6.1 Estimation when Paths are Known

3.6.2 Estimation when Paths are Unknown

3.7 HMMs with Silent States

3.8 Profile HMMs

3.9 Multiple Sequence Alignment by Profile HMMs

Exercises

X Contents

4 Protein Folding

4.1 Levels of Protein Structure

4.2 Prediction by Profile HMMs

4.3 Threading

4.4 MoleCular Modeling

4.5 Lattice HP-Model

Exercises

5 Phylogenetic Reconstruction

5.1 Phylogenetic Trees

5.2 Parsimony Methods

5.3 Distance Methods

5.4 Evolutionary Models

5.4.1 The Jukes-Cantor Model

5.4.2 The Kimura Model

5.4.3 The Felsenstein Model

5.4.4 The Hasegawa-Kishino-Yano (HKY) Model

5.5 Maximum Likelihood Method

5.6 Model Comparison

Exercises

Part II Mathematical Background for Sequence Analysis

6 Elements of Probability Theory

6.1 Sample Spaces and Events

6.2 Probability Measure

6.3 Conditional Probability

6.4 Random Variables

6.5 Integration of Random Variables

6.6 Monotone Functions on the Real Line

6.7 Distribution Functions

6.8 Common Types of Random Variables

6.8.1 The Discrete Type

6.8.2 The Continuous Type

6.9 Common Discrete and Continuous Distribution,,

6.9.1 The Discrete Case

6.9.2 The Continuous Case

6.10 Vector-Valued Random Variables

6.11 Sequences of Random Variables

Exercises

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《生物信息学中的数学方法引论》的特色之一就是没有对所有的生物信息学问题进行泛泛的介绍，而是选择了生物信息学中核心问题之一--序列分析作为《生物信息学中的数学方法引论》的主要内容。由于缩小了范围，作者可以在有限的篇幅中更详尽的介绍序列分析的各种数学模型和算法。

This book looks at the mathematical foundations of the modelscurrently in use. This is crucial for the correct interpretation of theoutputs of the models. A bioinformatician should be able not onlyto use software packages， but also to know the mathematics behindthese packages. From this point of view， mathematics departmentsthroughout the world have a major role to play in bioinformaticseducation by teaching courses on the mathematical foundations ofthe subject. Based on the courses taught by the author the bookcombines several topics in biological sequence analysis withmathematical and statistical material required for such analysis.