Bioinformatics: Sequence alignment and Markov models

338 Pages·2009·1.1 MB·English

by  Sharma K.

Bioinformatics

Sequence Alignment and
Markov Models
Kal Renganathan Sharma, Ph.D., P.E.
Adjunct Professor
Department of Chemical Engineering
Prairie View A&M University
Prairie View, Texas
New York Chicago San Francisco
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DOI: 10.1036/0071593063
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This work is dedicated to my son
R. Hari Subrahmanyan Sharma
(alias Ramkishan, born August 13, 2001)
with unconditional love.
About the Author
Kal Renganathan Sharma,Ph.D., P.E., has written five
books, 12 journal articles, and 448 conference papers.
He has earned three degrees in chemical engineering—
a B.Tech. from the Indian Institute of Technology,
Chennai, and an M.S. and a Ph.D. from West Virginia
University, Morgantown. He has held a number of high-
level positions at engineering colleges and universities.
Dr. Sharma currently teaches at Prairie View A&M
University in Prairie View, Texas.
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Molecular Biology . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Amino Acids and Proteins . . . . . . . 2
1.1.2 Structures of Proteins . . . . . . . . . . . . . . 3
1.1.3 Sequence Distribution of Insulin . . . . 6
1.1.4 Bioseparation Techniques . . . . . . . . . . 9
1.1.5 Nucleic Acids and Genetic Code . . . . 12
1.1.6 Genomes—Diversity, Size, and
Structure . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.2 Probability and Statistics . . . . . . . . . . . . . . . . . 23
1.2.1 Three Defi nitions of Probability . . . . . 24
1.2.2 Bayes’ Theorem and Conditional
Probability . . . . . . . . . . . . . . . . . . . . . . . 25
1.2.3 Independent Events and
Bernoulli’s Theorem . . . . . . . . . . . . . . . 25
1.2.4 Discrete Probability Distributions . . . 26
1.2.5 Continuous Probability
Distributions . . . . . . . . . . . . . . . . . . . . . 28
1.2.6 Statistical Inference and
Hypothesis Testing . . . . . . . . . . . . . . . . 30
1.3 Which Is Larger, 2n or n2? . . . . . . . . . . . . . . . . . 31
1.4 Big O Notation and Asymptotic
Order of Functions . . . . . . . . . . . . . . . . . . . . . . . 32
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
References and Sources . . . . . . . . . . . . . . . . . . . . . . . . 34
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Part 1 Sequence Alignment and Representation
2 Alignment of a Pair of Sequences . . . . . . . . . . . . . . 41
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.1 Introduction to Pairwise Sequence
Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 Why Study Sequence Alignment . . . . . . . . . . 43
2.3 Alignment Grading Function . . . . . . . . . . . . . . 47
v
vi Contents
2.4 Optimal Global Alignment of a Pair
of Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4.1 Needleman and Wunsch
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5 Dynamic Programming . . . . . . . . . . . . . . . . . . 55
2.6 Time Analysis and Space Effi ciency . . . . . . . . 56
2.7 Dynamic Arrays and O(N) Space . . . . . . . . . . 56
2.8 Subquadratic Algorithms for Longest
Common Subsequence Problems . . . . . . . . . . 57
2.9 Optimal Local Alignment of a Pair
of Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.9.1 Smith and Waterman
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 59
2.10 Affi ne Gap Model . . . . . . . . . . . . . . . . . . . . . . . 60
2.11 Greedy Algorithms for Pairwise
Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.12 Other Alignment Methods . . . . . . . . . . . . . . . . 65
2.13 Pam and Blosum Matrices . . . . . . . . . . . . . . . . 66
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3 Sequence Representation and String Algorithms. . . 85
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.1 Suffi x Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.1.1 Overview of Suffi x Trees
in Sequence Analysis . . . . . . . . . . . . . 85
3.2 Algorithm for Suffi x Tree
Representation of a Sequence . . . . . . . . . . . . . 88
3.3 Streaming a Sequence Against a Suffi x Tree . . . 89
3.4 String Algorithms . . . . . . . . . . . . . . . . . . . . . . . 91
3.4.1 Rabin-Karp Algorithm . . . . . . . . . . . . . 92
3.4.2 Knuth-Morris-Pratt (KMP) Algorithm . 92
3.4.3 Boyer-Moore Algorithm . . . . . . . . . . . 94
3.4.4 Finite Automaton . . . . . . . . . . . . . . . . . 96
3.5 Suffi x Trees in String Algorithms . . . . . . . . . . 97
3.6 Look-up Tables . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4 Multiple-Sequence Alignment . . . . . . . . . . . . . . . . . 115
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.1 What Is Multiple-Sequence Alignment? . . . . 115
Contents vii
4.2 Defenitions of Multiple Global Alignment
and Sum of Pairs . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2.1 Multiple Global Alignment . . . . . . . . . 117
4.2.2 Sum of Pairs . . . . . . . . . . . . . . . . . . . . . . 117
4.3 Optimal MSA by Dynamic Programming . . . 117
4.4 Theorem of Wang and Jiang [2] . . . . . . . . . . . . 118
4.5 What Are NP Complete Problems? . . . . . . . . . 118
4.6 Center-Star-Alignment Algorithm [4] . . . . . . 119
4.6.1 Time Analysis . . . . . . . . . . . . . . . . . . . . 119
4.7 Progressive Alignment Methods . . . . . . . . . . . 121
4.8 The Consensus Sequence . . . . . . . . . . . . . . . . . 122
4.9 Greedy Method . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.10 Geometry of Multiple Sequences . . . . . . . . . . 123
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Part 2 Probability Models
5 Hidden Markov Models and Applications . . . . . . . . 133
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2 kth-order Markov Chain . . . . . . . . . . . . . . . . . . 134
5.3 DNA Sequence and Geometric
Distribution [2–4] . . . . . . . . . . . . . . . . . . . . . . . . 135
5.4 Three Questions in the HMM . . . . . . . . . . . . . 143
5.5 Evaluation Problem and Forward
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.6 Decoding Problem and Viterbi Algorithm . . . 146
5.7 Relative Entropy . . . . . . . . . . . . . . . . . . . . . . . . 147
5.8 Probabilistic Approach to Phylogeny . . . . . . . 149
5.9 Sequence Alignment Using HMMs . . . . . . . . 152
5.10 Protein Families . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.11 Wheel HMMs to Model Periodicity
in DNA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.12 Generalized HMM (GHMM) . . . . . . . . . . . . . . 157
5.13 Database Mining . . . . . . . . . . . . . . . . . . . . . . . . 160
5.14 Multiple Alignments . . . . . . . . . . . . . . . . . . . . . 160
5.15 Classifi cation Using HMMs . . . . . . . . . . . . . . . 161
5.16 Signal Peptide and Signal Anchor
Prediction by HMMs . . . . . . . . . . . . . . . . . . . . . 162
5.17 Markov Model and Chargaff's Parity Rules . 163
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
viii Contents
6 Gene Finding, Protein Secondary Structure . . . . . 179
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.2 Relative Entropy Site-Selection Problem . . . . 180
6.2.1 Greedy Approach . . . . . . . . . . . . . . . . . 180
6.2.2 Gibbs Sampler . . . . . . . . . . . . . . . . . . . . 181
6.3 Maximum-Subsequence Problem . . . . . . . . . . 182
6.3.1 Bates and Constable Algorithm . . . . . 182
6.3.2 Binomial Heap [4–7] . . . . . . . . . . . . . . . 182
6.4 Interpolated Markov Model (IMM) . . . . . . . . 184
6.5 Shine Dalgarno SD Sites Finding . . . . . . . . . . 185
6.6 Gene Annotation Methods . . . . . . . . . . . . . . . . 187
6.7 Secondary Structures of Proteins . . . . . . . . . . 191
6.7.1 Neural Networks . . . . . . . . . . . . . . . . . 193
6.7.2 PHD Architecture of Rost and
Sander . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
6.7.3 Ensemble Method of Riis and
Krogh [23] . . . . . . . . . . . . . . . . . . . . . . . 198
6.7.4 Protein Secondary Structure
Using HMMs . . . . . . . . . . . . . . . . . . . . . 199
6.7.5 DAG RNNs: Directed Acyclic
Graphs and Recursive NN
Architecture and 3D Protein
Structure Prediction . . . . . . . . . . . . . . 200
6.7.6 Annotate Subcellular Localization
for Protein Structure . . . . . . . . . . . . . . . 201
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Part 3 Measurement Techniques
7 Biochips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
7.1.1 Microarrays, Biochips, and
Disease . . . . . . . . . . . . . . . . . . . . . . . . . . 214
7.1.2 Five Steps and Ten Tips . . . . . . . . . . . . 218
7.1.3 Applications of Microarrays . . . . . . . . 220
7.2 Microarray Detection . . . . . . . . . . . . . . . . . . . . 223
7.2.1 Fluorescence Detection and
Optical Requirements . . . . . . . . . . . . . . 223
7.2.2 Confocal Scanning Microscope . . . . . 224
7.3 Microarray Surfaces . . . . . . . . . . . . . . . . . . . . . 227
7.4 Phosphoramadite Synthesis . . . . . . . . . . . . . . . 231