DNA, Words and Models: Statistics of

An important problem in computational biology is identifying short DNA sequences (mathematically, 'words’) associated to a biological function. One approach consists in determining whether a particular word is simply random or is of statistical significance, for example, because of its frequency or location. This book introduces the mathematical and statistical ideas used in solving this so-called exceptional word problem. It begins with a detailed description of the principal models used in sequence analysis: Markovian models are central here and capture compositional information on the sequence being analysed. There follows an introduction to several statistical methods that are used for finding exceptional words with respect to the model used. The second half of the book is illustrated with numerous examples provided from the analysis of bacterial genomes, making this a practical guide for users facing a real situation and needing to make an adequate procedure choice.

List of figures

vii

List of tables

ix

Preface

xi

Preliminary notions and notations

xiv

Introduction

1

(10)

The context

1

(2)

Randomness and models

3

(3)

A bit of biology

6

(5)

Simple models for biological sequences

11

(16)

Why a model?

11

(1)

Permutation model

12

(9)

Bernoulli model

21

(6)

Introduction to Markov chain models

27

(12)

Assumptions

27

(1)

Markov chain of order 1

28

(3)

Markov chain of order m

31

(2)

Estimation of the parameters

33

(6)

Taking heterogeneities into account

39

(18)

Phased chains

39

(4)

Piecewise homogeneous Markov chains

43

(8)

Translation conditional models

51

(6)

Statistical properties of word occurrences

57

(42)

Count

60

(14)

Positions and distances

74

(15)

Distribution along the sequence

89

(10)

Words with unexpected frequencies

99

(24)

Exact distribution and approximations

101

(5)

Influence of the model

106

(6)

Over-representation of Chi sites in E. coli and H. influenzae

112

(6)

Under-representation of palindromes of length 6 in E. coli and in the phage Lambda

118

(5)

Words with unexpected locations

123

(8)

Chi sites in the genome of H. influenzae

123

(4)

Distribution of palindromes in E. coli's genome

127

(1)

Detection of promoter sites in B. subtilis

128

(3)

The last word

131

(3)

References

134

(3)

Index

137

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DNA, Words and Models: Statistics of Exceptional Words

Summary

Table of Contents

Supplemental Materials