生物信息学中的数学方法

PREFACE

CHAPTER 1 SOME BIOLOGICAL CONCEPTS

1.1 Cell

1.2 Genetic Material： DNA, Gene and RNA

1.2.1 DNA

1.2.2 Gene

1.2.3 RNA

1.3 Protein and Amino Acids

1.4 Chromosome

1.5 Omics

1.5.1 Genomics

1.5.2 Microarray

1.5.3 Proteomics

1.5.4 Lipidomics

REFERENCES

CHAPTER 2 GRAPHICAL REPRESENTATIONS OF DNA SEQUENCE

2.1 Three-Dimension （3-D） GraphicaIRepresentation

2.2 2-DGraphicalRepresentatio

2.3 2-D GraphicalRepresentations Without Degeneracy

2.4 Used a 1-D NumerioalRepresentation offourNucleotides to Construct a 2-D Graplucal Representation ofthe DNA Sequence

REFERENCES

CHAPTER 3 NUMERICAL REPRESENTATIONS OF DNA SEQUENCE

3.1 4-D and 3-D Numerical Representations of a DNA Sequence

3.2 2-D Numerical Representations of a DNA Sequence

3.3 The Complex NumericalRepresentation

3.4 1-D Numerical Representations of four Nucleotides and 2-D Graphical

Representation of a DNA Sequence

3.5 The Representations ofFeature Vector, Genome Space and Matrix Representation of DNA Sequence

3.6 The Numerical Representation Based on Physical, Chemical and Structural

Properties of DNA Sequence

3.6.1 The numericalrepresentations based on some attribute equivalences

ofnucleotides

3.6.2 The representation of DNA by the inspiration from codon and the idea ofthree attribute equivalences

3.6.3 EIIPnumericalrepresentationfornucleotides

REFERENCES

CHAPTER 4 NUMERICAL REPRESENTATIONS OF PROTEIN

4.1 1-D Numericaland GraphicalRepresentations ofthe AminoAcid Sequence

4.2 2-DNumericaland GraphicalRepresentations ofthe AminoAcid Sequence

4.3 A 2-D Graphical Representation and Moment Vector Representation of Protein

4.4 3-D Numerical Representation of Protein

4.5 The 10-D Representation ofan Amino Acid

4.6 The Vector andMatrix Representations of Protein Sequence and Protein Space

4.7 Other Schemes of the Representation for Protein

REFERENCES

CHAPTER 5 PRACTICAL ORTHOGONAL TRANSFORM

5.1 Some Features and Algorithms for the Discrete Fourier Transform

5.1.1 Fourier transforms ofthe original sequence and its subsequence

5.1.2 The independency ofthe Fourier transforms at several frequencies

5.1.3 The Fourier transform ofsymbolic sequence

5.1.4 Fourier transform ofbinary sequence

5.1.5 Several algorithms ofFourier transform

5.1.6 The properties ofFourier transform ofreal sequence

5.2 WaveletAnalysis

5.2.1 Introduction

5.2.2 Multiresolution analysis ofa function by Haar scaling and wavelet

function

5.2.3 Construction of wavelet systems

5.2.4 Mallet transform

REFERENCES

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CHAPTER 6 IDENTIFYING PROTEIN-CODING REGIONS （EXONS） BY NUCLEOTIDEDIS TRIBUTIONS

CHAPTER 7 PROTEIN COMPARISON BY ORTHOGONAL TRANSFORMS

CHAPTER 8 THE APPLICATION OF VECTOR REPRESENTATIONSTOBIOLOGICAL MOLECULE ANALYSIS

CHAPTER 9 THE STATISTICS ANALYSIS OF LARGE AMOUNT OF EXPERIMENTAL DATA

CHAPTER 10 APPLY SINGULAR VALUE DECOMPOSITION TO MICROARRAY ANALYSIS

CHAPTER 11 DYNAMICALANALYSIS MODELS OF GENE EXPRESSION

CHAPTER 12 MISSING MICROARRAY DATAINPUTTING

PLATE

Numerical Methods in Bioinformatics An Introduction presents the numerical methods for Bioinformatics as following： several numerical substitutions represent the DNA and protein sequences as the numerical or graphical sequences;Fourier and wavelet transforms are used in gene identification and protein comparison;based on the data set of microarray or lipidomics with huge amount experiment data，suitable statistical and algebraic methods are used in studying biological features of two sets，under the representations of feature vectors，the classifications of two biological molecules are completed by clustering analysis;the models of differential and difference equations have been constructed which represent the biological dynamic process;and the techniques of missing data inputting have helped to estimate the missing entries coming from biological observations and experiments，and so on.In addition，some biological concepts involved by these methods are introduced also.