Contents PREFACE CHAPTER 1 SOME BIOLOGICAL CONCEPTS 1 1.1 Cell 1 1.2 Genetic Material: DNA，Gene and RNA 1 1.2.1 DNA 1 1.2.2 Gene 3 1.2.3 RNA 5 1.3 Protein and Amino Acids 7 1A Chromosome 9 1.5 Omics 10 1.5.1 Genomics 11 1.5.2 Microarray 11 1.5.3 Proteomics 11 1.5.4 Lipidomics 12 REFERENCES 13 CHAPTER 2 GRAPHICAL REPRESENTATIONS OF DNA SEQUENCE .14 2.1 Three-Dimension (3-D) Graphical Representation 14 2.2 2-D Graphical Representation 15 2.3 2-D Graphical Representations Without Degeneracy 17 2.4 Used a 1-D Numerical Representation of four Nucleotides to Construct a 2-D Graphical Representation of the DNA Sequence 22 REFERENCES 22 CHAPTER 3 NUMERICAL REPRESENTATIONS OF DNA SEQUENCE 24 3.1 4-D and 3-D Numerical Representations of a DNA Sequence 24 3.2 2-D Numerical Representations of a DNA Sequence 25 3.3 The Complex Numerical Representation 26 3.4 1-D Numerical Representations of four Nucleotides and 2-D Graphical Representation of a DNA Sequence 27 3.5 The Representations of Feature Vector, Genome Space and Matrix Representation of DNA Sequence 27 3.6 The Numerical Representation Based on Physical, Chemical and Structural Properties of DNA Sequence 29 3.6.1 The numerical representations based on some attribute equivalences of nucleotides 29 3.6.2 The representation of DNA by the inspiration from codon and the idea of three attribute equivalences 31 3.6.3 EIIP numerical representation for nucleotides 31 REFERENCES 32 CHAPTER 4 NUMERICAL REPRESENTATIONS OF PROTEIN 33 4.1 1-D Numerical and Graphical Representadons of the Amino Acid Sequence 33 4.2 2-D Numerical and Graphical Representations of the Amino Add Sequence 34 4.3 A 2-D Graphical Representation and Moment Vector Representation of Protein 41 4.4 3-D Numerical Representation of Protein 44 4.5 The 10-D Representation of an Amino Acid 45 4.6 The Vector and Matrix Representations of Protein Sequence and Protein Space . 46 4.7 Other Schemes of the Representation for Protein 46 REFERENCES 47 CHAPTER 5 PRACTICAL ORTHOGONAL TRANSFORM 49 5.1 Some Features and Algorithms for the Discrete Fourier Transform .49 5.1.1 Fourier transforms of the original sequence and its subsequence ..49 5.1.2 The independency of fee Fourier transforms at several frequencies 52 5.1.3 The Fourier transform of symbolic sequence 53 5.1.4 Fourier transform of binary sequence 56 5.1.5 Several algorithms of Fourier transform 57 5.1.6 The properties of Fourier transform of real sequence 59 5.2 Wavelet Analysis 64 5.2.1 Introduction 64 5.2.2 Multiresolution analysis of a fimction by Haar scaling and wavelet function 65 5.2.3 Construction of wavelet systems 73 5.2.4 Mallet transform 78 REFERENCES 82 CHAPTER 6 IDENTIFYING PROTEIN-CODING REGIONS (EXONS) BY NUCLEOTIDE DISTRIBUTIONS 83 6.1 Portein Coding Regions Finding in DNA Sequence 83 6.1.1 Introduction 83 6.1.2 The stochastic simulation and several computing formulae 84 6.1.3 FEND algorithm，predicting protein coding regions from nucleotide distributions on the three positions of a DNA sequence 97 6.1.4 Performance evaluation of FEND algorithm 104 6.2 The Experiment for Distinguishing Exon and Intron Sequences by a Threshold 105 6.2.1 Motivation 105 6.2.2 Idea of distinguishing exon and intron sequences 106 6.2.3 Results and discussion 108 REFERENCES 109 CHAPTER 7 PROTEIN COMPARISON BY ORTHOGONAL TRANSFORMS 7.1 Protein Comparison by Discrete Fourier Transformation (DFT) 111 7.1.1 EIIP representation of protein sequence 111 7.1.2 Symmetry of discrete Fourier transform of real sequence 112 7.1.3 Cross-spectral function 112 7.2 Protein Comparison by Discrete Wavelet Transformation 115 7.2.1 Several techniques needed for DWT method 115 7.2.2 The performance of the DWT method 120 REFERENCES 124 CHAPTER 8 THE APPLICATION OF VECTOR REPRESENTATIONS TO BIOLOGICAL MOLECULE ANALYSIS 125 8.1 Use Feature Vector to Analyze DNA Sequences 125 8.1.1 Feature vector representation of DNA sequence 125 8.1.2 Comparing DNA sequences 126 8.2 A Protein Map and its Applications 129 8.2.1 Recalling a 2-D graphical representation and moment vector representation of protein 129 8.2.2 Protein map and cluster analysis 129 8.3 An Appendix: Introduction to Cluster Analysis 133 REFERENCES 137 CHAPTER 9 THE STATISTICS ANALYSIS OF LARGE AMOUNT OF EXPERIMENTAL DATA 138 9.1 A Way to Process Microarray Data 138 9.1.1 Data form 138 9.1.2 Microarray data set 140 9.1.3 Preliminary filtering 140 9.1.4 Assessing normalization 141 9.1.5 Hypothesis test 144 9.1.6 Conclusion 146 9.2 The Statistical Analysis of a Set ofLipidomics Data 146 9.2.1 Introduction 146 9.2.2 Statistical techniques of initial data processing 148 9.2.3 Initial data arrangement 150 9.2.4 Hypothesis testing analysis 154 REFERENCES 155 CHAPTER 10 APPLY SINGULAR VALUE DECOMPOSITION TO MICRO ARRAY ANALYSIS 156 10.1 SVD, PCAand GSVD 156 10.1.1 Singular value decomposition 156 10.1.2 Principal component analysis 157 10.1.3 Generalized singular value decomposition 159 10.2 Apply SVD/PCA to Microarray Analysis 161 10.3 GSVD Analyzes the Microarray Data 165 REFERENCES 169 CHAPTER 11 DYNAMICAL ANALYSIS MODELS OF GENE EXPRESSION 170 11.1 Differential Equations Model of Gene Expression 170 11.1.1 Transcription model 170 11.1.2 Nonlinear dynamic equations 171 11.1.3 Linearization of the nonlinear transcription model 172 11.1.4 Approximating coefficient matrix M by Fourier series 173 11.1.5 Solution to transcription matrix C and V 175 11.2 Modified Linear Differential Equations Model 176 11.3 Dynamical Model Based on Singular Value Decomposition 178 11.3.1 Introduction 178 11.3.2 Reducing gene’s number 179 11.3.3 The approach based on singular value decomposition (SVD) 179 11.3.4 The methods of solving dynamical models 182 REFERENCES 183 CHAPTER 12 MISSING MICROARRAY DATA INPUTTING 184 12.1 The Ad Hoc Methods 184 12.2 Missing Data Inputting Based on SVD 186 12.2.1 A new way for missing data inputting 186 12.2.2 Other method based on SVD 188 12.3 Weighted K-Nearest Neighbors, KNN，Impute Algorithm 189 12.4 Estimation of Missing Values in Microarray Data Based on the Least Square Principle 190 12.4.1 Least squares estimate of the unknown variable 190 12.4.2 The least square estimation of missing data based on genes 191 12.4.3 The least square estimation of missing data based on arrays 192 12.4.4 Combining the gene and array based estimates 192 12.5 Local Least Square Inputting (LLSinpute) 193 12.5.1 Selecting genes 194 12.5.2 Gene-wise formulation of local least squares imputation 195 12.6 The Comparison of the Methods of Missing Data Inputting 197 REFERENCES 199 PLATE
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