Mathematical Principles in Bioinformatics (Interdisciplinary Applied Mathematics, 58)

Preface
Acknowledgments
Contents
1 Biological Overview
	1.1 Basic Information on Macromolecules
	1.2 The Central Dogma
	1.3 Nucleotides and Amino Acids
	1.4 DNA
	1.5 RNA
	1.6 Protein
	1.7 The Genetic Code
2 Bioinformatics Databases
	2.1 Introduction to Bioinformatics Databases
	2.2 Nucleotide Sequence Databases
		2.2.1 EMBL (http://www.ebi.ac.uk/embl/)
		2.2.2 DDBJ (http://www.ddbj.nig.ac.jp/)
		2.2.3 GenBank (http://www.ncbi.nlm.nih.gov/genbank/)
	2.3 Protein Sequence Databases
		2.3.1 Swiss-Prot (https://www.uniprot.org/uniprotkb?query=reviewed:true)
		2.3.2 TrEMBL (https://www.uniprot.org/uniprotkb?query=reviewed:false)
		2.3.3 PIR (http://pir.georgetown.edu)
	2.4 Sequence Motif Databases
		2.4.1 Pfam (http://pfam.xfam.org/)
		2.4.2 PROSITE (http://prosite.expasy.org/)
	2.5 Macromolecular 3D Structure Databases
		2.5.1 PDB (http://www.rcsb.org/)
		2.5.2 SCOP (http://scop.mrc-lmb.cam.ac.uk/scop/)
		2.5.3 CATH (http://www.cathdb.info)
		2.5.4 DALI (http://ekhidna2.biocenter.helsinki.fi/dali/)
3 Sequence Alignment
	3.1 Sequence Similarity
	3.2 Global Alignment
	3.3 Local Alignment
	3.4 Alignment with Affine Gap Model
	3.5 Heuristic Alignment Algorithms
		3.5.1 FASTA
		3.5.2 BLAST
	3.6 Multiple Alignment
		3.6.1 MSA
		3.6.2 Progressive Alignment
4 The Time-Frequency Spectral Analysis and Applications in Bioinformatics
	4.1 Introduction
	4.2 Discrete Fourier Transform
	4.3 Exon Prediction Based on Fourier Spectral Analysis
		4.3.1 Eukaryotic Gene Structure
		4.3.2 Fourier Spectrum Analysis of DNA Sequences
		4.3.3 The 3-Base Periodicity in Exon Sequences
		4.3.4 PS(N/3) Is Determined by the Unbalanced Nucleotide Distributions of the Three Codon Positions
		4.3.5 Algorithm for Finding Exons by Nucleotide Distribution (FEND)
	4.4 DNA Comparison Based on Fourier Spectral Analysis
		4.4.1 Even Scaling Method of Fourier Power Spectrum
		4.4.2 Power Spectrum Moment Method
		4.4.3 Cumulative Power Spectrum Moment Method
5 Graphical Representation of Sequences and Its Application
	5.1 Graphical Representation by Curves Without Degeneracy
		5.1.1 A Construction Without Degeneracy
		5.1.2 Other Constructions Without Degeneracy
			5.1.2.1 A Construction with Corresponding Moment Vectors
			5.1.2.2 A Construction with Corresponding Probability Distribution
		5.1.3 Constructions for Proteins
			5.1.3.1 A Protein Map Based on Amino Acid Hydrophobicity
			5.1.3.2 Protein Maps Based on Various Properties of Amino Acids
		5.1.4 Yau-Hausdorff Distance
	5.2 Chaos Game Representation
		5.2.1 Chaos Game Representation for DNA Sequences
		5.2.2 Chaos Game Representation for Proteins
6 The Development and Applications of the Natural Vector Method
	6.1 The Natural Vector Method for DNA Sequences
	6.2 The Properties and Advantages of the Natural Vector Method
		6.2.1 The One-to-One Correspondence Between DNA Sequence and Its Natural Vector
		6.2.2 The Convergence to 0 for High-Order Moments
		6.2.3 Advantages
	6.3 The Natural Vector Method for Protein Sequences
	6.4 The Natural Graph Method
	6.5 Applications
		6.5.1 12-Dimensional Viral Genome Space
			6.5.1.1 The Genome Space for Only Single-Segmented Viruses
			6.5.1.2 The Genome Space with Multiple-Segmented Viruses
		6.5.2 60-Dimensional Protein Space
			6.5.2.1 The Classification of the PKC-Like Superfamily
			6.5.2.2 The Evolutionary Origin of the SAR11 Clade Marine Bacteria
			6.5.2.3 The Phylogenetic Analysis of the Zika Virus
			6.5.2.4 The Protein Universe
	6.6 Other Alignment-Free Methods Motivated by the Natural Vector Method
7 Convex Hull Principle and Distinguishing Proteins from Arbitrary Amino Acid Sequences
	7.1 The Convex Hull Principle
		7.1.1 Methods for Determining Whether Two Convex Hulls Intersect
			7.1.1.1 The Projection-Line Method and the Normal Vector Method
			7.1.1.2 The Subset Determination Method
			7.1.1.3 The Linear Programming Method
			7.1.1.4 The Minimum Distance Method
		7.1.2 The Verification of the Convex Hull Principle
			7.1.2.1 The Verification by Protein Sequences
			7.1.2.2 The Verification by DNA Sequences
		7.1.3 New Sequence Detection
			7.1.3.1 Determination of the Nucleotide Composition of Genome Sequences
			7.1.3.2 Heuristic Methods to Detect New Sequences
	7.2 Distinguishing Proteins from Arbitrary Amino Acid Sequences
		7.2.1 The Principle and the Algorithm
		7.2.2 The Verification by Real Protein Sequences
		7.2.3 Derivation for the Equations of the Boundaries of Amino Acid Space
			7.2.3.1 The Boundaries of Amino Acid k in the (nk, μk) Plane
			7.2.3.2 The Boundaries of Amino Acid k in the (nk,D2k) Plane
8 New Features or Metric on Sequence Comparison
	8.1 The K-mer Natural Vector Method and Its Application
	8.2 New Features Based on the Singular Value Decomposition
		8.2.1 The K-mer Sparse Matrix Model and Its Applications
		8.2.2 Noise Reduction Based on the Singular Value Decomposition
	8.3 DFA7: A Novel Approach for Discriminating Intron-Containing and Intronless Genes
	8.4 The Lempel–Ziv Complexity and Its Application in Sequence Comparison
	8.5 An Information-Based Network Approach for Protein Classification
References