Preface xv
About the Companion Website xvii
1 The Tree of Life (I) 1
1.1 Introduction 1
1.2 Emergence of Life 1
1.2.1 Timeline Disagreements 3
1.3 Classifications and Mechanisms 4
1.4 Chromatin Structure 5
1.5 Molecular Mechanisms 9
1.5.1 Precursor Messenger RNA 9
1.5.2 Precursor Messenger RNA to Messenger RNA 10
1.5.3 Classes of Introns 10
1.5.4 Messenger RNA 10
1.5.5 mRNA to Proteins 11
1.5.6 Transfer RNA 12
1.5.7 Small RNA 12
1.5.8 The Transcriptome 13
1.5.9 Gene Networks and Information Processing 13
1.5.10 Eukaryotic vs. Prokaryotic Regulation 14
1.5.11 What Is Life? 14
1.6 Known Species 14
1.7 Approaches for Compartmentalization 15
1.7.1 Two Main Approaches for Organism Formation 16
1.7.2 Size and Metabolism 16
1.8 Sizes in Eukaryotes 16
1.8.1 Sizes in Unicellular Eukaryotes 17
1.8.2 Sizes in Multicellular Eukaryotes 17
1.9 Sizes in Prokaryotes 17
1.10 Virus Sizes 18
1.10.1 Viruses vs. the Spark of Metabolism 20
1.11 The Diffusion Coefficient 20
1.12 The Origins of Eukaryotic Cells 21
1.12.1 Endosymbiosis Theory 21
1.12.2 DNA and Organelles 22
1.12.3 Membrane-bound Organelles with DNA 23
1.12.4 Membrane-bound Organelles Without DNA 23
1.12.5 Control and Division of Organelles 24
1.12.6 The Horizontal Gene Transfer 24
1.12.7 On the Mechanisms of Horizontal Gene Transfer 25
1.13 Origins of Eukaryotic Multicellularity 26
1.13.1 Colonies Inside an Early Unicellular Common Ancestor 26
1.13.2 Colonies of Early Unicellular Common Ancestors 26
1.13.3 Colonies of Inseparable Early Unicellular Common Ancestors
1.13.4 Chimerism and Mosaicism 28
1.14 Conclusions 29
2 Tree of Life: Genomes (II) 31
2.1 Introduction 31
2.2 Rules of Engagement 31
2.3 Genome Sizes in the Tree of Life 32
2.3.1 Alternative Methods 33
2.3.2 The Weaving of Scales 33
2.3.3 Computations on the Average Genome Size 36
2.3.4 Observations on Data 38
2.4 Organellar Genomes 40
2.4.1 Chloroplasts 40
2.4.2 Apicoplasts 40
2.4.3 Chromatophores 42
2.4.4 Cyanelles 42
2.4.5 Kinetoplasts 42
2.4.6 Mitochondria 43
2.5 Plasmids 43
2.6 Virus Genomes 44
2.7 Viroids and Their Implications 46
2.8 Genes vs. Proteins in the Tree of Life 47
2.9 Conclusions 49
3 Sequence Alignment (I) 51
3.1 Introduction 51
3.2 Style and Visualization 51
3.3 Initialization of the Score Matrix 54
3.4 Calculation of Scores 57
3.4.1 Initialization of the Score Matrix for Global Alignment 57
3.4.2 Initialization of the Score Matrix for Local Alignment 62
3.4.3 Optimization of the Initialization Steps 65
3.4.4 Curiosities 66
3.5 Traceback 71
3.6 Global Alignment 75
3.7 Local Alignment 79
3.8 Alignment Layout 84
3.9 Local Sequence Alignment – The Final Version 87
3.10 Complementarity 91
3.11 Conclusions 97
4 Forced Alignment (II) 99
4.1 Introduction 99
4.2 Global and Local Sequence Alignment 100
4.2.1 Short Notes 100
4.2.2 Understanding the Technology 101
4.2.3 Main Objectives 102
4.3 Experiments and Discussions 102
4.3.1 Alignment Layout 106
4.3.2 Forced Alignment Regime 106
4.3.3 Alignment Scores and Significance 109
4.3.4 Optimal Alignments 110
4.3.5 The Main Significance Scores 110
4.3.6 The Information Content 110
4.3.7 The Match Percentage 112
4.3.8 Significance vs. Chance 113
4.3.9 The Importance of Randomness 113
4.3.10 Sequence Quality and the Score Matrix 114
4.3.11 The Significance Threshold 115
4.3.12 Optimal Alignments by Numbers 116
4.3.13 Chaos Theory on Sequence Alignment 116
4.3.14 Image-Encoding Possibilities 116
4.4 Advanced Features and Methods 117
4.4.1 Sequence Detector 117
4.4.2 Parameters 117
4.4.3 Heatmap 118
4.4.4 Text Visualization 123
4.4.5 Graphics for Manuscript Figures and Didactic Presentations 124
4.4.6 Dynamics 124
4.4.7 Independence 125
4.4.8 Limits 125
4.4.9 Local Storage 125
4.5 Conclusions 128
5 Self-Sequence Alignment (I) 129
5.1 Introduction 129
5.2 True Randomness 130
5.3 Information and Compression Algorithms 130
5.4 White Noise and Biological Sequences 131
5.5 The Mathematical Model 131
5.5.1 A Concrete Example 132
5.5.2 Model Dissection 133
5.5.3 Conditions for Maxima and Minima 136
5.6 Noise vs. Redundancy 137
5.7 Global and Local Information Content 137
5.8 Signal Sensitivity 138
5.9 Implementation 140
5.9.1 Global Self-Sequence Alignment 140
5.9.2 Local Self-Sequence Alignment 144
5.10 A Complete Scanner for Information Content 147
5.11 Conclusions 149
6 Frequencies and Percentages (II) 151
6.1 Introduction 151
6.2 Base Composition 152
6.3 Percentage of Nucleotide Combinations 152
6.4 Implementation 153
6.5 A Frequency Scanner 156
6.6 Examples of Known Significance 158
6.7 Observation vs. Expectation 160
6.8 A Frequency Scanner with a Threshold 161
6.9 Conclusions 163
7 Objective Digital Stains (III) 165
7.1 Introduction 165
7.2 Information and Frequency 166
7.3 The Objective Digital Stain 169
7.3.1 A 3D Representation Over a 2D Plane 173
7.3.2 ODSs Relative to the Background 177
7.4 Interpretation of ODSs 181
7.5 The Significance of the Areas in the ODS 183
7.6 Discussions 184
7.6.1 A Similarity Between Dissimilar Sequences 186
7.7 Conclusions 186
8 Detection of Motifs (I) 187
8.1 Introduction 187
8.2 DNA Motifs 187
8.2.1 DNA-binding Proteins vs. Motifs and Degeneracy 188
8.2.2 Concrete Examples of DNA Motifs 188
8.3 Major Functions of DNA Motifs 191
8.3.1 RNA Splicing and DNA Motifs 191
8.4 Conclusions 195
9 Representation of Motifs (II) 197
9.1 Introduction 197
9.2 The Training Data 197
9.3 A Visualization Function 198
9.4 The Alignment Matrix 200
9.5 Alphabet Detection 203
9.6 The Position-Specific Scoring Matrix (PSSM) Initialization 206
9.7 The Position Frequency Matrix (PFM) 207
9.8 The Position Probability Matrix (PPM) 208
9.8.1 A Kind of PPM Pseudo-Scanner 209
9.9 The Position Weight Matrix (PWM) 212
9.10 The Background Model 215
9.11 The Consensus Sequence 218
9.11.1 The Consensus – Not Necessarily Functional 219
9.12 Mutational Intolerance 221
9.13 From Motifs to PWMs 222
9.14 Pseudo-Counts and Negative Infinity 226
9.15 Conclusions 229
10 The Motif Scanner (III) 231
10.1 Introduction 231
10.2 Looking for Signals 232
10.3 A Functional Scanner 235
10.4 The Meaning of Scores 239
10.4.1 A Score Value Above Zero 239
10.4.2 A Score Value Below Zero 241
10.4.3 A Score Value of Zero 241
10.5 Conclusions 242
11 Understanding the Parameters (IV) 243
11.1 Introduction 243
11.2 Experimentation 243
11.2.1 A Scanner Implementation Based on Pseudo-Counts 244
11.2.2 A Scanner Implementation Based on Propagation of Zero Counts 246
11.3 Signal Discrimination 249
11.4 False-Positive Results 250
11.5 Sensitivity Adjustments 251
11.6 Beyond Bioinformatics 252
11.7 A Scanner That Uses a Known PWM 253
11.8 Signal Thresholds 256
11.8.1 Implementation and Filter Testing 258
11.9 Conclusions 262
12 Dynamic Backgrounds (V) 263
12.1 Introduction 263
12.2 Toward a Scanner with Two PFMs 263
12.2.1 The Implementation of Dynamic PWMs 264
12.2.2 Issues and Corrections for Dynamic PWMs 271
12.2.3 Solutions for Aberrant Positive Likelihood Values 274
12.3 A Scanner with Two PFMs 280
12.4 Information and Background Frequencies on Score Values 283
12.5 Dynamic Background vs. Null Model 285
12.6 Conclusions 285
13 Markov Chains: The Machine (I) 287
13.1 Introduction 287
13.2 Transition Matrices 287
13.3 Discrete Probability Detector 292
13.3.1 Alphabet Detection 292
13.3.2 Matrix Initialization 293
13.3.3 Frequency Detection 295
13.3.4 Calculation of Transition Probabilities 297
13.3.5 Particularities in Calculating the Transition Probabilities 306
13.4 Markov Chains Generators 307
13.4.1 The Experiment 308
13.4.2 The Implementation 312
13.4.3 Simulation of Transition Probabilities 315
13.4.4 The Markov machine 315
13.4.5 Result Verification 317
13.5 Conclusions 318
14 Markov Chains: Log Likelihood (II) 319
14.1 Introduction 319
14.2 The Log-Likelihood Matrix 319
14.2.1 A Log-Likelihood Matrix Based on the Null Model 320
14.2.2 A Log-Likelihood Matrix Based on Two Models 322
14.3 Interpretation and Use of the Log-Likelihood Matrix 326
14.4 Construction of a Markov Scanner 328
14.5 A Scanner That Uses a Known LLM 337
14.6 The Meaning of Scores 340
14.7 Beyond Bioinformatics 344
14.8 Conclusions 345
15 Spectral Forecast (I) 347
15.1 Introduction 347
15.2 The Spectral Forecast Model 347
15.3 The Spectral Forecast Equation 349
15.4 The Spectral Forecast Inner Workings 350
15.4.1 Each Part on a Single Matrix 351
15.4.2 Both Parts on a Single Matrix 352
15.4.3 Both Parts on Separate Matrices 353
15.4.4 Concrete Example 1 354
15.4.5 Concrete Example 2 357
15.4.6 Concrete Example 3 359
15.5 Implementations 360
15.5.1 Spectral Forecast for Signals 362
15.5.2 What Does the Value of d Mean? 364
15.5.3 Spectral Forecast for Matrices 368
15.6 The Spectral Forecast Model for Predictions 372
15.6.1 The Spectral Forecast Model for Signals 372
15.6.2 Experiments on the Similarity Index Values 381
15.6.3 The Spectral Forecast Model for Matrices 384
15.7 Conclusions 389
16 Entropy vs. Content (I) 391
16.1 Introduction 391
16.2 Information Entropy 391
16.3 Implementation 395
16.4 Information Content vs. Information Entropy 400
16.4.1 Implementation 403
16.4.2 Additional Considerations 409
16.5 Conclusions 409
17 Philosophical Transactions 411
17.1 Introduction 411
17.2 The Frame of Reference 411
17.2.1 The Fundamental Layer of Complexity 412
17.2.2 On the Complexity of Life 414
17.3 Random vs. Pseudo-random 415
17.4 Random Numbers and Noise 418
17.5 Determinism and Chaos 419
17.5.1 Chaos Without Noise 420
17.5.2 Chaos with Noise 427
17.5.3 Limits of Prediction 430
17.5.4 On the Wings of Chaos 431
17.6 Free Will and Determinism 431
17.6.1 The Greatest Disappointment 432
17.6.2 The Most Powerful Processor in Existence 433
17.6.3 Certainty vs. Interpretation 435
17.6.4 A Wisdom that Applies 436
17.7 Conclusions 439
Appendix A 441
A.1 Association of Numerical Values with Letters 441
A.2 Sorting Values on Columns 443
A.3 The Implementation of a Sequence Logo 446
A.4 Sequence Logos Based on Maximum Values 451
A.5 Using Logarithms to Build Sequence Logos 455
A.6 From a Motif Set to a Sequence Logo 459
References 467
Index 489
