Power Laws, Scale-Free Networks and Genome Biology

0387258833......Page 1
Preface......Page 12
CONTENTS......Page 5
1. Power Laws in Biological Networks......Page 19
Power Laws in Network Topology......Page 20
Network Models......Page 21
Power Laws in Network Utilization......Page 24
2. Graphical Analysis of Biocomplex Networks and Transport Phenomena......Page 30
The Degree Distribution, the Degree Correlation Function and the Clustering Coefficient......Page 31
Graph Theoretic Analysis of the Yeast Protein Interaction Network......Page 32
Classification of Scale-Free Networks......Page 34
3. Large-Scale Topological Properties of Molecular Networks......Page 43
Topological Properties of Protein Networks......Page 44
Multi-Node Properties: Correlation Profile......Page 51
Robustness of the Correlation Profile with Respect to Potential Errors in the Data......Page 54
Discussion: What It May All Mean?......Page 55
4. The Connectivity of Large Genetic Networks: Design, History, or Mere Chemistry?......Page 58
Metabolic Networks and Planetary Atmospheres......Page 60
Protein Interaction Networks......Page 62
Connectivity and Protein Age......Page 64
5. The Drosophila Protein Interaction Network May Be neither Power-Law nor Scale-Free......Page 71
Observed Vertex Degree Distribution......Page 73
Vertex Degree Distributions and Power-Law Fits......Page 74
Bait and Prey Distributions Reconciled......Page 76
Determining the Length Scale of the Network......Page 77
Power Laws, Scale-Free Networks, and Models of Genome Evolution......Page 83
Definitions, Assumptions and Empirical Data......Page 85
Asymptotic Behaviors of the Ergodic Distribution of the Model......Page 87
Linear Stochastic BDIM and Its Applications......Page 89
Nonlinear Modifications of the Model: Polynomial BDIM......Page 91
Nonlinear Rational BDIM......Page 93
The Mean Number of Elementary Events before Family Extinction and Formation......Page 97
7. Scale-Free Evolution: From Proteins to Organisms......Page 104
Protein Evolutionary Relationships from Structure Similarities......Page 106
Protein Evolutionary Relations within and between Individual Proteomes......Page 107
Sequence Divergence......Page 108
Why It May Be Impossible to Reconstruct Hereditary Relations between Proteins Based Solely on Their Sequence Similarity?......Page 109
The Underlying Scenario of Protein Evolution......Page 110
Reconstructing Evolutionary Relations between Proteins......Page 111
Properties of the Protein Domain Universe Graphs......Page 112
Evolution of Proteins and Organisms......Page 115
Reconstruction of Protein Structure-Function Relations......Page 116
The Importance of Independent Functional Hierarchical Description......Page 117
Divergent Evolution Observed......Page 118
8. Gene Regulatory Networks......Page 124
Inferring Gene Expression Networks from Microarray Data......Page 125
Global Properties of Gene Expression Networks......Page 129
Gene Duplication Model of Expression Networks......Page 131
Transcription Factor Networks......Page 133
9. Power Law Correlations in DNA Sequences......Page 141
Critical Phenomena and Long Range Correlations......Page 142
One-Dimensional Ising Model......Page 143
Markovian Processes......Page 144
Exponential versus Power Law Correlations......Page 146
Correlation Analysis of DNA Sequences......Page 149
Correlation Function......Page 150
Fourier Power Spectrum......Page 154
Discrete Fourier Transform......Page 155
Detrended Fluctuation Analysis (DFA)......Page 158
A Relation between DFA and Power Spectrum......Page 159
Duplication-Mutation Model of DNA Evolution......Page 162
Alternation of Nucleotide Frequencies......Page 163
Models of Long Range Anti-Correlations......Page 167
Analysis of DNA Sequences......Page 169
Distribution of Simple Repeats......Page 172
10. Analytical Evolutionary Model for Protein Fold Occurrence in Genomes, Accounting for the Effects of Gene Duplication, Deletion, Acquisition and Selective Pressure......Page 183
Minimal Model: Gene Duplication and New Fold Acquisition......Page 185
Extended Model: Including the Effects of Random Gene Deletion......Page 188
The Effects of Selection Pressure......Page 192
Fitting the Models to Genomic Data......Page 194
Appendix A: Analytic Solution of the Minimal Model......Page 198
Appendix B: Crossover Behavior......Page 200
Appendix D: Solution to the Extended Mrodel When 0 < Q < 1 and R = 0......Page 202
Appendix E: Analytical Results for Higher Moments......Page 203
Appendix F: Perturbation Theory Approximation for the Extended Model......Page 204
Appendix G: The Effects of Selection Pressure......Page 207
Appendix H: A Useful Normalization Identity......Page 210
11. The Protein Universes: Some Informatic Issues in Protein Classification......Page 212
General Methodology......Page 213
Protein Sequences......Page 214
Protein Structures......Page 216
12. The Role of Computation in Complex Regulatory Networks......Page 224
The Evidence for Computing Networks......Page 226
Modeling......Page 227
Irreducibihty......Page 229
The Boolean Idealization......Page 230
The Evolutionary Point of View......Page 234
Redundancy......Page 236
Degeneracy......Page 237
Evolvability......Page 238
Modularity......Page 239
Gene Family Sizes (GFS) Distributions......Page 244
Modeling Genome Evolution......Page 245
Comparative Deconstruction of the Gene Family Sizes Distribution......Page 246
Pleiotropy → Duplication → Subfunctionalization......Page 250
Comparing Genomic Features across Genomes......Page 254
Scaling in Functional Gene-Content Statistics......Page 255
Principle Component Analysis......Page 261
Evolutionary Interpretation......Page 265
Methods......Page 269
F......Page 272
O......Page 273
U......Page 274