Preface xiii

1. Power Laws in Biological Networks 1

Eivind Almaas and Albert-Ldszld Barabdsi

Power Laws in Network Topology 2

Network Models 3

Power Laws in Network Utilization 6

2. Graphical Analysis of Biocomplex Networks and Transport Phenomena 12

Kwang-Il Goh, Byungnam Kahng and Doochul Kim The Degree Distribution, the Degree Correlation

Function and the Clustering Coefficient 13

Graph Theoretic Analysis of the Yeast Protein

Interaction Network 14

Classification of Scale-Free Networks 16

3. Large-Scale Topological Properties of Molecular Networks 25

Sergei Maslov and Kim Sneppen

Topological Properties of Protein Networks 26

Multi-Node Properties: Correlation Profile 33

Robustness of the Correlation Profile with Respect to Potential Errors in the Data 36

Discussion: What It May All Mean? 37

4. The Connectivity of Large Genetic Networks:

Design, History, or Mere Chemistry? 40

Andreas Wagner

Metabolic Networks and Planetary Atmospheres 42

Protein Interaction Networks 44

Connectivity and Protein Age 46

5. The Drosophila Protein Interaction Network

May Be neither Power-Law nor Scale-Free 53

J.S. Bader

Observed Vertex Degree Distribution 55

Vertex Degree Distributions and Power-Law Fits 56

Bait and Prey Distributions Reconciled 58

Determining the Length Scale of the Network 59

6. Birth and Death Models of Genome Evolution 65

Georgy P. Karev, Yuri I. Wolf and Eugene V. Koonin Power Laws, Scale-Free Networks, and Models of Genome Evolution 65

Definitions, Assumptions and Empirical Data 67

Asymptotic Behaviors of the Ergodic Distribution of the Model 69

Linear Stochastic BDIM and Its Applications 71

Nonlinear Modifications of the Model: Polynomial BDIM 73

Nonlinear Rational BDIM 75

Simulation of Gene Family Evolution under BDIMs of Different Degrees 79

The Mean Number of Elementary Events before Family

Extinction and Formation 79

7. Scale-Free Evolution: From Proteins to Organisms 86

Nikolay V. Dokholyan and Eugene I. Shakhnovich Protein Evolutionary Relationships from Structure Similarities 88

Protein Structure-Function Relations from an Evolutionary Perspective 89

Protein Evolutionary Relations within and between Individual Proteomes 89

Sequence Divergence 90

Why It May Be Impossible to Reconstruct Hereditary Relations between Proteins Based Solely on Their Sequence Similarity? 91

The Underlying Scenario of Protein Evolution 92

Reconstructing Evolutionary Relations between Proteins 93

Properties of the Protein Domain Universe Graphs 94

Evolution of Proteins and Organisms 97

Reconstruction of Protein Structure-Function Relations 98

The Importance of Independent Functional

Hierarchical Description 99

Divergent Evolution Observed 100

8. Gene Regulatory Networks 106

T. Gregory Dewey and David J. Galas Inferring Gene Expression Networks from Microarray Data 107

Global Properties of Gene Expression Networks Ill

Gene Duplication Model of Expression Networks 113

Transcription Factor Networks 115

9. Power Law Correlations in DNA Sequences 123

Sergey V. Buldyrev

Critical Phenomena and Long Range Correlations 124

One-Dimensional Ising Model 125

Markovian Processes 126

Exponential versus Power Law Correlations 128

Correlation Analysis of DNA Sequences 131

Correlation Function 132

Fourier Power Spectrum 136

Discrete Fourier Transform 137

Detrended Fluctuation Analysis (DFA) 140

A Relation between DFA and Power Spectrum 141

Duplication-Mutation Model of DNA Evolution 144

Alternation of Nucleotide Frequencies 145

Models of Long Range Anti-Correlations 149

Analysis of DNA Sequences 151

Distribution of Simple Repeats 154

10. Analytical Evolutionary Model for Protein Fold Occurrence in Genomes, Accounting for the Effects of Gene Duplication, Deletion, Acquisition and Selective Pressure 165

Michael KamaL, Nicholas M. Luscombe, Jiang Qian and Mark Gerstein

Minimal Model: Gene Duplication and New Fold Acquisition 167

Extended Model: Including the Effects of Random

Gene Deletion 170

The Effects of Selection Pressure 174

Fitting the Models to Genomic Data 176

Appendix A: Analytic Solution of the Minimal Model 180

Appendix B: Crossover Behavior 182

Appendix C: Arbitrary Initial Distribution 184

Appendix D: Solution to the Extended Model

Appendix E: Analytical Results for Higher Moments 185

Appendix F: Perturbation Theory Approximation for the Extended Model 186

Appendix G: The Effects of Selection Pressure 189

Appendix H: A Useful Normalization Identity 192

11. The Protein Universes: Some Informatic Issues in Protein Classification 194

S. Rackovsky

General Methodology 195

Protein Sequences 196

Protein Structures 198

12. The Role of Computation in Complex Regulatory Networks 206

Pau Fernández and Ricard V. Soli

The Evidence for Computing Networks 208

Modeling 209

Irreducibility 211

The Boolean Idealization 212

The Evolutionary Point of View 216

Redundancy 218

Degeneracy 219

Evolvability 220

Modularity 221

13. Neutrality and Selection in the Evolution of Gene Families 226

Itai Yanai

Gene Family Sizes (GFS) Distributions 226

Modeling Genome Evolution 227

Comparative Deconstruction of the Gene Family

Sizes Distribution 228

Pleiotropy —» Duplication —» Subfunctionalization 232

14. Scaling Laws in the Functional Content of Genomes:

Fundamental Constants of Evolution? 236

Erik van Nimwegen

Power Laws in Genomic Quantities 236

Comparing Genomic Features across Genomes 236

Scaling in Functional Gene-Content Statistics 237

Principle Component Analysis 243

Evolutionary Interpretation 247

Methods 251

Index 255

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