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Preface xiii 1. Power Laws in Biological Networks 1 Eivind Almaas and Albert-L¿szl¿ Barab¿si 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, Scalefree 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 111 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 When 0 < Q < 1 and R = 0 184 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 Fern¿ndez and Ricard V. Sol¿ 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
Library of Congress Subject Headings for this publication:
Genomics -- Mathematical models.