Table of contents for Power laws, scale-free networks and genome biology / [edited by] Eugene V. Koonin, Yuri I. Wolf, Georgy P. Karev.

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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.
Genomics -- Mathematical models.
Computational biology.
Biological models.
Genomics.
Algorithms.
Computational Biology.
Models, Biological.