Analysis of Biological Networks

This is the first book of its kind to provide readers with a comprehensive introduction to the structural analysis of biological networks at the interface of biology and computer science. It begins with a brief overview of biological networks and graph theory/graph algorithms and goes on to explore: global network properties, network centralities, network motifs, network clustering, Petri nets, signal transduction and gene regulation networks, protein interaction networks, metabolic networks, phylogenetic networks, ecological networks, and correlation networks.

Björn H. Junker is a biologist with a strong background in bioinformatics. His current research activities include the quantitative analysis and modeling of metabolic networks, as well as pathway databases and visual data mining. Mr. Junker has been at the Leibniz Institute of Plant Genetics and Crop Plant Research in Germany since 2003. He worked at Brookhaven National Laboratory in New York during 2006 and was appointed as project leader at the Leibniz Institute in 2007.

Falk Schreiber is a computer scientist who has worked in bioinformatics for more than ten years. His current research areas include modeling, analysis, and visualization of biological networks; graph algorithms; and data exploration and information visualization in the life sciences. Since 2003, he has been head of the Network Analysis Research Group at the Leibniz Institute of Plant Genetics and Crop Plant Research. He was appointed professor of bioinformatics at the Martin Luther University Halle-Wittenberg, Germany, in 2007.

Foreword	p. xiii
Preface	p. xv
Contributors	p. xix
Introduction	p. 1
Networks in Biology	p. 3
Introduction	p. 3
Biology 101	p. 4
Biochemistry and Molecular Biology	p. 4
Cell Biology	p. 6
Ecology and Evolution	p. 7
Systems Biology	p. 8
Properties of Biological Networks	p. 8
Networks on a Microscopic Scale	p. 9
Networks on a Macroscopic Scale	p. 11
Other Biological Networks	p. 11
Summary	p. 12
Exercises	p. 12
References	p. 12
Graph Theory	p. 15
Introduction	p. 15
Basic Notation	p. 16
Sets	p. 16
Graphs	p. 16
Graph Attributes	p. 19
Special Graphs	p. 19
Undirected, Directed, Mixed, and Multigraphs	p. 19
Hypergraphs and Bipartite Graphs	p. 20
Trees	p. 21
Graph Representation	p. 23
Adjacency Matrix	p. 23
Adjacency List	p. 23
Graph Algorithms	p. 24
Running Times of Algorithms	p. 24
Traversal	p. 25
Summary	p. 27
Exercises	p. 27
References	p. 28
Network Analysis	p. 29
Global Network Properties	p. 31
Introduction	p. 31
Global Properties of Complex Networks	p. 33
Distance, Average Path Length, and Diameter	p. 33
Six Degrees of Separation: Concepts of a Small World	p. 35
The Degree Distribution	p. 35
Assortative Mixing and Degree Correlations	p. 38
The Clustering Coefficient	p. 39
The Matching Index	p. 41
Network Centralities	p. 42
Eigenvalues and Spectral Properties of Networks	p. 43
Models of Complex Networks	p. 43
The Erdos-Renyi Model	p. 44
The Watts-Strogatz Model	p. 45
The Barabasi-Albert Model	p. 46
Extensions of the BA Model	p. 48
Additional Properties of Complex Networks	p. 48
Structural Robustness and Attack Tolerance	p. 49
Modularity, Community Structures and Hierarchies	p. 50
Subgraphs and Motifs in Networks	p. 51
Statistical Testing of Network Properties	p. 52
Generating Networks and Null Models	p. 53
The Conceptualization of Cellular Networks	p. 54
Bipartite Graphs	p. 55
Correlation Networks	p. 57
Summary	p. 57
Exercises	p. 58
References	p. 59
Network Centralities	p. 65
Introduction	p. 65
Centrality Definition and Fundamental Properties	p. 67
Comparison of Centrality Values	p. 68
Disconnected Networks	p. 68
Degree and Shortest Path-Based Centralities	p. 69
Degree Centrality	p. 69
Eccentricity Centrality	p. 71
Closeness Centrality	p. 72
Shortest Path Betweenness Centrality	p. 73
Algorithms	p. 74
Example	p. 76
Feedback-Based Centralities	p. 77
Katz's Status Index	p. 77
Bonacich's Eigenvector Centrality	p. 78
PageRank	p. 79
Tools	p. 80
Summary	p. 80
Exercises	p. 81
References	p. 81
Network Motifs	p. 85
Introduction	p. 85
Definitions and Basic Concepts	p. 86
Definitions	p. 86
Modeling of Biological Networks	p. 88
Concepts of Motif Frequency	p. 88
Motif Statistics and Motif-Based Network Distance	p. 89
Determination of Statistical Significance of Network Motifs	p. 89
Randomization Algorithm for Generation of Null Model Networks	p. 90
Influence of the Null Model on Motif Significance	p. 91
Limitations of the Null Model on Motif Detection	p. 91
Measures of Motif Significance and for Network Comparison	p. 91
Complexity of Network Motif Detection	p. 94
Aspects Affecting the Complexity of Network Motif Detection	p. 94
Frequency Estimation by Motif Sampling	p. 96
Methods and Tools for Network Motif Analysis	p. 96
Pajek	p. 96
Mfinder	p. 96
MAVisto	p. 97
FANMOD	p. 97
Analyses and Applications of Network Motifs	p. 97
Network Motifs in Complex Networks	p. 97
Dynamic Properties of Network Motifs	p. 98
Higher Order Structures Formed by Network Motifs	p. 102
Network Comparison Based on Network Motifs	p. 104
Evolutionary Origin of Network Motifs	p. 106
Summary	p. 106
Exercises	p. 108
References	p. 108
Network Clustering	p. 113
Introduction	p. 113
Notations and Definitions	p. 115
Network Clustering Problem	p. 118
Clique-Based Clustering	p. 119
Minimum Clique Partitioning	p. 120
Min-Max k-Clustering	p. 122
Center-Based Clustering	p. 125
Clustering with Dominating Sets	p. 126
k-Center Clustering	p. 129
Conclusion	p. 131
Summary	p. 133
Exercises	p. 133
References	p. 134
Petri Nets	p. 139
Introduction	p. 139
Qualitative Modeling	p. 141
The Model	p. 141
The Behavioral Properties	p. 148
Qualitative Analysis	p. 152
Structural Analysis	p. 152
Invariant Analysis	p. 155
MCT-Sets	p. 162
Dynamic Analysis of General Properties	p. 164
Dynamic Analysis of Special Properties	p. 166
Model Validation Criteria	p. 168
Quantitative Modeling and Analysis	p. 169
Tool Support	p. 171
Case Studies	p. 172
Summary	p. 174
Exercises	p. 175
References	p. 177
Biological Networks	p. 181
Signal Transduction and Gene Regulation Networks	p. 183
Introduction	p. 183
Decisive Role of Regulatory Networks in the Evolution and Existence of Organisms	p. 184
Gene Regulatory Network as a System of Many Subnetworks	p. 186
Databases on Gene Regulation and Software Tools for Network Analysis	p. 187
Peculiarities of Signal Transduction Networks	p. 188
Topology of Signal Transduction Networks	p. 190
Topology of Transcription Networks	p. 191
Intercellular Molecular Regulatory Networks	p. 198
Summary	p. 200
Exercises	p. 201
References	p. 202
Protein Interaction Networks	p. 207
Introduction	p. 207
Detecting Protein Interactions	p. 209
The Yeast Two-Hybrid System	p. 211
Affinity Capture of Protein Complexes	p. 216
Computational Methods to Predict Protein Interactions	p. 218
Other Ways to Identify Protein Interactions	p. 219
Establishing Protein Interaction Networks	p. 220
Data Storage and Network Generation	p. 220
Benchmarking High-Throughput Interaction Data	p. 222
Analyzing Protein Interaction Networks	p. 223
Network Topology and Functional Implications	p. 223
Functional Modules in Protein Interaction Networks	p. 223
Evolution of Protein Interaction Networks	p. 224
Comparative Interactomics	p. 225
Summary	p. 225
Exercises	p. 226
References	p. 227
Metabolic Networks	p. 233
Introduction	p. 233
Visualization and Graph Representation	p. 234
Reconstruction of Genome-Scale Metabolic Networks	p. 234
Connectivity and Centrality in Metabolic Networks	p. 239
Modularity and Decomposition of Metabolic Networks	p. 242
Modularity Coefficient	p. 244
Modularity-Based Decomposition	p. 245
Elementary Flux Modes and Extreme Pathways	p. 246
Summary	p. 249
Exercises	p. 249
References	p. 251
Phylogenetic Networks	p. 255
Introduction	p. 255
Character Selection, Character Coding, and Matrices for Phylogenetic Reconstruction	p. 257
Tree Reconstruction Methodologies	p. 260
Phylogenetic Networks	p. 264
Galled Trees	p. 266
Statistical Parsimony	p. 267
Median Network	p. 269
Median-Joining Networks	p. 270
Pyramids	p. 271
Example of a Pyramidal Clustering Model	p. 271
Split Decomposition	p. 274
Summary	p. 276
Exercises	p. 276
References	p. 277
Ecological Networks	p. 283
Introduction	p. 283
Binary Food Webs	p. 289
Introduction and Definitions	p. 289
Descriptors of the Network	p. 289
Operational Problems	p. 291
Aims and Results	p. 291
Conclusion	p. 293
Quantitative Trophic Food Webs	p. 293
Introduction, Definitions, and Database	p. 293
Multiple Commodities	p. 295
Descriptors of the Network and Information to be Gained	p. 295
Conclusion	p. 298
Ecological Information Networks	p. 298
Summary	p. 300
Exercises	p. 301
References	p. 301
Correlation Networks	p. 305
Introduction	p. 305
General Remarks	p. 306
Basic Notation	p. 307
Data, Unit, Variable, and Observation	p. 307
Sample, Profiles, and Replica Set	p. 308
Measures of Association	p. 309
Simple Correlation Measures	p. 310
Complex Correlation and Association Measures	p. 311
Probability, Confidence, and Power	p. 313
Matrices	p. 314
Construction and Analyses of Correlation Networks	p. 314
Data and Profiles	p. 315
Data Set and Matrix	p. 316
Correlation Matrix	p. 318
Network Matrix	p. 318
Correlation Network Analysis	p. 319
Interpretation and Validation	p. 321
Biological Use of Correlation Networks	p. 321
The Global Analysis Approach	p. 321
The Guide Gene Approach	p. 322
A Simple Coregulation Test: Photosynthesis	p. 324
A Complex Coregulation Test: Brassinosteroids	p. 327
Summary	p. 328
Exercises	p. 329
References	p. 330
Index	p. 335
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