Modeling Biomolecular Networks in Cells (eBook)

Luonan Chen received his M.E. and Ph.D. degrees in electrical engineering from Tohoku University, Sendai, Japan, in 1988 and 1991, respectively. From 1997, he was a member of the faculty of Osaka Sangyo University, Osaka, Japan, and then became a full Professor in the Department of Electrical Engineering and Electronics. He was also the founding director of Institute of Systems Biology, Shanghai University. Since 2010, he has been a professor at Key Laboratory of Systems Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences. His fields of interest are systems biology, bioinformatics, and nonlinear dynamics. He serves as associate editor or editorial board member for many systems biology related journals, e.g. BMC Systems Biology, IEEE/ACM Trans. on Computational Biology and Bioinformatics, IET Systems Biology, Mathematical Biosciences, International Journal of Systems and Synthetic Biology, and the Journal of Systems Science and Complexity. He also serves as Chair of Technical Committee of Systems Biology at the IEEE SMC Society. Ruiqi Wang received an M.S. degree in mathematics from Yunnan University, Kunming, China, in 1999, and a Ph. D. degree in mathematics from the Academy of Mathematics and Systems Science, CAS, Beijing, China, in 2002. Since 2007, he has been a member of the faculty of Shanghai University, Shanghai, China, where he is currently an Associate Professor at Institute of Systems Biology. His fields of interest are systems biology and nonlinear dynamics. Chunguang Li received an M.S. degree in Pattern Recognition and Intelligent Systems and a Ph.D. degree in Circuits and Systems from the University of Electronic Science and Technology of China, Chengdu, China, in 2002 and 2004, respectively. Currently, he is a Professor with the Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China. His current research interests include computational neuroscience, statistical signal processing, and machine intelligence. Kazuyuki Aihara received a B.E. degree of electrical engineering in 1977 and a Ph.D. degree of electronic engineering 1982 from the University of Tokyo, Japan. Currently, he is Professor of the Institute of Industrial Science, Professor of the Graduate School of Information Science and Technology, and Director of Collaborative Research Center for Innovative Mathematical Modelling at the University of Tokyo. His research interests include mathematical modeling of complex systems, parallel distributed processing with spatio-temporal chaos, and time series analysis of complex data.

Preface 6
Contents 8
1 Introduction 12
1.1 Biological Processes and Networks in Cellular Systems 13
1.1.1 Gene Regulation: Gene Regulatory Networks 14
1.1.2 Signal Transduction: Signal Transduction Networks 17
1.1.3 Protein Interactions: Protein Interaction Networks 19
1.1.4 Metabolism: Metabolic Networks 19
1.1.5 Cell Cycles and Cellular Rhythms: Nonlinear Network Dynamics 22
1.2 A Primer to Networks 24
1.2.1 Basic Concepts of Networks 25
1.2.2 Topological Properties of Networks 26
1.3 A Primer to Dynamics 28
1.3.1 Dynamics and Collective Behavior 28
1.3.2 System States 29
1.3.3 Structures and Functions 29
1.3.4 Cellular Noise 31
1.3.5 Time Delays 31
1.3.6 Multiple Time Scales 32
1.3.7 Robustness and Sensitivity 33
1.4 Network Systems Biology and Synthetic Systems Biology 34
1.5 Outline of the Book 35
2 Dynamical Representations of Molecular Networks 42
2.1 Biochemical Reactions 42
2.2 Molecular Networks 49
2.3 Graphical Representation 49
2.3.1 Example of Interaction Graphs 50
2.3.2 Example of Incidence Graphs 53
2.3.3 Example of Species-reaction Graphs 53
2.4 Biochemical Kinetics 54
2.5 Stochastic Representation 55
2.5.1 Master Equations for a General Molecular Network 56
2.5.2 Stochastic Simulation 62
2.5.3 Analysis of Sensitivity and Robustness of Master Equations 67
2.5.4 Langevin Equations 68
2.5.5 Fokker–Planck Equations 73
2.5.6 Cumulant Equations 76
2.6 Deterministic Representation 79
2.6.1 Basic Kinetics 79
2.6.2 Deterministic Representation of a General Molecular System 81
2.6.3 Michaelis–Menten and Hill Equations 82
2.6.4 Total Quasi-steady-state Approximation 86
2.6.5 Deriving Rate Equations 88
2.6.6 Modeling Transcription and Translation Processes 90
2.7 Hybrid Representation and Reducing Molecular Networks 93
2.7.1 Decomposition of Biomolecular Networks 93
2.7.2 Approximation of Continuous Variables in Molecular Networks 97
2.7.3 Gaussian Approximation in Molecular Networks 98
2.7.4 Deterministic Approximation in Molecular Networks 100
2.7.5 Prefactor Approximation of Deterministic Representation 102
2.7.6 Stochastic Simulation of Hybrid Systems 105
2.8 Stochastic versus Deterministic Representation 109
3 Deterministic Structures of Biomolecular Networks 112
3.1 A General Structure of Molecular Networks 114
3.1.1 Basic Definitions 115
3.1.2 A General Structure for Gene Regulatory Networks 118
3.2 Gene Regulatory Networks with Cell Cycles 120
3.2.1 Gene Regulatory Networks for Eukaryotes 123
3.2.2 Gene Regulatory Networks for Prokaryotes 125
3.3 Interaction Graphs and Logic Gates 129
3.3.1 Interaction Graphs and Types of Interactions 129
3.3.2 Logic Gates 132
4 Qualitative Analysis of Deterministic Dynamical Networks 135
4.1 Stability Analysis 135
4.2 Bifurcation Analysis 139
4.3 Examples for Analyzing Stability and Bifurcations 142
4.3.1 A Simplified Gene Network 142
4.3.2 A Two-gene Network 145
4.3.3 A Three-gene Network 149
4.4 Robustness and Sensitivity Analysis 151
4.4.1 Robustness Measures 152
4.4.2 Sensitivity Analysis 153
4.5 Control Analysis 155
4.5.1 Control Coefficients of Metabolic Systems 155
4.5.2 Metabolic Control Theorems 157
4.6 Monotone Dynamical Systems 158
4.6.1 Notation 158
4.6.2 Decomposition of Monotone Systems 161
5 Stability Analysis of Genetic Networks in Lur’e Form 169
5.1 A Genetic Network Model 169
5.2 Stability Analysis of Genetic Networks Without Noise 172
5.3 Stochastic Stability of Gene Regulatory Networks 175
5.3.1 Mean-square Stability 175
5.3.2 Stochastic Stability with Disturbance Attenuation 179
5.4 Examples 184
6 Design of Synthetic Switching Networks 188
6.1 Types of Switches 190
6.2 Simple Switching Networks 194
6.2.1 Bistability in a Single Gene Network 194
6.2.2 The Toggle Switch 196
6.2.3 The MAPK Cascade Model 197
6.3 Design of Switching Networks with Positive Loops 199
6.4 Detection of Multistability 210
6.5 Enzyme-driven Switching Networks 217
7 Design of Synthetic Oscillating Networks 226
7.1 Simple Oscillatory Networks 227
7.1.1 Delayed Autoinhibition Networks 228
7.1.2 Goldbeter’s Models 231
7.1.3 Relaxation Oscillators 235
7.1.4 Stochastic Oscillators 239
7.2 Design of Oscillating Networks with Negative Loops 241
7.2.1 Theoretical Model of Cyclic Feedback Networks 242
7.2.2 A Special Cyclic Feedback Network 244
7.2.3 A General Cyclic Feedback Network 251
7.3 Construction of Oscillators by Non-monotone Dynamical Systems 253
7.4 Design of Molecular Oscillators with Hybrid Networks: General Formalism 264
8 Multicellular Networks and Synchronization 275
8.1 A General Multicellular Network for Deterministic Models 276
8.2 Deterministic Synchronization of Cellular Oscillators 279
8.2.1 Complete Synchronization 279
8.2.2 Other Types of Synchronization 282
8.3 Spontaneous Synchronization of Deterministic Models 283
8.4 Entrained Synchronization for Deterministic Models 287
8.5 Noise-driven Synchronization for Stochastic Models Without Coupling 291
8.6 A General Multicellular Network for Stochastic Models with Coupling 294
8.6.1 A Model 294
8.6.2 Example of a Gene Regulatory Network 296
8.6.3 Theoretical Analysis 302
8.6.4 Algorithm for Stochastic Simulation 307
8.6.5 Numerical Simulation 308
8.7 Deterministic Synchronization of Genetic Networks in Lur’e Form 311
8.8 Stochastic Synchronization of Genetic Networks in Lur’e Form 319
8.9 Transient Resetting for Synchronization Without Coupling 325
References 333
Index 346