Modeling Biomolecular Networks in Cells

by Chen, Luonan; Wang, Ruiqi; Li, Chunguang; Aihara, Kazuyuki

• ISBN13: 9781849962131
• ISBN10: 1849962138
• Format: Hardcover
• Copyright: 2010-09-01
• Publisher: Springer Verlag

Summary

Taking ideas from nature has been a theme of humanity’s technological progress but it is only our newfound expertise in molecular manipulation and complex nonlinear dynamics that allows us the prospect of conscripting the building blocks of life as a means of furthering our abilities in circuits, systems and computers by the control of cellular networks.Modeling Biomolecular Networks shows how the interaction between the molecular components of basic living organisms can be modelled mathematically and the models used to create artificial biological entities within cells. Such forward engineering is a difficult task because of the ill-posed nature of the problems and because of the fundamental complexity of the interactions within even the most primitive biological cell. The nonlinear dynamical methods espoused in this book simplify the biology so that it can be successfully understood and the synthesis of simple biological oscillators and rhythm-generators made feasible. Such simple but, from an engineering point of view, unconventional units can then be co-ordinated using intercellular signal biomolecules. The formation of such man-made multicellular networks with a view to the production of biosensors, logic gates, new forms of integrated circuitry based on "gene-chips" and even biological computers is an important step in the design of faster and more flexible "electronics" for the future. The book also provides theoretical frameworks and tools with which to analyze the nonlinear dynamical phenomena, such as collective behaviour, which arise from the connection of building blocks in a biomolecular network.Researchers and graduate students from a variety of disciplines: engineering, applied mathematics, computer science and quantitative biology will find this book instructive and valuable. The text assumes a basic understanding of differential equations and the necessary molecular biology is dealt with chapter by chapter so only high-school biology is required.

Table of Contents

Introduction	p. 1
Biological Processes and Networks in Cellular Systems	p. 2
Gene Regulation: Gene Regulatory Networks	p. 3
Signal Transduction: Signal Transduction Networks	p. 6
Protein Interactions: Protein Interaction Networks	p. 8
Metabolism: Metabolic Networks	p. 8
Cell Cycles and Cellular Rhythms: Nonlinear Network Dynamics	p. 11
A Primer to Networks	p. 13
Basic Concepts of Networks	p. 14
Topological Properties of Networks	p. 15
A Primer to Dynamics	p. 17
Dynamics and Collective Behavior	p. 17
System States	p. 18
Structures and Functions	p. 18
Cellular Noise	p. 20
Time Delays	p. 20
Multiple Time Scales	p. 21
Robustness and Sensitivity	p. 22
Network Systems Biology and Synthetic Systems Biology	p. 23
Outline of the Book	p. 24
Dynamical Representations of Molecular Networks	p. 31
Biochemical Reactions	p. 31
Molecular Networks	p. 38
Graphical Representation	p. 38
Example of Interaction Graphs	p. 39
Example of Incidence Graphs	p. 42
Example of Species-reaction Graphs	p. 42
Biochemical Kinetics	p. 43
Stochastic Representation	p. 44
Master Equations for a General Molecular Network	p. 45
Stochastic Simulation	p. 51
Analysis of Sensitivity and Robustness of Master Equations	p. 56
Langevin Equations	p. 57
Fokker-Planck Equations	p. 62
Cumulant Equations	p. 65
Deterministic Representation	p. 68
Basic Kinetics	p. 68
Deterministic Representation of a General Molecular System	p. 70
Michaelis-Menten and Hill Equations	p. 71
Total Quasi-steady-state Approximation	p. 75
Deriving Rate Equations	p. 77
Modeling Transcription and Translation Processes	p. 79
Hybrid Representation and Reducing Molecular Networks	p. 82
Decomposition of Biomolecular Networks	p. 82
Approximation of Continuous Variables in Molecular Networks	p. 86
Gaussian Approximation in Molecular Networks	p. 87
Deterministic Approximation in Molecular Networks	p. 89
Prefactor Approximation of Deterministic Representation	p. 91
Stochastic Simulation of Hybrid Systems	p. 94
Stochastic versus Deterministic Representation	p. 98
Deterministic Structures of Biomolecular Networks	p. 101
A General Structure of Molecular Networks	p. 103
Basic Definitions	p. 104
A General Structure for Gene Regulatory Networks	p. 107
Gene Regulatory Networks with Cell Cycles	p. 109
Gene Regulatory Networks for Eukaryotes	p. 112
Gene Regulatory Networks for Prokaryotes	p. 114
Interaction Graphs and Logic Gates	p. 118
Interaction Graphs and Types of Interactions	p. 118
Logic Gates	p. 121
Qualitative Analysis of Deterministic Dynamical Networks	p. 125
Stability Analysis	p. 125
Bifurcation Analysis	p. 129
Examples for Analyzing Stability and Bifurcations	p. 132
A Simplified Gene Network	p. 132
A Two-gene Network	p. 135
A Three-gene Network	p. 139
Robustness and Sensitivity Analysis	p. 141
Robustness Measures	p. 142
Sensitivity Analysis	p. 143
Control Analysis	p. 145
Control Coefficients of Metabolic Systems	p. 145
Metabolic Control Theorems	p. 147
Monotone Dynamical Systems	p. 148
Notation	p. 148
Decomposition of Monotone Systems	p. 151
Stability Analysis of Genetic Networks in Lur'e Form	p. 159
A Genetic Network Model	p. 159
Stability Analysis of Genetic Networks Without Noise	p. 162
Stochastic Stability of Gene Regulatory Networks	p. 165
Mean-square Stability	p. 165
Stochastic Stability with Disturbance Attenuation	p. 169
Examples	p. 174
Design of Synthetic Switching Networks	p. 179
Types of Switches	p. 181
Simple Switching Networks	p. 185
Bistability in a Single Gene Network	p. 185
The Toggle Switch	p. 187
The Mapk Cascade Model	p. 188
Design of Switching Networks with Positive Loops	p. 190
Detection of Multistability	p. 201
Enzyme-driven Switching Networks	p. 208
Design of Synthetic Oscillating Networks	p. 217
Simple Oscillatory Networks	p. 218
Delayed Autoinhibition Networks	p. 219
Goldbeter's Models	p. 222
Relaxation Oscillators	p. 226
Stochastic Oscillators	p. 230
Design of Oscillating Networks with Negative Loops	p. 232
Theoretical Model of Cyclic Feedback Networks	p. 233
A Special Cyclic Feedback Network	p. 235
A General Cyclic Feedback Network	p. 242
Construction of Oscillators by Non-monotone Dynamical Systems	p. 244
Design of Molecular Oscillators with Hybrid Networks: General Formalism	p. 255
Multicellular Networks and Synchronization	p. 267
A General Multicellular Network for Deterministic Models	p. 268
Deterministic Synchronization of Cellular Oscillators	p. 271
Complete Synchronization	p. 271
Other Types of Synchronization	p. 274
Spontaneous Synchronization of Deterministic Models	p. 275
Entrained Synchronization for Deterministic Models	p. 279
Noise-driven Synchronization for Stochastic Models Without Coupling	p. 283
A General Multicellular Network for Stochastic Models with Coupling	p. 286
A Model	p. 286
Example of a Gene Regulatory Network	p. 288
Theoretical Analysis	p. 294
Algorithm for Stochastic Simulation	p. 299
Numerical Simulation	p. 300
Deterministic Synchronization of Genetic Networks in Lur'e Form	p. 303
Stochastic Synchronization of Genetic Networks in Lur'e Form	p. 311
Transient Resetting for Synchronization Without Coupling	p. 317
References	p. 325
Index	p. 339
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