Modeling Biomolecular Networks in Cells: Structures and Dynamics

Preface
Contents
1 Introduction
	1.1 Biological Processes and Networks in Cellular Systems
		1.1.1 Gene Regulation: Gene Regulatory Networks
		1.1.2 Signal Transduction: Signal Transduction Networks
		1.1.3 Protein Interactions: Protein Interaction Networks
		1.1.4 Metabolism: Metabolic Networks
		1.1.5 Cell Cycles and Cellular Rhythms: Nonlinear Network Dynamics
	1.2 A Primer to Networks
		1.2.1 Basic Concepts of Networks
		1.2.2 Topological Properties of Networks
	1.3 A Primer to Dynamics
		1.3.1 Dynamics and Collective Behavior
		1.3.2 System States
		1.3.3 Structures and Functions
		1.3.4 Cellular Noise
		1.3.5 Time Delays
		1.3.6 Multiple Time Scales
		1.3.7 Robustness and Sensitivity
	1.4 Network Systems Biology and Synthetic Systems Biology
	1.5 Outline of the Book
2 Dynamical Representations of Molecular Networks
	2.1 Biochemical Reactions
	2.2 Molecular Networks
	2.3 Graphical Representation
		2.3.1 Example of Interaction Graphs
		2.3.2 Example of Incidence Graphs
		2.3.3 Example of Species-reaction Graphs
	2.4 Biochemical Kinetics
	2.5 Stochastic Representation
		2.5.1 Master Equations for a General Molecular Network
		2.5.2 Stochastic Simulation
		2.5.3 Analysis of Sensitivity and Robustness of Master Equations
		2.5.4 Langevin Equations
		2.5.5 Fokker–Planck Equations
		2.5.6 Cumulant Equations
	2.6 Deterministic Representation
		2.6.1 Basic Kinetics
		2.6.2 Deterministic Representation of a General Molecular System
		2.6.3 Michaelis–Menten and Hill Equations
		2.6.4 Total Quasi-steady-state Approximation
		2.6.5 Deriving Rate Equations
		2.6.6 Modeling Transcription and Translation Processes
	2.7 Hybrid Representation and Reducing Molecular Networks
		2.7.1 Decomposition of Biomolecular Networks
		2.7.2 Approximation of Continuous Variables in Molecular Networks
		2.7.3 Gaussian Approximation in Molecular Networks
		2.7.4 Deterministic Approximation in Molecular Networks
		2.7.5 Prefactor Approximation of Deterministic Representation
		2.7.6 Stochastic Simulation of Hybrid Systems
	2.8 Stochastic versus Deterministic Representation
3 Deterministic Structures of Biomolecular Networks
	3.1 A General Structure of Molecular Networks
		3.1.1 Basic Definitions
		3.1.2 A General Structure for Gene Regulatory Networks
	3.2 Gene Regulatory Networks with Cell Cycles
		3.2.1 Gene Regulatory Networks for Eukaryotes
		3.2.2 Gene Regulatory Networks for Prokaryotes
	3.3 Interaction Graphs and Logic Gates
		3.3.1 Interaction Graphs and Types of Interactions
		3.3.2 Logic Gates
4 Qualitative Analysis of Deterministic Dynamical Networks
	4.1 Stability Analysis
	4.2 Bifurcation Analysis
	4.3 Examples for Analyzing Stability and Bifurcations
		4.3.1 A Simplified Gene Network
		4.3.2 A Two-gene Network
		4.3.3 A Three-gene Network
	4.4 Robustness and Sensitivity Analysis
		4.4.1 Robustness Measures
		4.4.2 Sensitivity Analysis
	4.5 Control Analysis
		4.5.1 Control Coefficients of Metabolic Systems
		4.5.2 Metabolic Control Theorems
	4.6 Monotone Dynamical Systems
		4.6.1 Notation
		4.6.2 Decomposition of Monotone Systems
5 Stability Analysis of Genetic Networks in Lur’e Form
	5.1 A Genetic Network Model
	5.2 Stability Analysis of Genetic Networks Without Noise
	5.3 Stochastic Stability of Gene Regulatory Networks
		5.3.1 Mean-square Stability
		5.3.2 Stochastic Stability with Disturbance Attenuation
	5.4 Examples
6 Design of Synthetic Switching Networks
	6.1 Types of Switches
	6.2 Simple Switching Networks
		6.2.1 Bistability in a Single Gene Network
		6.2.2 The Toggle Switch
		6.2.3 The MAPK Cascade Model
	6.3 Design of Switching Networks with Positive Loops
	6.4 Detection of Multistability
	6.5 Enzyme-driven Switching Networks
7 Design of Synthetic Oscillating Networks
	7.1 Simple Oscillatory Networks
		7.1.1 Delayed Autoinhibition Networks
		7.1.2 Goldbeter’s Models
		7.1.3 Relaxation Oscillators
		7.1.4 Stochastic Oscillators
	7.2 Design of Oscillating Networks with Negative Loops
		7.2.1 Theoretical Model of Cyclic Feedback Networks
		7.2.2 A Special Cyclic Feedback Network
		7.2.3 A General Cyclic Feedback Network
	7.3 Construction of Oscillators by Non-monotone Dynamical Systems
	7.4 Design of Molecular Oscillators with Hybrid Networks: General Formalism
8 Multicellular Networks and Synchronization
	8.1 A General Multicellular Network for Deterministic Models
	8.2 Deterministic Synchronization of Cellular Oscillators
		8.2.1 Complete Synchronization
		8.2.2 Other Types of Synchronization
	8.3 Spontaneous Synchronization of Deterministic Models
	8.4 Entrained Synchronization for Deterministic Models
	8.5 Noise-driven Synchronization for Stochastic Models Without Coupling
	8.6 A General Multicellular Network for Stochastic Models with Coupling
		8.6.1 A Model
		8.6.2 Example of a Gene Regulatory Network
		8.6.3 Theoretical Analysis
		8.6.4 Algorithm for Stochastic Simulation
		8.6.5 Numerical Simulation
	8.7 Deterministic Synchronization of Genetic Networks in Lur’e Form
	8.8 Stochastic Synchronization of Genetic Networks in Lur’e Form
	8.9 Transient Resetting for Synchronization Without Coupling
References
Index