Note: Intro -- Preface -- Acknowledgments -- Contents -- Acronyms -- 1 Introduction and Preliminaries -- 1.1 Systems Biology -- 1.1.1 Overviews -- 1.1.2 Developments -- 1.1.3 Implications and Applications -- 1.2 Complex Networks -- 1.2.1 Overviews -- 1.2.2 Mathematical Description -- 1.2.3 Four Types of Networks -- 1.2.3.1 Regular Networks -- 1.2.3.2 Erdös-Rényi (ER) Random Networks -- 1.2.3.3 Scale-Free Networks -- 1.2.3.4 Small-World Networks -- 1.2.4 Statistical Metrics of Networks -- 1.2.4.1 Average Degree and Degree Distribution -- 1.2.4.2 Average Path Length -- 1.2.4.3 Diameter -- 1.2.4.4 Assortativity and Disassortativity -- 1.2.4.5 Small Worldness -- 1.2.4.6 Hierarchical Modularity -- 1.2.4.7 Modularity -- 1.2.4.8 Network Structure Entropy -- 1.2.5 Datasets for Real-World Complex Networks -- 1.3 Central Dogma of Molecular Biology -- 1.4 Bio-Molecular Networks -- 1.5 Several Statistical Methods -- 1.5.1 Descriptive Statistics -- 1.5.2 Cluster Analysis -- 1.5.2.1 Hierarchical Clustering -- 1.5.2.2 k-Means Clustering -- 1.5.3 Principal Component Analysis -- 1.6 Software for Network Visualization and Analysis -- 1.6.1 Pajek -- 1.6.2 Gephi -- 1.6.3 Cytoscape -- 1.6.4 MATLAB Packages and Others -- 1.7 Software for Statistical and Dynamical Analysis -- 1.7.1 SAS -- 1.7.2 SPSS -- 1.7.3 MATLAB -- 1.7.4 R -- 1.7.5 Some Other Software -- 1.7.5.1 Small Software for Clustering Analysis -- 1.7.5.2 Venn Diagrams -- 1.7.5.3 Software for Bifurcation and Dynamical Analysis -- 1.8 Organization of the Book -- References -- Part I Modeling and Dynamical Analysis of Bio-molecular Networks -- 2 Reconstruction of Bio-molecular Networks -- 2.1 Backgrounds -- 2.2 Reconstruction of Bio-molecular Networks Based on Online Databases -- 2.2.1 Regulatory Networks -- 2.2.2 Protein-Protein Interaction Networks -- 2.2.3 Signal Transduction Networks -- 2.2.4 Metabolic Networks. , 2.3 Artificial Algorithms for Generating Bio-molecular Networks -- 2.3.1 Algorithms for Artificial Regulatory Networks -- 2.3.2 Algorithms for Artificial PPI Networks -- 2.4 Statistical Reconstruction of Bio-molecular Networks -- 2.4.1 Association Methods -- 2.4.1.1 Various Similarity Measures -- 2.4.1.2 The Mean Variance Method -- 2.4.2 Information Theoretic Approaches -- 2.4.3 Partial Correlation/Gaussian Graphical Models -- 2.4.4 Granger Causality Methods -- 2.4.4.1 Granger Causality -- 2.4.4.2 Partial Granger Causality -- 2.4.4.3 Windowed Granger Causality -- 2.4.5 Statistical Regression Methods -- 2.4.6 Bayesian Methods -- 2.4.7 Variational Bayesian Methods -- 2.5 Topological Identification via Dynamical Networks -- 2.6 Discussions and Conclusions -- References -- 3 Modeling and Analysis of Simple Genetic Circuits -- 3.1 Backgrounds -- 3.2 Mathematical Modeling Techniques of Biological Networks -- 3.2.1 The Chemical Master Equation -- 3.2.2 Stochastic Simulation Algorithms -- 3.2.3 The Chemical Langevin Equation -- 3.2.4 Numerical Regimes for Stochastic Differential Equations -- 3.2.5 The Reaction Rate Equation -- 3.2.6 Numerical Regimes for Ordinary Differential Equations -- 3.3 Network Motifs and Motif Detection -- 3.4 The Feed-Forward Genetic Circuits -- 3.4.1 Related Works and Motivations -- 3.4.2 Methods for Parameter Sensitivities Analysis -- 3.4.2.1 Local Relative Parameter Sensitivities -- 3.4.2.2 A Traditional GPS Method: RS-HDMR -- 3.4.2.3 The New Global Relative Parameter Sensitivities Approach -- 3.4.3 Global Relative Parameter Sensitivities of the FFLs -- 3.4.3.1 Mathematical Models for the FFLs in GRNs -- 3.4.3.2 The GRPS of the FFLs -- 3.4.3.3 The Global Relative Parameter Sensitivities of CFFLs -- 3.4.3.4 The Global Relative Parameter Sensitivities of ICFFLs -- 3.4.3.5 The Effect of Input x on GRPS. , 3.4.3.6 The Effect of the Hill Coefficient n on the GRPS -- 3.4.3.7 RS-HDMR Versus GRPS on FFLs -- 3.4.4 GRPS and Biological Functions of the FFLs -- 3.4.4.1 GRPS and Biological Abundance of FFLs -- 3.4.4.2 Relations Between GRPS and Noise Characteristics -- 3.4.4.3 GRPS and Fold-Change Detection -- 3.4.5 Global Relative Input-Output Analysis of the FFLs -- 3.4.5.1 A GRIOS Index -- 3.4.5.2 GRIOS of the FFLs -- 3.4.5.3 GRIOS of the FFLs Versus Its Structural and Functional Characteristics -- 3.4.6 Summary -- 3.5 The Coupled Positive and Negative Feedback Genetic Circuits -- 3.5.1 Related Works and Motivations -- 3.5.2 Mathematical Models -- 3.5.2.1 Deterministic Models: Without Time Delay -- 3.5.2.2 Deterministic Models with Time Delays -- 3.5.2.3 Stochastic Model Directly from the Deterministic ODE: The Undeveloped Case -- 3.5.2.4 Stochastic Model from Table 3.9: The Developed Case -- 3.5.2.5 Stochastic Simulations -- 3.5.3 Dynamical Analysis and Functions -- 3.5.3.1 Bifurcation Analysis -- 3.5.3.2 Molecular Noise -- 3.5.3.3 Deterministic Versus Stochastic Dynamics for Parameters Near the Deterministic Bifurcation Points -- 3.5.3.4 Deterministic Versus Stochastic Dynamics for Parameters Locating in the Deterministic Excitable Region -- 3.5.3.5 Deterministic Versus Stochastic Dynamics for Parameters Locating in the Deterministic Bistable Region -- 3.5.3.6 Deterministic Versus Stochastic Dynamics for Parameters Locating in the Deterministic Oscillation Region -- 3.5.4 Summary -- 3.6 The Multi-Positive Feedback Circuits -- 3.6.1 Related Works and Motivations -- 3.6.2 Mathematical Models -- 3.6.3 Dynamical Analysis and Functions -- 3.6.3.1 The APFL Strength Can Tune the Size of the Bistable Region -- 3.6.3.2 The APFL Can Tune the Attractiveness of the Stable Steady States -- 3.6.3.3 The APFL Can Change the Global Relative I/O Sensitivities. , 3.6.3.4 Functional Characteristics of the APFL on Noisy Signal Processing -- 3.6.3.5 Effect of the APFL on Stochastic Bistable Switch -- 3.6.4 Summary -- 3.7 Exploring Simple Bio-molecular Networks with Specific Functions -- 3.7.1 Motivations -- 3.7.2 Exploring Enzymatic Regulatory Networks with Adaption -- 3.7.2.1 Searching for Circuits Capable of Adaptation -- 3.7.2.2 Identifying Minimal Adaptation Networks -- 3.7.2.3 Key Parameters in Minimal Adaptation Networks -- 3.7.2.4 Negative Feedback Loop with a Buffer Node -- 3.7.2.5 Incoherent FFL with a Proportioner Node -- 3.7.2.6 Exploration of All Possible 3-Node Networks: An NFBLB or IFFLP Architecture is Necessary for Adaptation -- 3.7.2.7 Motif Combinations Can Improve Adaptation -- 3.7.3 Exploring GRNs with Chaotic Behavior -- 3.7.3.1 GRNs and Mathematical Models -- 3.7.3.2 Conditions and Indicators for Chaos -- 3.7.3.3 Main Results -- 3.7.4 Summary -- 3.8 Discussions and Conclusions -- References -- 4 Modeling and Analysis of Coupled Bio-molecular Circuits -- 4.1 Backgrounds -- 4.2 Dynamical Analysis of a Composite Genetic Oscillator -- 4.2.1 Related Works and Motivations -- 4.2.2 Mathematical Models -- 4.2.2.1 The Hysteresis-Based Oscillator -- 4.2.2.2 The Repressilator -- 4.2.2.3 The Composite Oscillator -- 4.2.3 Dynamical Analysis of the Merged Genetic Oscillator -- 4.2.3.1 The Two Oscillatory Mechanisms Support Each Other -- 4.2.3.2 Oscillatory Mechanisms Are Distinct -- 4.2.4 Population Dynamics of Coupled Composite Oscillators -- 4.2.5 Summary -- 4.3 Modeling and Analysis of the Genetic Toggle Switch Circuit -- 4.3.1 Related Works and Motivations -- 4.3.2 Modeling and Analysis of the Single Toggle Switch System -- 4.3.2.1 Deterministic Model -- 4.3.2.2 Bistability -- 4.3.2.3 Stochastic Model for the Single Toggle Switch System -- 4.3.3 Modeling the Networked Toggle Switch Systems. , 4.3.4 Statistical Measurements -- 4.3.5 Stochastic Switch in the Single Toggle Switch System -- 4.3.6 Synchronized Switching in Networked Toggle Switch Systems -- 4.3.6.1 Feature Comparison Between White and Colored Noises Induced Synchronized Switching -- 4.3.6.2 Colored Noise Can Promote the Mean Protein Numbers -- 4.3.6.3 Robustness of Synchronized Switching Against Parameter Perturbations -- 4.3.6.4 Effect of Noise Autocorrelation Time -- 4.3.7 Physical Mechanisms of Bistable Switch -- 4.3.8 Some Further Issues -- 4.3.9 Summary -- 4.4 Discussions and Conclusions -- References -- 5 Modeling and Analysis of Large-Scale Networks -- 5.1 Backgrounds -- 5.2 Continuous Models for the Yeast Cell Cycle Network -- 5.2.1 Related Works and Motivations -- 5.2.2 Dynamical Analysis -- 5.2.3 Summary -- 5.3 Discrete Models for the Yeast Cell Cycle Network -- 5.3.1 Related Works and Motivations -- 5.3.2 Dynamical Analysis -- 5.3.3 Statistical Analysis -- 5.3.3.1 Comparison with Random Networks -- 5.3.3.2 Network Perturbations -- 5.3.4 Summary -- 5.4 Percolating Flow Model for a Mammalian Cellular Network -- 5.4.1 Related Works and Motivations -- 5.4.2 Dynamical Analysis -- 5.4.3 Statistical Analysis -- 5.4.4 Summary -- 5.5 A Hybrid Model for Mammalian Cell Cycle Regulation -- 5.5.1 Related Works and Motivations -- 5.5.2 The Hybrid Model -- 5.5.3 Dynamical Analysis of the Hybrid Model -- 5.5.4 Summary -- 5.6 General Hybrid Model for Large-Scale Bio-Molecular Networks -- 5.6.1 Related Works and Motivations -- 5.6.2 The General Hybrid Model -- 5.6.3 Hybrid Modeling and Analysis of a Toy Genetic Network -- 5.6.3.1 Dynamical Analysis of the Hybrid Model -- 5.6.3.2 Statistical Analysis -- 5.6.4 Summary -- 5.7 Discussions and Conclusions -- References -- Part II Statistical Analysis of Biological Networks -- 6 Evolutionary Mechanisms of Network Motifs in PPI Networks. , 6.1 Backgrounds.