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| Preface | |
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| Introduction | |
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| Systems Biology and Synthetic Biology | |
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| What Is a Dynamic Mathematical Model? | |
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| Why Are Dynamic Mathematical Models Needed? | |
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| How Are Dynamic Mathematical Models Used? | |
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| Basic Features of Dynamic Mathematical Models | |
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| State Variables and Model Parameters | |
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| Steady-State Behavior and Transient Behavior | |
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| Linearity and Nonlinearity | |
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| Global and Local Behavior | |
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| Deterministic Models and Stochastic Models | |
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| Dynamic Mathematical Models in Molecular Cell Biology | |
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| Drug Target Prediction in Trypanosoma brucei Metabolism | |
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| Identifying the Source of Oscillatory Behavior in NF-�B Signaling | |
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| Model-Based Design of an Engineered Genetic Toggle Switch | |
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| Establishing the Mechanism for Neuronal Action Potential Generation | |
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| Suggestions for Further Reading | |
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| Modeling of Chemical Reaction Networks | |
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| Chemical Reaction Networks | |
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| Closed and Open Networks | |
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| Dynamic Behavior of Reaction Networks | |
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| Simple Network Examples | |
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| Numerical Simulation of Differential Equations | |
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| Separation of Timescales and Model Reduction | |
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| Separation of Timescales: The Rapid Equilibrium Assumption | |
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| Separation of Timescales: The Quasi-Steady-State Assumption | |
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| Suggestions for Further Reading | |
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| Problem Set | |
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| Biochemical Kinetics | |
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| Enzyme Kinetics | |
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| Michaelis-Menten Kinetics | |
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| Two-Substrate Reactions | |
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| Regulation of Enzyme Activity | |
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| Competitive Inhibition | |
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| Allosteric Regulation | |
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| Cooperativity | |
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| Compartmental Modeling and Transport | |
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| Diffusion | |
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| Facilitated Transport | |
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| Generalized Mass Action and S-System Modeling | |
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| Suggestions for Further Reading | |
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| Problem Set | |
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| Analysis of Dynamic Mathematical Models | |
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| Phase Plane Analysis | |
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| Direction Fields | |
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| Nullclines | |
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| Stability | |
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| Stable and Unstable Steady States | |
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| Linearized Stability Analysis | |
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| Limit-Cycle Oscillations | |
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| Bifurcation Analysis | |
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| Sensitivity Analysis | |
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| Local Sensitivity Analysis | |
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| Determination of Local Sensitivity Coefficients | |
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| Parameter Fitting | |
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| Suggestions for Further Reading | |
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| Problem Set | |
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| Metabolic Networks | |
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| Modeling of Metabolism | |
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| Example: A Pathway Model | |
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| Sensitivity Analysis of Metabolic Networks: Metabolic Control Analysis | |
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| Metabolic Pathways | |
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| Flux Control of Unbranched Pathways | |
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| Regulation of Unbranched Pathways | |
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| Branched Pathways | |
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| Modeling of Metabolic Networks | |
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| Model Construction | |
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| Case Study: Modeling the Regulation of the Methionine Cycle | |
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| Stoichiometric Network Analysis | |
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| Metabolic Pathway Analysis | |
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| Constraint-Based Modeling: Metabolic Flux Analysis | |
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| Suggestions for Further Reading | |
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| Problem Set | |
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| Signal Transduction Pathways | |
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| Signal Amplification | |
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| Bacterial Two-Component Signaling Pathways | |
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| G-Protein Signaling Pathways | |
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| Ultrasensitivity | |
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| Zero-Order Ultrasensitivity | |
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| Ultrasensitive Activation Cascades | |
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| Adaptation | |
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| Bacterial Chemotaxis | |
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| Memory and Irreversible Decision-Making | |
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| Apoptosis | |
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| Frequency Encoding | |
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| Calcium Oscillations | |
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| Frequency Response Analysis | |
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| Definition of the Frequency Response | |
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| Interpretation of the Frequency Response | |
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| Construction of the Frequency Response | |
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| Suggestions for Further Reading | |
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| Problem Set | |
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| Gene Regulatory Networks | |
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| Modeling of Gene Expression | |
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| Unregulated Gene Expression | |
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| Regulated Gene Expression | |
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| Gene Regulatory Networks | |
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| Genetic Switches | |
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| The lac Operon | |
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| The Phage Lambda Decision Switch | |
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| The Collins Toggle Switch | |
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| Oscillatory Gene Networks | |
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| The Goodwin Oscillator | |
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| Circadian Rhythms | |
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| Synthetic Oscillatory Gene Networks | |
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| Cell-to-Cell Communication | |
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| Bacterial Quorum Sensing | |
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| Engineered Cell-to-Cell Communication | |
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| Synchronization of Oscillating Cells | |
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| Computation by Gene Regulatory Networks | |
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| Promoters as Logic Gates | |
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| Digital Representations of Gene Circuits | |
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| Complex Gene Regulatory Networks | |
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| Stochastic Modeling of Biochemical and Genetic Networks | |
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| A Discrete Modeling Framework | |
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| The Chemical Master Equation | |
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| Gillespie's Stochastic Simulation Algorithm | |
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| Examples | |
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| Suggestions for Further Reading | |
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| Problem Set | |
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| Electrophysiology | |
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| Membrane Potential | |
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| The Nernst Potential | |
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| The Membrane Model | |
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| Excitable Membranes | |
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| Voltage-Gated Ion Channels | |
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| The Morris-Lecar Model | |
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| Intercellular Communication | |
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| Synaptic Transmission | |
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| Spatial Modeling | |
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| Propagation of Membrane Voltage | |
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| Passive Membrane | |
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| Excitable Membrane: Action Potential Propagation | |
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| Suggestions for Further Reading | |
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| Problem Set | |
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| Molecular Cell Biology | |
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| Cells | |
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| The Chemistry of Life | |
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| Macromolecules | |
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| Model Organisms | |
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| Mathematical Fundamentals | |
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| Differential Calculus | |
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| Linear Algebra | |
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| Probability | |
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| Computational Software | |
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| XPPAUT | |
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| MATLAB | |
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| Bibliography | |
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| Index | |