• Preface vii
• 1 Introductory Concepts 1 1.1 Systems biology: Modeling, analysis and role of feedback 1 1.2 The cell as a system 8 1.3 Control and dynamical systems tools 11 1.4 Input/output modeling 18 1.5 From systems to synthetic biology 22 1.6 Further reading 28
• 2 Dynamic Modeling of Core Processes 29 2.1 Modeling chemical reactions 29 2.2 Transcription and translation 44 2.3 Transcriptional regulation 55 2.4 Post-transcriptional regulation 70 2.5 Cellular subsystems 81 Exercises 86
• 3 Analysis of Dynamic Behavior 89 3.1 Analysis near equilibria 89 3.2 Robustness 103 3.3 Oscillatory behavior 113 3.4 Bifurcations 124 3.5 Model reduction techniques 127 Exercises 133
• 4 Stochastic Modeling and Analysis 139 4.1 Stochastic modeling of biochemical systems 139 4.2 Simulation of stochastic systems 154 4.3 Input/output linear stochastic systems 157 Exercises 164
• 5 Biological Circuit Components 169 5.1 Introduction to biological circuit design 169 5.2 Negative autoregulation 171 5.3 The toggle switch 177 5.4 The repressilator 180 5.5 Activator-repressor clock 184 5.6 An incoherent feedforward loop (IFFL) 189 5.7 Bacterial chemotaxis 191 Exercises 203
• 6 Interconnecting Components 205 6.1 Input/output modeling and the modularity assumption 205 6.2 Introduction to retroactivity 206 6.3 Retroactivity in gene circuits 209 6.4 Retroactivity in signaling systems 214 6.5 Insulation devices: Retroactivity attenuation 219 6.6 A case study on the use of insulation devices 236 Exercises 239
• 7 Design Tradeoffs 243 7.1 Competition for shared cellular resources 243 7.2 Stochastic effects: Design tradeoffs in systems with large gains 253 Exercises 257 Bibliography 259 Index 267.
• (source: Nielsen Book Data)

This book provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. It begins with modeling tools such as reaction-rate equations, reduced-order models, stochastic models, and specific models of important core processes. It then describes in detail the control and dynamical systems tools used to analyze these models. These include tools for analyzing stability of equilibria, limit cycles, robustness, and parameter uncertainty. Modeling and analysis techniques are then applied to design examples from both natural systems and synthetic biomolecular circuits. In addition, this comprehensive book addresses the problem of modular composition of synthetic circuits, the tools for analyzing the extent of modularity, and the design techniques for ensuring modular behavior. It also looks at design trade-offs, focusing on perturbations due to noise and competition for shared cellular resources. Featuring numerous exercises and illustrations throughout, Biomolecular Feedback Systems is the ideal textbook for advanced undergraduates and graduate students. For researchers, it can also serve as a self-contained reference on the feedback control techniques that can be applied to biomolecular systems. Provides a user-friendly introduction to essential concepts, tools, and applications Covers the most commonly used modeling methods Addresses the modular design problem for biomolecular systems Uses design examples from both natural systems and synthetic circuits Solutions manual (available only to professors at press.princeton.edu) An online illustration package is available to professors at press.princeton.edu.
(source: Nielsen Book Data)

• Preface 1. Overview 1.0 Chaos, Fractals, and Dynamics 1.1 Capsule History of Dynamics 1.2 The Importance of Being Nonlinear 1.3 A Dynamical View of the World PART I. ONE-DIMENSIONAL FLOWS 2. Flows on the Line 2.0 Introduction 2.1 A Geometric Way of Thinking 2.2 Fixed Points and Stability 2.3 Population Growth 2.4 Linear Stability Analysis 2.5 Existence and Uniqueness 2.6 Impossibility of Oscillations 2.7 Potentials 2.8 Solving Equations on the Computer
• Exercises 3. Bifurcations 3.0 Introduction 3.1 Saddle-Node Bifurcation 3.2 Transcritical Bifurcation 3.3 Laser Threshold 3.4 Pitchfork Bifurcation 3.5 Overdamped Bead on a Rotating Hoop 3.6 Imperfect Bifurcations and Catastrophes 3.7 Insect Outbreak
• Exercises 4. Flows on the Circle 4.0 Introduction 4.1 Examples and Definitions 4.2 Uniform Oscillator 4.3 Nonuniform Oscillator 4.4 Overdamped Pendulum 4.5 Fireflies 4.6 Superconducting Josephson Junctions
• Exercises PART II. TWO-DIMENSIONAL FLOWS 5. Linear Systems 5.0 Introduction 5.1 Definitions and Examples 5.2 Classification of Linear Systems 5.3 Love Affairs
• Exercises 6. Phase Plane 6.0 Introduction 6.1 Phase Portraits 6.2 Existence, Uniqueness, and Topological Consequences 6.3 Fixed Points and Linearization 6.4 Rabbits versus Sheep 6.5 Conservative Systems 6.6 Reversible Systems 6.7 Pendulum 6.8 Index Theory
• Exercises 7. Limit Cycles 7.0 Introduction 7.1 Examples 7.2 Ruling Out Closed Orbits 7.3 Poincare-Bendixson Theorem 7.4 Lienard Systems 7.5 Relaxation Oscillators 7.6 Weakly Nonlinear Oscillators
• Exercises 8. Bifurcations Revisited 8.0 Introduction 8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations 8.2 Hopf Bifurcations 8.3 Oscillating Chemical Reactions 8.4 Global Bifurcations of Cycles 8.5 Hysteresis in the Driven Pendulum and Josephson Junction 8.6 Coupled Oscillators and Quasiperiodicity 8.7 Poincare Maps
• Exercises PART III. CHAOS 9. Lorenz Equations 9.0 Introduction 9.1 A Chaotic Waterwheel 9.2 Simple Properties of the Lorenz Equations 9.3 Chaos on a Strange Attractor 9.4 Lorenz Map 9.5 Exploring Parameter Space 9.6 Using Chaos to Send Secret Messages
• Exercises 10. One-Dimensional Maps 10.0 Introduction 10.1 Fixed Points and Cobwebs 10.2 Logistic Map: Numerics 10.3 Logistic Map: Analysis 10.4 Periodic Windows 10.5 Liapunov Exponent 10.6 Universality and Experiments 10.7 Renormalization
• Exercises 11. Fractals 11.0 Introduction 11.1 Countable and Uncountable Sets 11.2 Cantor Set 11.3 Dimension of Self-Similar Fractals 11.4 Box Dimension 11.5 Pointwise and Correlation Dimensions
• Exercises 12. Strange Attractors 12.0 Introductions 12.1 The Simplest Examples 12.2 Henon Map 12.3 Rossler System 12.4 Chemical Chaos and Attractor Reconstruction 12.5 Forced Double-Well Oscillator
• Exercises Answers to Selected Exercises References Author Index Subject Index.
• (source: Nielsen Book Data)

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.
(source: Nielsen Book Data)

• Preface ix
• Chapter 1. Introduction 1 1.1 What Is Feedback? 1 1.2 What Is Control? 3 1.3 Feedback Examples 5 1.4 Feedback Properties 17 1.5 Simple Forms of Feedback 23 1.6 Further Reading 25 Exercises 25
• Chapter 2. System Modeling 27 2.1 Modeling Concepts 27 2.2 State Space Models 34 2.3 Modeling Methodology 44 2.4 Modeling Examples 51 2.5 Further Reading 61 Exercises 61
• Chapter 3. Examples 65 3.1 Cruise Control 65 3.2 Bicycle Dynamics 69 3.3 Operational Amplifier Circuits 71 3.4 Computing Systems and Networks 75 3.5 Atomic Force Microscopy 81 3.6 Drug Administration 84 3.7 Population Dynamics 89 Exercises 91
• Chapter 4. Dynamic Behavior 95 4.1 Solving Differential Equations 95 4.2 Qualitative Analysis 98 4.3 Stability 102 4.4 Lyapunov Stability Analysis 110 4.5 Parametric and Nonlocal Behavior 120 4.6 Further Reading 126 Exercises 126
• Chapter 5. Linear Systems 131 5.1 Basic Definitions 131 5.2 The Matrix Exponential 136 5.3 Input/Output Response 145 5.4 Linearization 158 5.5 Further Reading 163 Exercises 164
• Chapter 6. State Feedback 167 6.1 Reachability 167 6.2 Stabilization by State Feedback 175 6.3 State Feedback Design 183 6.4 Integral Action 195 6.5 Further Reading 197 Exercises 197
• Chapter 7. Output Feedback 201 7.1 Observability 201 7.2 State Estimation 206 7.3 Control Using Estimated State 211 7.4 Kalman Filtering 215 7.5 A General Controller Structure 219 7.6 Further Reading 226 Exercises 226
• Chapter 8. Transfer Functions 229 8.1 Frequency Domain Modeling 229 8.2 Derivation of the Transfer Function 231 8.3 Block Diagrams and Transfer Functions 242 8.4 The Bode Plot 250 8.5 Laplace Transforms 259 8.6 Further Reading 262 Exercises 262
• Chapter 9. Frequency Domain Analysis 267 9.1 The Loop Transfer Function 267 9.2 The Nyquist Criterion 270 9.3 Stability Margins 278 9.4 Bode's Relations and Minimum Phase Systems 283 9.5 Generalized Notions of Gain and Phase 285 9.6 Further Reading 290 Exercises 290
• Chapter 10. PID Control 293 10.1 Basic Control Functions 293 10.2 Simple Controllers for Complex Systems 298 10.3 PID Tuning 302 10.4 Integrator Windup 306 10.5 Implementation 308 10.6 Further Reading 312 Exercises 313
• Chapter 11. Frequency Domain Design 315 11.1 Sensitivity Functions 315 11.2 Feedforward Design 319 11.3 Performance Specifications 322 11.4 Feedback Design via Loop Shaping 326 11.5 Fundamental Limitations 331 11.6 Design Example 340 11.7 Further Reading 343 Exercises 344
• Chapter 12. Robust Performance 347 12.1 Modeling Uncertainty 347 12.2 Stability in the Presence of Uncertainty 352 12.3 Performance in the Presence of Uncertainty 358 12.4 Robust Pole Placement 361 12.5 Design for Robust Performance 369 12.6 Further Reading 374 Exercises 374
• Bibliography 377 Index 387.
• (source: Nielsen Book Data)

This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, "Feedback Systems" develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Astrom and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators.The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Astrom and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. "Feedback Systems" is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences. It covers the mathematics needed to model, analyze, and design feedback systems. It serves as an introductory textbook for students and a self-contained resource for researchers. It includes exercises at the end of every chapter. It features an electronic solutions manual. It offers techniques applicable across a range of disciplines.
(source: Nielsen Book Data)

• INTRODUCTION TRANSCRIPTION NETWORKS, BASIC CONCEPTS Introduction The Cognitive Problem of the Cell Elements of Transcription Networks Dynamics and Response Time of Simple Gene Circuits AUTO-REGULATION, A NETWORK MOTIF Introduction Patterns, Randomized Networks and Network Motifs Autoregulation is a Network Motif Negative Auto-Regulation Speeds the Response Time of Gene
• Circuits Negative Auto-Regulation Promotes Robustness to Fluctuations
• in Production Positive auto-regulation speeds responses and widens cell-cell variability Summary THE FEEDFORWARD LOOP NETWORK MOTIF Introduction The Number of Appearances of a Subgraph in Random
• Networks The Feedforward Loop (FFL) is a Network Motif The Structure of the Feedforward Loop Circuit Dynamics of the Coherent FFL with AND-Logic The C1-FFL is a Sign-Sensitive Delay Element The Incoherent FFL: a pulse generator and response accelerator Why Are Some FFL Types Rare? Convergent Evolution of FFLs Summary TEMPORAL PROGRAMS AND THE GLOBAL STRUCTURE OF TRANSCRIPTION NETWORKS Introduction The Single-Input Module (SIM) Network Motif SIMs Can Generate Temporal Expression Programs Topological Generalizations of Network Motifs The Multi-Output FFL Can Generate FIFO Temporal Order Signal Integration and Combinatorial Control: Bi-Fans and
• Dense-Overlapping Regulons Network Motifs and the Global Structure of Sensory
• Transcription Networks NETWORK MOTIFS IN DEVELOPMENTAL, SIGNAL-TRANSDUCTION AND NEURONAL NETWORKS Introduction Network Motifs in Developmental Transcription Networks: Positive feedback loops and bistability Motifs in Signal Transduction Networks Information Processing Using Multi-Layer Perceptrons Composite Network Motifs: Negative Feedback and Oscillator
• Motifs Network Motifs in the Neuronal Network of C. Elegans Summary ROBUSTNESS OF PROTEIN CIRCUITS, THE EXAMPLE OF BACTERIAL CHEMOTAXIS The Robustness Principle Bacterial Chemotaxis, or How Bacteria 'Think' The Chemotaxis Protein Circuit of E. coli Two Models Can Explain Exact Adaptation, One is Robust and
• the Other Fine Tuned The Barkai-Leibler model Individuality and Robustness in Bacterial Chemotaxis ROBUST PATTERNING IN DEVELOPMENT Introduction to Morphogen Gradients Exponential Gradients Are Not Robust Increased Robustness by Self-Enhanced Morphogen
• Degradation Network Motifs That Provide Robust Patterning The Robustness Principle Can Distinguish Between
• Mechanisms of Fruit Fly Patterning KINETIC PROOFREADING Introduction Kinetic Proofreading of the Genetic Code Can Reduce Error
• Rates of Molecular Recognition Recognition of Self and Non-Self by the Immune System Kinetic Proofreading May Occur in Diverse Recognition
• Processes in the Cell OPTIMAL GENE CIRCUIT DESIGN Introduction Cost and Benefit Analysis of Gene circuits Optimal Expression Level of a Protein Under Constant
• Conditions To Regulate or Not to Regulate: Optimal Regulation in Variable
• Environments Environmental Selection of the Feedforward Loop Network Motif Summary RULES FOR GENE REGULATION BASED ON ERROR MINIMIZATION Introduction The Savageau Demand Rules Rules for Gene Regulation Based on Minimal Error Load Demand Rules for Genes with Multiple Regulators Summary EPILOGUE: Simplicity in Biology APPENDIX A: The Input-Function of a Gene, Michaelis-Menten and Hill Equations
• APPENDIX B: Multi-Dimensional Input-Functions APPENDIX C: Graph Properties of Transcription Networks APPENDIX D: Cell-Cell Variability in Gene Expression GLOSSARY BIBLIOGRAPHY.
• (source: Nielsen Book Data)

Thorough and accessible, this book presents the design principles of biological systems, and highlights the recurring circuit elements that make up biological networks. It provides a simple mathematical framework which can be used to understand and even design biological circuits. The text avoids specialist terms, focusing instead on several well-studied biological systems that concisely demonstrate key principles. "An Introduction to Systems Biology: Design Principles of Biological Circuits" builds a solid foundation for the intuitive understanding of general principles. It encourages the reader to ask why a system is designed in a particular way and then proceeds to answer with simplified models.
(source: Nielsen Book Data)

• Preface. Foreword. Part I: General Introduction.
• 1. Basic Principles.
• 2. Biology in a Nutshell.
• 3. Mathematics in a Nutshell.
• 4. Experimental Techniques in a Nutshell. Part II: Standard Models and Approaches in Systems Biology.
• 5. Metabolism.
• 6. Signal Transduction.
• 7. Selected Biological Processes.
• 8. Modeling of Gene Expression.
• 9. Analysis of Gene Expression Data.
• 10. Evolution and Self-organization.
• 11. Data Integration.
• 12. What's Next? Part III: Computer-based Information Retrieval and Examination.
• 13. Databases and Tools on the Internet.
• 14. Modeling Tools. Subject Index.
• (source: Nielsen Book Data)

Presenting the main concepts, this book leads students as well as advanced researchers from different disciplines to an understanding of current ideas in the complex field of comprehensive experimental investigation of biological objects, analysis of data, development of models, simulation, and hypothesis generation. It provides readers with guidance on how a specific complex biological question may be tackled: * How to formulate questions that can be answered * Which experiments to perform * Where to find information in databases and on the Internet * What kinds of models are appropriate * How to use simulation tools * What can be learned from the comparison of experimental data and modeling results * How to make testable predictions. The authors demonstrate how mathematical concepts can illuminate the principles underlying biology at a genetic, molecular, cellular and even organism level, and how to use mathematical tools for analysis and prediction.
(source: Nielsen Book Data)