# Difference between revisions of "Supplement: Biomolecular Feedback Systems"

Domitilla Del Vecchio (MIT) and Richard M. Murray (Caltech)

This supplement is intended for researchers interested in the application of feedback and control to biomolecular systems. The material has been designed so that it can be used in parallel with Feedback Systems as part of a course on biomolecular feedback and control systems, or as a standalone reference for readers who have had a basic course in feedback and control theory. The supplement is being written by Domitilla Del Vecchio and Richard Murray based on a variety of presentations, lectures and notes.

Note: These notes are in draft form and may contain errors. Permission is granted to download and print a copy for individual use, but this material may not be reproduced, in whole or in part, without written consent from the author.

##### News (archive)
• 12 Jul 2012: Updated outline; new PDFs posted.
• 16 Jan 2012: Updated outline; new PDFs for all chapters and appendices (coming later today)
• 23 Jan 2011: Updated Ch 3: split out robustness analysis section and added intro material for oscillations section

### Contents

 Preface and Contents (PDF) Chapter 1: Introductory Concepts (PDF) Systems Biology: Modeling, Analysis and the Role of Feedback Dynamics and Control in the Cell Control and Dynamical Systems Tools Input/Output Modeling From Systems to Synthetic Biology Chapter 2: Core Processes (PDF) Modeling Techniques Transcription and Translation Transcriptional Regulation Post-Transcriptional Regulation Cellular Subsystems Chapter 3: Dynamic Behavior (PDF) Input/Output Modeling Analysis Near Equilibria Robustness Analysis of Reaction Rate Equations Oscillatory Behavior Bifurcations Model Reduction Techniques Chapter 4: Stochastic Behavior (PDF) Stochastic Modeling of Biochemical Systems Simulation of Stochastic Systems Input/Output Linear Stochastic Systems Chapter 5: Feedback Examples (PDF) The lac Operon (Heat shock) (Phage ) Bacterial chemotaxis|bfs-chemotaxis (Signaling pathways in yeast) Chapter 6: Biological Circuit Components (PDF) Introduction to Biological Circuit Design Negative Autoregulation The Toggle Switch The Repressilator Activator-repressor Clock An Incoherent Feedforward Loop (IFFL) Chapter 7: Interconnecting Components (PDF) Input/Output Modeling and the Modularity Assumption Introduction to Retroactivity Retroactivity in Gene Circuits Retroactivity in Signaling Systems Insulation Devices: Retroactivity Attentuation Chapter 8: Design Tradeoffs (PDF)  Appendix A: Cell Biology Primer (from NCBI) Appendix B: A Primer on Control Theory (PDF) System modeling, Dynamic behavior Linear systems, Reachability Transfer functions, Frequency response PID control Limits of performance, Robust performance Appendix C: Random Processes (PDF) Random Variables Continuous-State Random Processes Discrete-State Random Processes Bibliography and Index (PDF)