Supplement: Biomolecular Feedback Systems

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

This textbook 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)
  • 6 Jan 2014: Updated chapter on stochastic modeling and analysis (Ch 4)
  • 11 Dec 2013: Updated chapter on dynamic behavior (Ch 3)
  • 7 Dec 2013: Updated chapter on core processes (Ch 2)
  • 5 Dec 2013: Updated contents, preface, introduction (Ch 1) and references
  • 20 Jul 2013: Updated outline and new PDFs are being posted over the next month.
  • 12 Jul 2012: Updated outline; new PDFs posted. A complete manuscript (PDF) is also available.
  • 16 Jan 2012: Updated outline; new PDFs for all chapters and appendices (coming later today)


  • Preface and Contents (PDF)
  • Chapter 1: Introductory Concepts (PDF)
    • Systems Biology: Modeling, Analysis and the Role of Feedback
    • The Cell as a System
    • 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)
    • Analysis Near Equilibria
    • Robustness
    • 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: Biological Circuit Components (PDF)
    • Introduction to Biological Circuit Design
    • Negative Autoregulation
    • The Toggle Switch
    • The Repressilator
    • Activator-repressor Clock
    • An Incoherent Feedforward Loop (IFFL)
    • Bacterial Chemotaxis
  • Chapter 6: 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
    • A Case Study on the Use of Insulation Devices
  • Chapter 7: Design Tradeoffs (PDF)
    • Competition for Shared Cellular Resources
    • Stochastic Effects: Design Tradeoffs in Systems with Large Gains
  • Appendix A: A Primer on Control Theory
  • Bibliography and Index (PDF)

Additional Information