Supplement: Biomolecular Feedback Systems

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Domitilla Del Vecchio (U. Mich) 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 {\em 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.

This page contains working notes for the material that is being prepared for the supplement. We anticipate that a preliminary version of the notes will be available by July 2009.


  1. Review of Core Processes
    • Modeling of transcription and translation
      • ODE models (coming from chemical reactions and thermodynamics)
      • time constants
      • cell affects (dilution, degradation)
    • Transcriptional Regulation
      • repression
      • activation
      • (Thermodynamics → chemical kinetics →Hill functions, Michaelis-Menten)
    • Intracellular sensing
    • Intracellular communication
    • Intracellular computation
  2. Dynamic behavior
    • Steady state analysis (log/log diagrams)
    • Phase plane analysis
    • Time response
    • Limit cycles
  3. Feedback examples
    • Lactose metabolism
    • Heat shock
    • Chemotaxis
  1. Stochastic behavior
    • Noise modeling (intrinsic/extrinsic), spectrum
    • Stochastic simulation analysis (SSA)
    • Markov modeling and analysis
    • Linearized modeling and analysis: include disturbance attenuation in freq domain (?)
  2. Biological circuit design
    • DNA-protein, vs protein-protein, etc.
    • Feedforward loops
    • PID in biocircuits
    • Activation vs repression (demand theory)
    • Modularity and retroactivity
    • Logical functions: AND, switches, inverters, toggles, etc.
  3. Design examples
  4. Robustness and evolvability
  5. Multicellular systems
    • Additional core processes
    • Quorum Sensing
    • Development


Additional Information