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.
Outline
The current plan for the supplement is based on the following draft outline. Comments are welcome on topics that are missing.
 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, MichaelisMenten)
 Intracellular sensing
 Intracellular communication
 Intracellular computation
 Dynamic behavior
 Steady state analysis (log/log diagrams)
 Phase plane analysis
 Time response
 Limit cycles
 Feedback examples
 Lactose metabolism
 Heat shock
 Chemotaxis

 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 (?)
 Biological circuit design
 DNAprotein, vs proteinprotein, etc.
 Feedforward loops
 PID in biocircuits
 Activation vs repression (demand theory)
 Modularity and retroactivity
 Logical functions: AND, switches, inverters, toggles, etc.
 Design examples
 Robustness and evolvability
 Multicellular systems
 Additional core processes
 Quorum Sensing
 Development

Examples
The material above is intended to be useful in analyzing a large variety of natural and engineered biomolecular feedback systems. Some of these examples will be included in the text, while others may be mentioned in exercises or simply left for the reader to explore on their own.
 Repressilator: eqs, simulations, limit cycle stability using PB+ and Hastings
 Toggle switch: eqs, nullclines and equilibria, stability, Lyapunov
 Self repression: frequency response, time response
 Self activation: dynamics plus Lyapunov
 Activatorrepressor clock (two implementations): eqs, simulations, PB for the 2D model reduction, Hopf Bifurcation for the 4D (singular perturbation for the 2D reduction?)
 Chemotaxis: integral feedback (Iglesias), modeling (incl methylation)
 Input adaptation: MAPK with feedback? (Kholodenko?)

 Development/differentiation: signal switching (Tomlin, Ashthagiri)
 Sporalation, fate choice (Elowitz)
 MAPK cascades (Sauro, Kholodenko)
 Quorum Sensing (Weiss, ?), synchronization
 Methabolic Pathways/engineering (yeast demand analysis, Hoffmeyer)
 Hemoglobin (Kirshner) for allostery feedback?
 Glucose/Lactose (Jacob and Monod)
 Antisense switches (Smolke)
 FFL (Alon)?
 Heat Shock (El Samad)
 Calcium Regulation (Khammash)

Additional Information