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Chapters

  • 0. Configuring your computer to use Python for scientific computing
  • 1. Introduction to biological circuit design
  • 2. Design principles governing the rate of gene expression
  • 3. Sticky switches: bistability through positive feedback
  • 4. Analysis of feedforward loops
  • 5. Incoherent feed-forward loops serve as dosage compensators
  • 6. Exact adaptation in the chemotaxis pathway
  • 8. Kinetic proofreading: Multi-step processes reduce error rates in molecular recognition
  • 9. Blinking bacteria: The repressilator enables self-sustaining oscillations
  • 10. Uses, simplifications, and elaborations of negative feedback oscillators
  • 11. Time-based regulation in cells
  • 12. Molecular titration generates ultrasensitive responses in biological circuits
  • 13. Promiscuous receptor-ligand interactions increase the bandwidth and specificity of cell-cell communication systems
  • 14. MultiFate enables expandable and controllable multistability
  • 15. The noisy, noisy nature of gene expression: How stochastic fluctuations create variation
  • 16. Bursty gene expression
  • 17. Cellular bet-hedging
  • 18. Excitability enables probabilistic, transient differentiation
  • 20. Lateral Inhibition: Spontaneous symmetry allows spontaneous developmental patterning
  • 21. Turing patterns
  • 22. Scaling reaction-diffusion patterns

Technical Appendices

  • 2a. Approximate solutions to autorepressive dynamics
  • 2b. Numerical solutions to ODEs with SciPy
  • 2c. Interactive plotting with Bokeh
  • 3a. Nondimensionalization
  • 4a. Numerical solution of FFLs
  • 9a. Fixed points and composite functions
  • 9b. Linear stability analysis
  • 9c. Numerical one-dimensional bounded root finding
  • 10a. Stability diagrams by numerical computation of eigenvalues
  • 10b. The Greshgorin circle theorem
  • 10c. Numerical solution of delay differential equations
  • 10d. Linear stability analysis of delay differential equations
  • 16a. Stochastic (Gillespie) simulation
  • 16b. Profiling code for speed and an application of the Gillespie algorithm

Appendices

  • Appendix A: Mathematical review
  • Appendix B: Introduction to Python
  • Appendix C: Numerical solutions of ODES
  • Appendix D: Regulatory functions and their derivatives

Package docs

  • biocircuits package documentation
Biological Circuit Design
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Last updated on Mar 23, 2025.

© 2021–2025 Michael Elowitz and Justin Bois. With the exception of pasted graphics, where the source is noted, this work is licensed under a Creative Commons Attribution License CC BY-NC-SA 4.0. All code contained herein is licensed under an MIT license.

This document was prepared at Caltech with financial support from the Donna and Benjamin M. Rosen Bioengineering Center.



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