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

Appendix A: Mathematical review
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Appendix A: Mathematical review

A review of mathematical concepts put to use in this book will be added here.

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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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