Appendices
B
Mathematical review
Welcome
Small circuits
1
Introduction to biological circuit design
2
Design principles governing the rate of gene expression
3
Sticky switches: bistability through positive feedback
Recurrent circuit motifs
4
Analysis of feedforward loops
5
Incoherent feed-forward loops serve as dosage compensators
Precision and amplification
6
Exact adaptation in the chemotaxis pathway
7
Two component systems enable robust linear amplification
8
Signaling cascades can give ultrasensitivity
Dynamic behavior
9
Kinetic proofreading: Multi-step processes reduce error rates in molecular recognition
10
Blinking bacteria: The repressilator enables self-sustaining oscillations
11
Uses, simplifications, and elaborations of negative feedback oscillators
12
Time-based regulation in cells
Cellular communication
13
Molecular titration generates ultrasensitive responses in biological circuits
14
Promiscuous receptor-ligand interactions increase the bandwidth and specificity of cell-cell communication systems
15
MultiFate enables expandable and controllable multistability
Noise: Bug and feature
16
The noisy, noisy nature of gene expression: How stochastic fluctuations create variation
17
Bursty gene expression
18
Cellular bet-hedging
19
Excitability enables probabilistic, transient differentiation
Patterning circuits
20
Lateral Inhibition: Spontaneous symmetry allows spontaneous developmental patterning
21
Turing patterns
22
Scaling reaction-diffusion patterns
References
Technical appendices
Technical Appendix 2a: Approximate solutions of autorepressive dynamics
Technical Appendix 2b: Numerical solutions to ODEs with SciPy
Technical Appendix 2c: Interactive plotting with Bokeh
Technical Appendix 3a: Nondimensionalization
Technical Appendix 4a: Numerical solution of FFLs
Technical Appendix 6a: Michaelis-Menten enzyme kinetics
Technical Appendix 7a: Signaling cascades
Technical Appendix 7b: Cascades of multiply phosphorylated signaling molecules
Technical Appendix 7c: Phosphorylation cascade with saturation
Technical Appendix 10a: Fixed points and composite functions
Technical Appendix 10b: Linear stability analysis
Technical Appendix 10c: Numerical one-dimensional bounded root finding
Technical Appendix 11a: Stability diagrams by numerical computation of eigenvalues
Technical Appendix 11b: The Greshgorin circle theorem
Technical Appendix 11c: Numerical solution of delay differential equations
Technical Appendix 11d: Linear stability analysis of delay differential equations
Technical Appendix 17a: Stochastic (Gillespie) simulation
Technical Appendix 17b: Profiling code for speed and an application of the Gillespie algorithm
Technical Appendix 20a: Lateral Inhibition: Spontaneous symmetry breaking to form a spatial pattern of cells
Exercises
Exercise 1.1: Strategies for controlling protein expression
Exercise 1.2: Separation of time scales
Exercise 1.3: Rate of production of gene product by an activator
Exercise 1.4: Activators vs. repressors
Exercise 1.5: Bound and unbound promoter regions
Exercise 2.1: Cost of a steady state
Exercise 2.2: Event handling for discontinuous derivatives
Exercise 3.1: Modes of bistability
Exercise 3.2: Controlling an autoactivation circuit
Exercise 3.3: Autoactivation, bistability, and the importance of leakage
Exercise 3.4: Modeling inducers in a toggle switch
Exercise 3.5: Negative autoregulation including mRNA dynamics
Exercise 3.6: Noncooperative bistability with a growth-determined positive feedback circuit
Exercise 3.7: Design principles for toggles
Exercise 4.1: Accelerated responses with FFLs
Exercise 4.2: Statistics of random genetic circuits
Exercise 4.3: XOR gates
Exercise 5.1: Robustness in a C1-FFL
Exercise 6.1: Co-substrate compensation
Exercise 7.1: Interpretations of sensitivity
Exercise 7.2: Signal propagation in a kinase cascade
Exercise 7.3: Dependence of signaling response on total histidine kinase and response regulator concentrations
Exercise 9.1: Kinetic proofreading in the immune system
Exercise 10.1: Coupled repressilators
Exercise 10.2: The KaiABC clock
Exercise 10.3: Linear stability analysis of the repressilator with mRNA
Exercise 11.1: Coupled delay oscillators
Exercise 11.2: Tuning delay oscillators with positive feedback
Exercise 11.3: Controlling p53 levels
Exercise 12.1: Temporal gene expression and inferring a circuit
Exercise 14.1: Programming cellular response
Exercise 15.1: A tri-stable cell-fate determinant circuit
Exercise 17.1: Dynamics of noise
Exercise 17.2: Noise in a switchable promoter
Exercise 17.3: A possible mechanism for bursty gene expression
Exercise 22.1: Turing patterns with expanders
Appendices
A
Configuring your computer to use Python for scientific computing
Computing basics
Appendix B1: Hello, world.
Appendix B2: Variables, operators, and types
Appendix B3: Lists and tuples
Appendix B4: Iteration
Appendix B5: Introduction to functions
Appendix B6: String methods
Appendix B7: Dictionaries
Appendix B8: Comprehensions
Appendix B9: Packages and modules
Appendix B10: Errors and exception handling
Appendix B11: Introduction to Numpy and Scipy
Appendix B12: Introduction to Pandas
Appendix B13: Tidy data and split-apply-combine
Appendix B14: Making plots
B
Mathematical review
C
Numerical solutions of ODES
D
Regulatory functions and their derivatives
Appendices
B
Mathematical review
Appendix B — Mathematical review
A review of mathematical concepts put to use in this book will be added here.
Appendix B14: Making plots
C
Numerical solutions of ODES