Physics 282: Spatiotemporal Dynamics in Biological Systems
| Instructor: | Prof. Terry Hwa; office: Urey 7222 phone: 4-7263; e-mail: TA: Shiqi Liu |
| Time: | M W 9:30am – 10:50 am |
| Location: | 6120 Urey Hall |
| Office Hour: | after class or by appointment |
| Course URL: | this page (https://matisse.ucsd.edu/courses/f24-biodynamics/) |
| Grade | 3-4 problem sets and 1-2 group projects |
| Prerequisite: | a solid first course in ordinary differential equation; exposure to partial differential equation; interest in biological phenomena. |
Course description:
This course is aimed for advanced undergraduates and beginning graduate students in biophysics and bioengineering, and for quantitative-minded BIO students. The course teaches and applies basic concepts in dynamical systems (phase plots, stability analysis, Lyapunov function) and pattern formation in spatially extended systems (Fisher wave, Keller-Segel, Turing instability, excitable systems, etc) on topics taken from microbial ecology and evolution, and developmental biology. Lessons learned from the analysis will be gleaned for biological insight.
Course outline
- Introduction to bacterial growth, population dynamics, and ecology
- Lotka-Volterra model and its generalization: fixed points and phase diagrams
- Consumer-Resource model: coexistence and global stability
- Trophic interactions, cross-feeding, cooperation, and cheating
- Spatial range expansion: Fisher-Kolmogorov wave and the stability criterion
- Bacterial chemotaxis: coordination of migration and growth
- Turing instability and patterns in developmental biology
- Excitable systems: pulses and spiral waves
Tentative course outline:
| Date | Topics | assignment | |
| L1 | M, Sept 30 | course overview and intro to population dynamics; logistic equation; effect of predation [note] | |
| L2 | W, Oct 2 | two species interaction: fixed point, flow and phase diagram [note] | HW1 due Wed Oct 16 |
| L3 | M, Oct 7 | predator & prey; spread of infection [note] | |
| L4 | W, Oct 9 | generalized Lotka-Volterra model: competition and cooperation [note] | |
| L5 | M, Oct 14 | stability of gLV models; oscillatory dynamics and stable limit cycles [note] | HW1 soln |
| L6 | W, Oct 16 | excitable systems; relaxational oscillators [note] | HW2 due Wed Oct 30 |
| L7 | M, Oct 21 | Consumer-resource model: bacterial growth physiology [note] | |
| L8 | W, Oct 23 | Monod growth law for two nutrients; growth in continuous culture [note] |
|
| M, Oct 28 | no class (makeup on Nov 1) | ||
| L9 | W, Oct 30 | CR model of competition: 2-species and 2-nutrients [note] | |
| L10 | F, Nov 1 (makeup) |
Tilman’s graphic method [note] | HW3 due Mon Nov 18 |
| L11 | M, Nov 4 | MacArthur’s ecological exclusion principle [note] | HW2 soln |
| L12 | W, Nov 6 | phase diagram and feasibility space [note] | |
| M, Nov 11 | no class (Veteran’s Day) | ||
| W, Nov 13 | no class (makeup on Nov 22) | ||
| L13 | M, Nov 18 | CR model of symbiosis I: Syntrophic interaction from metabolic exchanges [note] | |
| W, Nov 20 | class canceled | ||
| L14 | F, Nov 22 (makeup) |
CR model of symbiosis II: effect of spatial compartmentalization [note] | HW4 due Wed Dec 11 |
| L15 | M, Nov 25 | CR model of symbiosis III: producers, cheaters, and cooperators [note] | HW3 soln |
| L16 | W, Nov 27 | Population range expansion: Fisher-Kolmogorov equation and marginal stability; trigger wave [note] | HW4 amended |
| L17 | M, Dec 2 | Chemotaxis: Keller-Segel equation; growth and expansion [note] [long note on chemotaxis] |
|
| L18 | W, Dec 4 | Spatiotemporal patterns in development: Turing instability, Turing space, and mode selection [note] [long note on Turing pattern] |
|
| L19 | F, Dec 6 (makeup) |
intro to Swift-Hohenberg model: amplitude equation and pattern selection [long note on amplitude equation] | HW4 soln |