Physics 282: Spatiotemporal Dynamics in Biological Systems
| Instructor: | Prof. Terry Hwa; office: Urey 7222 phone: 4-7263; e-mail: |
| Time: | Tu/Th 11:00am – 12:20 pm (make-up lectures: Nov 10, Nov 24 at 3-4:20pm) |
| Location: | 6120 Urey Hall |
| Office Hour: | after class or by appointment |
| Course URL: | this page (https://matisse.ucsd.edu/courses/f25-biodynamics/) |
| Grade | 4-5 problem sets (to be assessed in person) |
| 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 fronts and patterns 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 equation and the stability criterion
- Chemotaxis: Keller-Segel equation; coordination of migration with growth
- Population genetics: birth-death process, genetic drift, selection
- Turing instability and patterns in developmental biology
- Excitable systems: pulses and spiral waves
Tentative course outline:
| Date | Topics | assignment | |
| L1 | Tu, Sept 30 | course overview and intro to population dynamics; logistic equation; qualitative effect of predation [note] | |
| L2 | Th, Oct 2 | two species interaction: fixed point, flow and phase diagram [note] | HW1 due Oct 16 |
| L3 | Tu, Oct 7 | generalized Lotka-Volterra model: competition and cooperation; phase diagram [note] | |
| L4 | Th, Oct 9 | stability of random gLV models; oscillation from realistic predator-prey model [note] | |
| L5 | Tu, Oct 14 | oscillatory dynamics and stable limit cycles [note] | |
| L6 | Th, Oct 16 | FitzHugh-Nagumo model: excitable systems; relaxational oscillators [note]; intro to Consumer Resource model [note] | HW2 due Oct 30 |
| Mon, Oct 20 | Review of HW1 [soln1] [note on SIR model] | ||
| L7 | Tu, Oct 21 | review of bacterial growth physiology [note] | |
| L8 | Th, Oct 23 | nutrient utilization and growth dynamics in chemostat [note] | |
| Tu, Oct 28 | no class | ||
| L9 | Th, Oct 30 | CR model of two-species coexistence [note] | HW3 due Nov 13 |
| Mon, Nov 3 | Review of HW2 [soln2] | ||
| L10 | Tu, Nov 4 | Tilman’s graphical solution to CR-model [note] | |
| L11 | Th, Nov 6 | Generalized CR model: MacArthur’s exclusion principle [note] | |
| L12 | Mon, Nov 10 (makeup) |
Ecological and phenotypical landscapes [note] | |
| Tu, Nov 11 | no class (Veteran’s Day) | ||
| L13 | Th, Nov 13 | Synergistic interaction: Cross-feeding and mutualism [note] | HW4 due Dec 2 |
| Mon, Nov 17 | Review of HW3 [soln3] | ||
| L14 | Tu, Nov 18 | Trophic structure; cooperation and cheating [note] | |
| L15 | Th, Nov 20 | Front propagation: Fisher wave and trigger wave [note] | |
| L16 | Mon, Nov 24 (makeup) |
Chemotaxis: Keller-Siegel equation; growth-expansion model [note] | |
| L17 | Tu, Nov 25 | Turing patterns: Turing instability, Turing space and mode selection [note] [biological background] | |
| Th, Nov 27 | no class (Thanksgiving) | ||
| L18 | Mon, Dec 1 |
Amplitude fluctuation and secondary instabilities [note] | |
| L19 | Tu, Dec 2 | 2D pattern selection: stripes, squares, and hexagons [note] |
|
| Th, Dec 4 | Review of HW4 [soln4-1] [soln4-2] [soln4-3] [soln4-4] |