Syllabus (Updated 2/16)
- January 6: Class Overview
- January 8: Molecular Motions in the Cell B
- January 13: Molecular Motions in the Cell C
- January 15: No class
- January 20: Fluid Flow on the Scale of a Cell A
- January 22: Fluid Flow on the Scale of a Cell B
- January 27: Reaction Kinetics
- January 29: No class
- February 3: Single Molecule Kinetics
- February 5: Stability and Simple Bifurcations
- February 10: Kinetics of Gene Regulation
- February 12: Numerical Methods
- February 17: Bifurcations of 2-Dimensional Systems
- February 19: Multistability
- February 24: Oscillations A
- February 26: Oscillations B
- March 3: Reaction-Diffusion
- March 5: Metabolic Flux Analysis A
- March 10: Metabolic Flux Analysis B
- March 12: Guest Lecture
- March 12: Project Help / Support
- March 13: Project Help / Support
- March 13: Final Report DUE by 5pm email PDF to cavoigt@picasso.ucsf.edu
Abstract (less than 500 words)
Background and Prior Work 1 single-spaced page
The Model 1/2 page
Results and Discussion 2 pages
Figure 1
Draw a diagram of your system that includes the key interactions in your model, mark on the diagram your parameters
Table 1
Parameter symbol, name of parameter, value, and reference
Figure 2
Temporal behavior of your system - demonstrate different parameter regimes
Figure 3
Bistability analysis
References
BP205 Molecular Dynamics of the Cell
(download original syllabus)
10 weeks / 2 lectures per week
Room S204 Genentech Hall
January 6 - March 12, 2009
Tuesday 9:00 - 10:00am
Thursday 10:30 - 12:00pm
TAs:
Monica Tremont (Biophysics) monica.tremont@ucsf.edu (MATLAB)
David Burkhardt (Biophysics) david.h.burkhardt@gmail.com (Programming)
Grading:
4 Homework Sets (40%) Group Work OK
Midterm (20%) Individual
- 4 hour continuous time limit
- 1 week to complete
- no collaboration
- open everything except web
- no computer necessary
Homework and midterm handed out one week before they are due
- hand out on Tuesday / due next Tuesday
Final Report (40%)
- 4 page / form of a journal letter
Syllabus:
Molecular Motions in the Cell A
Brownian Motion
Random walks and 1-D diffusion
Calculation of a probability distribution from a random walk
Single molecule studies of repressor diffusion on DNA and Dynein on a microtubule
Fick's Law and the diffusion equation
Steady-state and time-dependent (Gaussian) solutions
Coordinate Systems (Cartesian, Cylindrical, Spherical)
Diffusion-limited binding in solution
Binding to membrane receptors on the cell surface
Flux as an external force
Lateral diffusion in a membrane (Saffman-Delbruck)
Single molecule measurement of lateral diffusion
Diffusion-limited binding on a cell surface
Brownian ratchets
Protein translocation as a Brownian ratchet
HOMEWORK #1 handed out (Monica)
Scaling arguments and dimensionless numbers
Life at low Reynold's Number
Turbulent versus laminar (time-reversible) flow
Why can't a bacterium swim like Flipper?
HOMEWORK #1 DUE
HOMEWORK #2 handed out (Monica)
Diffusion-advection equation
Peclet Number: convection versus advection
Can a bacteria get more food by swimming?
Can a cilia enhance food uptake by sweeping fluid against the cell surface?
Evolution of the volvocine green algae flagellum
Cilia and embriogenesis (Hensen's node and symmetry breaking)
Elementary mass action kinetics
De-dimensionalizing equations: protein dimerization example
Timescales: protein degradation example
Using timescales to simplify equations
Michaelis-Menton kinetics revisited
HOMEWORK #2 DUE
HOMEWORK #3 handed out (David) - include 1 MATLAB problem
Michaelis-Menton kinetics for a single enzyme
Kinetic rates and probabilities
Opening and closing single ion channels
Monica runs MATLAB tutorial on Friday, January 30
HOMEWORK #3 DUE
HOMEWORK #4 handed out (David) - include 1 AUTO problem
Steady-state analysis
Stability of the steady-state
Timescale for the response from perturbation
Autocatalysis example
Bifurcations / Autocatalysis II example
Network dynamics
Shea-Ackers formulation
Binding polynomials and cooperativity
Positive and Negative autoregulation
Biphasic response
David runs AUTO tutorial on Friday, Feb 6
HOMEWORK #4 DUE
Euler's Method
Improved Euler's Method
Runge-Kutta Method - adaptive step size
Stiff Equations
Numerical methods for bifurcation analysis (AUTO)
Jacobian, eigenvalues,
In vivo HIV dynamics
Spread of disease epidemics
Cell-cell communication
Negative autoregulation
MIDTERM HANDED OUT
Null clines and cooperativity
The appearance of multiple steady-states
Competition models
Positive feedback and bistability
MIDTERM DUE
Project Topic (Title, equations, 1 paragraph summary) DUE
Mass balance and steady-state analysis
Linear algebra
Inferring unknown fluxes from measured fluxes
Analysis of citric acid production in Candida
Objective functions and linear programming
Catabolic metabolism in lactic acid producing bacteria
Phenotype phase plane analysis
Evolution of glycerol utilization in E. col
Project Background and Prior Work (1 page) DUE
Format of Final Report (4 pages of text + figures):
- Build a system of equations using ideas from the paper you were assigned, but not exactly the system in the paper
- Like a short "letter" format for an actual journal
- If your paper has multiple concepts, pick one
- Need to simplify to (at least) a 2-D system if your paper does not
- Some papers may have concepts to references to models and not an actual model
- Statement of conclusions
- Describe your system and perform a literature search and summarize
- Roughly 10 references
- Write differential equations
- Describe assumptions and any simplifications (timescales, etc)
- Describe where the parameters are from (or basis of approximations or ranges that make physical sense)
- What is different between your model and other models?
- If you need to reduce the number of equations, make a timescale argument
- De-dimensionalize equations (if the paper you are assigned already has dedimensionalized equations, show the derivation of how they were obtained)
- Analytically solve for the steady-states and determine the range of possible behaviors
- Use MATLAB to identify parameter regions that produce each of the possible behaviors - make graphs showing how the parameters affect the time trajectories
- Use AUTO or other bifurcation analysis tool to perform a bifurcation analysis for one parameter that changes the behavior of the system
- Propose a "Reynolds' Number" or dimensionless parameter that dictates the behavior of your system