**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 analysisReferences

**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