Mathematical Biology 3380
Fall 2002
Tuesday/Thursday 10:00-11:20
THACKERAY 704
Bard Ermentrout
Recommended books
- Mathematical Biology J.D. Murray, Springer, 1989
- Mathematical Physiology J. Sneyd & J. Keener, Springer, 2000
- Computational Cell Biology C.P. Fall and others, Springer, 2002
On reserve!
- Computational cell Biology
- Mathematical Models in Biology (great intro book!)
- XPPAUT book
Prerequisites
- Mathematics
- Some differential equations
- Some basic linear algebra (eigenvalues, etc)
- Some Fourier series
- Computing. You will be required to do many computer exercises.
Free software XPPAUT is
available that will allow you to do most of the exercises. Here is how to install and start
Grading
- Homework 30%
- Exam(s) 30%
- Final Project 40%
Syllabus
- Part 1:Ecology & Population biology
- Discrete dynamics
- Ecological models - Birth and Death
- Continuous dynamics - delay equations
- Part 2: Mass action, enzymes, etc Book here
- Homework and notes on phaseplane analysis
- Enzyme models
- Here is a nice reference to enzyme kinetics
- HOMEWORK!!
- Switches and oscillations
- Cell cycle and circadian rhythms Goldbeter circadian paper and an ODE file
- More Homework Problems 1,2, 5 in chapter 9.7
(In the actual book, it is exercises 1,2,4) Note that in
the last exercise, the y equation should have a -gamma y
, not -gamma x See also Keller
- Tyson's circadian paper and an ODE file
- Cell cycle modeling (Chapt 10, book). There are three ODEs
The two-state switch between CDK and APC
; CDK/APC/Phosphatase ; and the model with cell mass
- Advanced cell cycle model Chen et al
- HOMEWORK Chapter 10: Problem 1a, Problem 5 (4 in published book) Here is an ODE , Problem 14 (8 in published book) Note that in
the code, k3' is denoted k3p and so on. Here are some HINTS to make the table fill-in easier!
- Here is Leibler's PNAS paper which has some interesting results about noise
- Boolean model for the cis-regulatory system
- Part 3: Stochastic models
- Part 4: Pattern formation
- Fibroblast aggregation
- Ant Mills
- Bacterial division and the MinD/MinC/MinE system
- Streaming of myxobacteria
- Part 5: Delay equations