Mathematical Biology 3380

• 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

• 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

• Homework 30%
• Exam(s) 30%
• Final Project 40%

• Part 1:Ecology & Population biology
  • Discrete dynamics
    • Ecological models - Birth and Death
      • Simple first and second order maps
        • Logistic map
        • Logistic map bifurcation diagram
        • Logistic map Liapunov exponent
        • Discrete predator-prey
      • Coherence and extinction Paper by Earn and Levin and Ring of 10 logistic maps
      • Trillium Here is a linear model And here is the nonlinear version
      • Of course there is Homework! and for your amusement, some examples of discrete disease models SIRS ; plague! ; and a viral disease
  • Continuous dynamics - delay equations
    • delayed logistic
    • Delay Theorems
    • Age-structured models The delayed gratification simulation
    • Handout
    • Another handout with numerics and an exmple
• Part 2: Mass action, enzymes, etc Book here
  • Homework and notes on phaseplane analysis
  • Enzyme models
  • Here is a nice reference to enzyme kinetics
    • Nomenclature
    • Simple enzyme kinetics
    • Reversible kinetics
    • Inhibition
  • 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
    • Diagram of the gene
    • Rules
    • Heirarchy of the module
• Part 3: Stochastic models
  • Channels
  • Langevin dynamics
  • LAST HOMEWORK!! Get it here!
    • Gillespie Brusselator
    • Stochastic ML equation
    • Two-state channel simulation
• Part 4: Pattern formation
  • Fibroblast aggregation
  • Ant Mills
  • Bacterial division and the MinD/MinC/MinE system
  • Streaming of myxobacteria
• Part 5: Delay equations
  • Blood disease
  • Epidemics