MATH 786 (Mathematical Biology)
2007, First Semester
James Sneyd, Antonio Politi, and David Bryant
This is an introductory course to mathematical biology, with emphasis on modeling in physiological and gene dynamics.
Preparation for the course
To succeed in this course, you need a good background in Stage II mathematics or its equivalent. In particular, you should have at least a B in Maths 253 and Maths 260 (Differential Equations) or in equivalent courses. If in doubt about whether you are adequately prepared for this course, contact the lecturer of the course. No biological knowledge will be assumed, although some wouldn't hurt you. That's pretty much a general rule of life, come to think of it. Computational methods will be used extensively, so if you hate computers this course wouldn't be a great choice.
Textbook
There is no text for the first module but a reading list and some lecture notes will be provided. The second module will be taught from the book "Mathematical Physiology" (Keener and Sneyd, Springer, 1998). Students will be provided with copies of the relevant chapters (look under the heading Lecture notes and handouts on the web page).
Lecturers
James Sneyd (Room 417 Math)
Antonio Politi (Room 428 Math)
David Bryant (Room 402 Math)
Lectures
Monday and Wednesday, 2:30pm - 4:00pm, Room 201 (Mondays) and Room 203 (Wednesdays), in the Bioengineering Institute.
Course work
Four assignments will be set and marked. They form an important part of the course and should be attempted by all students.
There will be two tests during class time (one test for each module) on
Test on Module 1 - Last lecture in first half of semester
Test on Module 2 - Last lecture in second half of semester.
All students should take these tests. Work on the assignments will be done in groups. There will be no examination.
If illness or other problems prevent you from completing any of the assignments please contact your lecturer as soon as possible. A medical certificate will be required if you wish to apply for an exemption from an assignment. If you are ill or have other problems at the time of the tests you should contact Student Health and Counselling (extn 87681) immediately to obtain aegrotat information.
Final Mark
Each assignment is worth 15% of the final grade, and each test is worth 20%.
Course Outline
The course will be taught in two separate modules.
Module 1 (David Bryant):
*Gene dynamics in large populations
-Model building and analysis]
-Genes, loci and Meiosis
-Mutation and Selection
-Linkage Disequilibrium
-Continuous and discrete models
-Sampling error
*Gene dynamics in small populations
-The Coalescent
-Genetic Diversity and its loss
-Diffusion equations
-The classic equations
-Inference with the coalescent
Module 2 (James Sneyd/Antonio Politi):
Enzyme kinetics:
-equilibrium and quasi-steady state approximations
-singular perturbations and slow manifolds
-cooperativity and Monod-Wyman-Changeux models
Ion channels and transporters:
-Nernst equation
-Goldman-Hodgkin-Katz equation
-Poisson-Nernst-Planck equation
-ATPases
-Markov models
-time scale reductions.
-Cell Volume Control (if time permits)
-Steady state and dynamic models.
-Excitability and action potentials
-Hodgkin-Huxley equations
-fast-slow reduction of the HH equations
-relaxation oscillations
-FitzHugh-Nagumo model
-traveling waves in nonlinear parabolic equations
-Piecewise linear models and exact solutions.
Course guide