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Spatio-Temporal Modeling in Biology
| Abstract | This course will give an overview to modeling spatial problems in biology, in particular on the cell and tissue level. A wide range of mathematical techniques will be presented as part of the course, including concepts from non-linear dynamics (ODE and PDE models), stochastic techniques (SDE, Master equations, Monte Carlo simulations), and thermodynamic descriptions. |
| Aims | The aim of the course is to introduce students to state-of-the-art mathematical modelling of spatial problems in biology. Students will learn how to chose from a wide range of modelling techniques and how to apply these to further our understanding of biological mechanisms. The course aims at equipping students with the tools and concepts to conduct successful research in this area; both classical as well as recent research work will be discussed. |
|
Lecture Notes |
can be downloaded here |
| Literature |
The course is based on material that is covered in a range of textbooks:
I. Spatial Modelling in Biology
II. General Mathematical Biology
III. Mathematical Methods
IV. Biology Background
|
| Audience |
The
course builds on introductory courses in Computational Biology. The
course assumes
no background in biology but a good foundation regarding mathematical
and computational techniques. |
Course details
636-0706-00L Spatio-Temporal Modelling in Biology
| Time | Room | |
| Lecture |
Fr 10-12 |
HG D1.2 |
|
Tutorials |
Wed 3-5 pm, biweekly |
HG G 26.1 |
Tutorials are held bi-weekly for two hours and cover two problem sheets each. The first tutorial takes place on Wed March 6. The tutor is Patrick Fried (patrick.fried@bsse.ethz.ch).
Schedule 2013
|
Date |
Lecture | Exercise | Solutions | Comments |
|
22/2 |
Introduction to Spatial Modelling |
Exercise 1 |
Solution 1 |
|
|
1/3 |
Morphogen Gradients: Formation |
Exercise 2 |
Solution 2 |
Tutorial 1 (6/3) |
|
8/3 |
Morphogen Gradients: Read-out |
Exercise 3 |
Solution 3 | |
| 15/3 |
Morphogen Gradients: Scaling |
Exercise 4 |
Solution 4 | Tutorial 2 (20/3) |
|
22/3 |
Turing Pattern | Exercise 5 | Solution 5 | |
|
29/3 |
GOOD FRIDAY |
|||
| 5/4 |
EASTER BREAK |
|
Tutorial 3 (10/4) | |
| 12/4 | Introduction to FEM & COMSOL |
Tutorial |
COMSOL file/Animation | |
| 19/4 | Simulating on Growing Domains |
Exercise 6 |
Solution 6 | Tutorial 4 (24/4) |
| 26/4 |
Fractals in Biology & Branching |
Exercise 7 | Solution 7 | |
|
3/5 |
Case Study I: Dorso-ventral Patterning | |||
|
10/5 |
Travelling Waves | Exercise 8 | Solution 8 | |
|
17/5 |
Chemotaxis | Exercise 9 | Solution 9 | Tutorial 5 (15/5) |
|
24/5 |
Case Study II: Modelling the Limb |
|||
|
31/5 |
Summary |
Tutorial 6 (29/5) |
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