The
official course plan for Chalmers
and the syllabus
for GU
An applet which illustrates the thermodynamic
sorting models for cells written by Rasmus Nisslert et al, in an
earlier biomath course. For some background of this, see for
example Gilbert's book, Developmental
Biology.
| Day,
time |
Place |
What |
| Mar 19, 13.15-15.00 |
MVL15 |
Introduction
and overview of the course. Broken
symmetries
and
biological patterns Diffusion, from Simple Random Walk to a parabolic PDE. |
| Mar 20, 10.00-15.00 |
MVF32 |
Chapter 1 - The cell: fundamental
unit of developmental system The principles of cell signalling. Short movie of cell signalling. |
| Mar 22, 13.15-15.00 |
MVL15 | Chapter 2 - Cleavage and blastula formation Cleavage movie, Gastrulation movie in Xenopus. |
| Mar 29, 13.15-15.00 |
MVL15 | Chapter 2 - Cleavage and blastula formation Cleavage movie, Gastrulation movie in Xenopus. Here are a few powerpoint-notes from the first part. Dead-line for the first home-work |
| Apr 10, 10.00-15.00 | MVF32 | Chapter 3 - Cell states: stability,
oscillation, differentiation |
| Apr 12, 13.15-15.00 | MVL15 | Chapter 4 - Cell adhesion,
compartmentalization, and lumen formation Cell sorting - see the applet above! (Maybe an introduction to Chapter 5) |
| April 16, 13-15 |
MVL15 |
Chapter 5 - Epithelial morphogenesis:
gastrulation and neurulation Appendix: Linear stability analysis. Dead-line for the second home-work |
| April 17 10-15 |
MVF32 | Chapter 6 - Mesenchymal morphogenesis |
| Apr 19, 13.15-15.00 | MVL15 | Chapter 6 - Mesenchymal morphogenesis, cont. See for example the Pourquie-model. |
| Apr 23, 13.15-15.00 | MVL15 | Chapter
7 - Pattern formation: segmentatio, axes, and asymetry (axes or axis?) |
| Apr 24, 10.00-15.00 | MVF32 | Reaction
Diffusion. More
reaction diffusion, numerical aspects Dead-line for the third home-work |
| Apr 26, 13.15-15.00 | MVL15 | Cont. of Reaction Diffusion (see the
power-points of the second part of the course.) |
| May 3, 13.15-15.00 | MVL15 | Cont. of Reaction Diffusion |
| May 7, 13.15-15.00 | MVL15 | Chapter 8 - Organogenesis |
| May 8, 10.00-15.00 | MVF32 | Continuation
of Chapter 8, and Chapter 9 - Fertilization: generation one living dynamical system for two Deadline for homework IV. |
| May 10, 13.15-15.00 |
MVL15 | Cont.
of Chapter 9 Chapter 10, Evolution of developmental mechanisms |
| May 14, 13.15-15.00 |
MVL15 | Scaling laws The metabolic 3/4-law |
| May 21, 13.15-15.00 |
MVF32 | Deadline
for your project! (Here is a list of last years project
suggestions) Summation of the course, see the ppt for the last part |
| May 24, 10.00-15.00 |
MVL15 | Examination 1,
presentation and
discussion of the projects |
| May 31 |
L2040 |
Examination 2, oral
examination 9.00 Sofia Tapani 9.30 Magnus Röding 10.00 Olof Görnerup 10.30 Konrad Krysiak-Baltyn 11.00 Germain Ledrut |
We will in this course discuss the possibility of such a theory, what it should look like, and if there are pieces out there today that might be useful in such a speculative general theory.
We will discuss concepts from PDE that are successfully used in
pattern formation models today. The most prominent of those are of
course the Reaction Diffusion model, firstly proposed by Alan Turing,
1953. In connection with that study we will discuss, and hopefully
experiment with the so called BZ chemical reaction and some
mathematical models of that, see the link at the end of this page.
We will disucuss general complexity both from i biological and.mathematical standpoint following Milnor's forthcomming books. Cellular automata, Lyaponov-exponents, Julia sets, etc. A lot of focus will be put on dynamics and different classes of transformations.
We will also study "the use and missuse of fractals" i biological studies, where we quoted Jim Murray.
There will also be a presentation of quite a number of open problems that hopefully can attract and inspire to your individual projects.
The aim of the course is to give an overview of future biological areas that might need not only applied mathematics, but brand new mathematics as well.
Key words:
Pattern formation, development, Reaction diffusion, cellular
automata, complexity, Lyaponov exponent, L-system, Hausdorff measure,
IFS, DLA, Eden model, 3/4-scaling law, symmetry breaking, BZ,
bifurcation, phyllotaxis, tensegrity, thermodynamic sorting, gradient
model, wound healing.
Examination:
There will be an oral exam, together with a couple of own projects that
will need both mathematical analytic work and modeling skills.
More concretely, there will be three short home-assignment, and one a
little more elaborate, plus a project where you can work in groups up
to the size of three. The project is to be hand in and distributed to
all participants in the course Friday March 3. On the following Friday
you will shortly (10 min) present your work, and discuss all the other
projects as well. On top of that, there will be a very short individual
interview (or oral examination) at the end of that day.
Some mixed, but relevant links are found below:
Some mathematics:
A
whole bunch links
to Chaos, dynamical systems, etc.
Complexity:
Java
applets
to "The Computational Beauty of Nature" by GW Flake
Complex Adaptive
Systems
(an international master's program at Chalmers)
Possible trends in
mathematics in coming decades, M. Gromov
Some physics:
Sorting with
surface
tension
Biological
Physics
in Gothenburg
Some chemistry:
A recipe of a BZ reaction taken from Ball's book
Some useful links for further
studies:
