The
official course plan
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 |
| 1/17, 13.15-15.00 |
MVH11 |
Introduction
of the course.
(Chapter 1.) Chapter 10. Broken symmetries and biological patterns |
| 1/18, 13.15-15.00 |
MVH11 | Continuation
of Chapter 10. Start of Chapter 2. Relationships between development and evolution |
| 1/20, 10.00-15.00 |
MVH11 | Continuation
of Chapter 2 with extensions. Cleavage movie, Gastrulation movie in Xenopus. |
| 1/24, 13.15-15.00 | MVH11 | Deadline
for homework I. Continuation of Chapter 3. |
| 1/25, 13.15-15.00 | MVH11 | Scaling laws |
| 1/27, 10.00-15.00 | MVH11 | Lecture 6. Chapter 3: The principles of cell signalling. Short movie of cell signalling. |
| 1/31, 13.15-15.00 | MVH11 | Lecture 7. Deadline for homework II. Chapter 4: From genotype to phenotype: looking into the black box Qualitative modellin and simulation of developmental regulatory networks Chapter 5: Placticity and reprogramming of differentiated cells in amphibian regeneration. |
| 2/1, 13.15-15.00 | MVH11 | Chapter
6. |
| 2/3, 10.00-15.00 | MVH11 | Chapter
7. Reaction Diffusion. Models for pattern formation and the position-specific activation of genes |
| 2/7, 13.15-15.00 | MVH11 | Deadline
for homework III. Chapter 8. Signalling in multicellular models of plant development Chapter 9. Computing an organism: on the interface between informatic and dynamic processes |
| 2/8, 13.15-15.00 | MVH11 | Chapter
11. Using mechanisms to map genotype to phenotype Chapter 12 How synthetic biology provides insights into contact-mediated lateral inhibition and other mechanisms Chapter 13. The evolution of evolvability |
| 2/10, 10.00-15.00 | MVH11 | Chapter
14, 15. Artificial genomes as models of gene regulation Evolving the program for a cell: from French flags to Boolean circuits |
| 2/21, 13.15-15.00 | MVH11 | Deadline
for homework IV. (Here is a comsol-file which solves a different,
simpler, but very similar problem; which hopefully will be helpful to
you.) Chapter 16. Combining developmental processes and their physics in an artificial evolutionary system to evolve shapes |
| 2/22, 13.15-15.00 | MVH11 | Chapter
17. Evolution of digital organisms |
| 2/24, 10.00-15.00 | MVH11 | Chapter
18, 19. Artificial life models of neural development Evolving computational neural systems using synthetic developmental mechanisms |
| 2/28, 13.15-15.00 | MVH11 | Chapter
20. A developmental model for the evolution of complete autonomous agents |
| 3/1, 13.15-15.00 | MVH11 | Chapter
21, 22. Harnessing morphogenesis Evolvable hardware: pumping life into dead silicon |
| Chapters 11 to 22 (ppt) |
||
| 3/3, 10.00-15.00 | MVH11 | Deadline for the project (this year
you are encourage to do individual projects). Repetition, review of the
course. (And possible some reserve
time if we are behind schedule.) |
| 3/10, 10-15 |
? |
Examination,
presentation and
discussion of the projects + oral examination. |
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:
Max Plank Research
School , dead-line for applications
Feb 28.
Norwich Research Park PhD Studentship - applications need to be
received by 1st March 2006.
