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.
of the course.
Chapter 10. Broken symmetries and biological patterns
of Chapter 10. Start of Chapter 2.
Relationships between development and evolution
of Chapter 2 with extensions.
Cleavage movie, Gastrulation movie in Xenopus.
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.
The principles of cell signalling. Short movie of cell signalling.
|1/31, 13.15-15.00||MVH11||Lecture 7.
Deadline for homework II.
From genotype to phenotype: looking into the black box
Qualitative modellin and simulation of developmental regulatory networks
Placticity and reprogramming of differentiated cells in amphibian regeneration.
7. Reaction Diffusion.
Models for pattern formation and the position-specific activation of genes
for homework III.
Signalling in multicellular models of plant development
Computing an organism: on the interface between informatic and dynamic processes
Using mechanisms to map genotype to phenotype
How synthetic biology provides insights into contact-mediated lateral inhibition and other mechanisms
The evolution of evolvability
Artificial genomes as models of gene regulation
Evolving the program for a cell: from French flags to Boolean circuits
for homework IV. (Here is a comsol-file which solves a different,
simpler, but very similar problem; which hopefully will be helpful to
Combining developmental processes and their physics in an artificial evolutionary system to evolve shapes
Evolution of digital organisms
Artificial life models of neural development
Evolving computational neural systems using synthetic developmental mechanisms
A developmental model for the evolution of complete autonomous agents
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.)
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.
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.
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:
A whole bunch links to Chaos, dynamical systems, etc.
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
Sorting with surface tension
Biological Physics in Gothenburg
A recipe of a BZ reaction taken from Ball's book
Some useful links for further
Max Plank Research School , dead-line for applications Feb 28.
Norwich Research Park PhD Studentship - applications need to be received by 1st March 2006.