Mathematical models for biological pattern formation -  Morphomatics, MVE075

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.

Period 3
Tue 13-15 (starts Jan. 17)
Wed 13-15
Fri 10-12
Fri 13-15

Day, time
1/17, 13.15-15.00
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.

... and some more background:

After successful genom project such as HUGO, etc,  have been  completed, increasingly more focus will be put on the questions how nature uses this genomic information for different pattern formations on the different levels of complexity during embryonic development.Quite a number of  voices in the science community have put forward the idea that we are still waiting for the biological Newtonian theory to be formulated. See for example, Ian Stewart, Lennart Carleson, M. Gromov (see link below), etc.

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.

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.

"On Growth, Form and Computers", Sanjeev Kumar, Peter J. Bentley, 2004. (<- Obs, this is not given in the official course plan!)
(parts from Jim Murray, Mathematical Biology I and II, 2nd ed. Springer, 2003.
John Milnor, Complexity in Science, forthcomming book, 2006?
+ a bunch of research papers.)

Some mixed, but relevant links are found below:

A reaction diffusion simulation by Joakim Linde.
 A Mathematica notebook on Cellular Automata.
Avida language manual
An Avida example.
An article about Avida, Feb. 2005

Some biology:
 Gilbert's "Developmental Biology"
"When human life begins" by Gilbert
 Visual Models of Morphogenesis (in Botany on line) by Prusinkiewicz et al (for more on this see below)
 Model Organisms
 Bioinformatics in Gothenburg
Virtual library in development

The following are links taken from Botany on line:

Interactions between Cells
Growth, Differentiation, Pattern Formation and Translocation
    H. MEINHARDT: Biological pattern formation: How cell talk with each other to achieve reproducible pattern formation
    P. PRUSINKIEWICZ, M. HAMEL, and R. MECH: Visual Models of Morphogenesis: A Guided Tour
    P. COOPER: Lindenmayer Systems * LSystems program written in Java
    G. OCHOA: An Introduction to Lindenmayer Systems
    G. THEISSEN 's Research Group: The MADS-box Gene Home Page
Protoplasts and Tissue Cultures as Models for the Study of Plant Development
Plant Responses to Light: Phototaxis, Photomorphogenesis, and Photoperiodism
Phytohormones (Plant Hormones) and other Growth Regularors
Growth Movements, Turgor Movements , and Circadian Rhythmics

Some mathematics:
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

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.

Torbjörn Lundh, Jan 2006,