# Mathematical models for biological pattern formation -  Morphomatics, MVE075 (Chalmers) and MAN560 (GU)

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 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

... 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.

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.

Litterature:
New book:
Biological Physics of the Developing Embryo, Forgacs and Newman, Cambridge University Press, 2005.
ISBN: 0-521-78337-2

"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
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.
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 chemistry:
A recipe of a BZ reaction taken from Ball's book

Some useful links for further studies:

Torbjörn Lundh, Feb 2007, torbjrn @math.chalmers.se