Getting back to Turing: Turing’s “reaction-diffusion” model for morphogenesis has inspired many mathematicians and computer scientists to get interested in biology – the first, because Turing’s non-linear equations are interesting to grapple with, and the latter, because the equations let them make interesting videos that may (perhaps) help us to understand the processes in real life.
There have been many, many papers along these lines. To get a feel of them, have a look at the beautiful images from this course on models of morphogenesis:
http://www.eecs.harvard.edu/~rad/courses/cs266/papers/lecture-morpho.pdf
To go a little deeper, here is a quite readable paper on the development of the pancreas that uses Turing’s approach:
http://www.wisdom.weizmann.ac.il/~harel/papers/Turing%20Morphogenesis.pdf
One exciting new piece of work, though, takes quite the opposite approach, by carefully measuring how the development and change of form happens in real life, and then developing a model based on that. The organism in question is Volvox globator, a tiny (approximately 2mm diameter) collection of algal cells that get together as a spherical shell and move as a unit through the beating of cilia on the outside of each shell. When the shell is first formed, though, the cilia are on the inside, and the shell has to invert itself to get them on the outside. Now researchers from the University of Cambridge have followed the process and developed a model to explain it.
This work is so new that it is not yet in print, but keep an eye open for:
- Höhn, Raymond E. Goldstein (contact author) et al., “Dynamics of a Volvox Embryo Turning Itself Inside Out,” Physical Review Letters (expected publication date: Apr 27 (2015))
It’s yet another example of the many different ways in which scientists think.
IMAGE: http://www.uni-bielefeld.de/biologie/Zellbiologie/volvo/volglob/inv1.html