Often considered the father of theoretical computer science and artificial intelligence, Turing was also active in the field of mathematical biology, publishing the “The Chemical Basis of Morphogenesis” in 1952. According to Wikipedia, morphogenesis is defined as the biological process that causes an organism to develop its shape. It is considered one of three fundamental aspects of developmental biology, along with the control of cell growth and cellular differentiation.
As io9’s Esther Inglis-Arkell reports, a Moscow State University team recently highlighted the first-ever biological example of Turing nanopatterns.
“Corneal surfaces of some insects are coated with nipple-like nanostructures reducing the light reflection. Using atomic force microscopy, we discover[ed] a striking diversity of corneal nanocoatings, omnipresent in arthropods,” the team explained in a PNAS article abstract. “These fascinating bionanostructures replicate the complete set of the Turing patterns—shapes resulting from the reaction−diffusion modeling underlying many examples of patterning in biological and physicochemical systems.”
In addition to highlighting what is likely the first-ever biological example of Turing nanopatterns, the above-mentioned research also sheds light on the molecular origin and evolutionary diversification of insect corneal nanostructures. Patrick Gill, a Principal Research Scientist at Rambus, told us that it is fascinating to see the types of diversity that arise from relatively simple rules.
“For example, Alan Turing cataloged some of the patterns that can arise from two or more interacting chemicals diffusing into each other; a ‘reaction-diffusion’ system,” he explained. “The kinds of shapes and patterns produced by relatively simple local rules can result in a variety of patterns reminiscent of animal pelt patterns: zebra stripes and leopard spots can arise from subtly different versions of Turing’s reaction-diffusion equations.”
According to Gill, James D. Murray applied the same equations to make surprisingly specific predictions – including the way zebra stripes bend at the junction of the legs and the body, as well as how animals may have a spotted body and a striped tail, but never vice versa. (See the 1988 Scientific American article here for more of Dr. Murray’s work.)
“Similarly, Artem Blagodatski and his Moscow University team are exploring the diversity of the antireflection (AR) coatings at the surface of insect eyes. These coatings are used to ease vibrations (in this case, light EM waves) from one medium (such as air) to a different one (such as the refractive material of an eye),” Gill continued. “Doing this abruptly would cause light to bounce off the eye surface, much like shouting at a swimming pool causes most of the energy to reflect off the top, rather than entering.”
One way to make an AR coating, says Gill, is to have a tiny surface roughness with structures much smaller than a wavelength that dithers between the two media. This allows the wave to encounter more gentle material property transitions.
“More specifically, though, the question Blagodatski et al. want to answer is how insect eyes are set up in such a way so as to produce AR coatings. Their remarkable finding is that every AR coating they found could be mimicked by Turing’s equations; and conversely that every pattern Turing predicted was found somewhere in the insect class,” Gill added. “This offers strong evidence that insect eye AR coatings are formed by a process that can be modeled by Turing’s nonlinear equations. As humans learn more about nonlinear systems in general, we will get better at finding simple recipes that result in complex desired behaviors. For example, if there were a simple process to use the same math to make thermal infrared AR coatings, there would be a growing market for the technology.”