A remarkable paper appeared online 09 December 2015:
- Denkov, N., S. Tcholakova, I. Lesov, D. Cholakova & S.K. Smoukov (2015). Self-shaping of oil droplets via the formation of intermediate rotator phases upon cooling. Nature 528, 392-395.
The authors, materials scientists from Bulgaria and the UK, mused out loud that their discovery that cooled oil droplets become polygonal had something to do with the morphogenesis of living creatures, but didn’t know which ones. I immediately started writing “On polygonal drops and centric diatoms” followed shortly by “The tensegrity origin of life via shaped droplets as protocells”, and some of the authors of “Self-shaping of oil droplets” are joining us as co-authors.
I had long been puzzling over the uncanny, nearly perfect symmetry of some centric diatoms, which I demonstrated by rotating a digital image of a diatom with n sectors by 360/n degrees and subtracting the images, in:
- Sterrenburg, F.A.S., R. Gordon, M.A. Tiffany & S.S. Nagy (2007). Diatoms: living in a constructal environment. In: Algae and Cyanobacteria in Extreme Environments. Series: Cellular Origin, Life in Extreme Habitats and Astrobiology, Vol. 11. Ed.: J. Seckbach. Dordrecht, The Netherlands, Springer: 141-172.
Here’s a less perfect example than those used in that paper, the diatom Triceratium favus with n = 3, so the rotation is 360/3 = 120o (with kind permission of Stephen S. Nagy of Montana Diatoms):
The subtraction image on the right is black where the match is best. The two published examples, with n = 5 and 11, came out almost totally black. You can try this yourself with any front-on image of a diatom you can find on the Internet, if you have software that allows rotation by any angle. For example, try Word: Format Picture: Size: Rotate and scale, after trimming the picture so that the center of the diatom is in the center of the image. I’d like to see what you get. Please send the original, rotated and difference images to me at: DickGordonCan@gmail.com, along with the exact source of the diatom image. Anyone mathematically inclined (and these diatoms instantiate a rotation group) may wish to write a computer program to quantify the degree of symmetry by coding some of the math in:
- Pawlak, M.l. (2006). Image Analysis by Moments: Reconstruction and Computational Aspects. WrocLaw, Oficyna Wydawnicza Politechniki WrocLawskiej.
We in polar climes are all aware of the beautiful, generally hexagonal symmetry of snowflakes, which has it explanation in the crystalline stacking of water molecules in ice. Some can approach triangular, although they are hexagons with edges of different lengths:
This is from:
Libbrecht, K.G. (2016). Guide to Snowflakes: Triangular Crystals.
with kind permission of Kenneth G. Libbrecht. More pointy triangular snowflakes may be seen at:
Bentley, W.A. & W.J. Humphreys (1931). Snow Crystals, McGraw-Hill. (reprinted by Dover Press in 2003).
But diatom shells are not crystalline at all. They are made of amorphous silica, which at higher temperatures would be molten glass. They are frozen in the glassy state. Are diatoms real life cases of the liquid metal robot T-1000 in the movie Terminator 2? That puzzle is why diatom symmetry is uncanny.
So we start the New Year with a newly discovered phenomenon: oil drops that “should” be mere spherical blobs looking like diatoms. I’ll just show one oil triangle here (with permission of Nature Publishing Group), though the polygons go up to 11 sides:
How can a liquid have sharp points like that?
Connections rattled in my brain. Denkov et al. suggest that the oil molecules line up at the perimeter, forming plastic-like bundles as cooling proceeds. Those bundles could be stiff, and prevent the drop from curving due to its surface tension. But then stiff rods confined by tension means that shaped droplets are tensegrity structures. But this is precisely what Steve Levin and I were complaining about the presentations at the origin of life conference we attended together last November: protocells, the blobs that supposedly led to life, had no postulated structure. Two problems solved at once! Diatoms and protocells are and might have been tensegrity shaped droplets. Martin Hanczyc’s oil droplet protocells might be polygonal under some conditions, and Vadim Annekov’s molecular dynamics simulations of diatom shell morphogenesis interacting with cytokeleton (in progress) may be enhanced. Not quite as good as the kids’ book “Seven in One Blow“, but a very satisfying pair of results.
And by the way, this is why theoretical biologists should be regarded as highly as theoretical physicists, although in general we don’t get no respect.