Monthly Archives: January 2016

Biotensegrity everywhere?


Statue from somewhere in Georgia that we saw celebrating a family watching murmuration.

Scientists are always looking for general rules, and then stretch what we know to fit assorted Procrustean beds. For example, the rule that “everything is a fractal”, which means it looks much the same no matter how much you magnify or shrink it, works just fine with mathematical fractals, but does have limits when applied to the real world. Take a branching structure, such as a lung (Glenny, 2011). At the bottom you hit the alveoli (air sacs), and at the other end is the trachea (windpipe), neither of which resembles the intermediate, fractal-like branching structure in between. Another grand unifying scenario is The Emergence of Everything (Morowitz, 2002), as if atoms forming crystals, birds forming murmurations, and galaxies forming clusters were somehow one and the same phenomenon. Maybe so, maybe not, maybe they just share some mathematical properties and we thus think they are somehow projections from Plato’s ideals (Wikipedia, 2016). In Embryogenesis Explained (Gordon & Gordon, 2016) we took a crack at the concept of wholeness, showing it is well supported by quantum mechanics, yet could not extend it readily to the seeming wholeness of embryos. Rob Stone and I settled on what we called the Cybernetic Embryo (Stone & Gordon, 2016), and indeed are now trying to extend it to all of evolution. So I’m equally guilty of attempting to find grandiose patterns in nature. It’s fun, but, as William Bateson said, keep your eyes open and “Treasure your exceptions” (Cock & Forsdyke, 2008).


Knee anatomy. If the knee is treated as tensigrity structure then knee pain can be explained as the structure having some part out of balance and pain can be alleviated by correcting the balance of the assorted parts.  Blausen 0597 Knee Anatomy Slide by BruceBlaus Wikiversity Journal of Medicine DOI:1015347/wjm/2014/010

Last November we spent two weeks with Steve (an orthopaedic surgeon by training) and Olga Levin, and he almost convinced me (as he is convinced) that tensegrity is everywhere, at every level, from molecules to our muscles and bones. Now I had indulged in the concept much earlier, regarding the cell state splitter as a tensegrity apparatus, which I modelled using a Tensegritoy set (pp. 141, 170, 310 in Gordon, 1999). Natalie and I used the Wurfel, a tensegrity toy for toddlers, as a model of how changes in the configuration of the whole genome could explain the changes in gene expression during cell differentiation. We included this concept in the “nuclear state splitter”, which we have elaborated in great detail in Embryogenesis Explained, shedding the Wurfel model in the process. So we were open to Steve’s proselytizing (Levin, 2006) resulting in seeing shaped oil droplets as tensegrity structures in a recent blog (Gordon, 2016), stretching the concept to include polygonal diatoms and protocells at the origin of life.

For the uninitiated, an object consisting of stiff parts held together by elastic parts under tension has “integrity”, i.e., holds itself together. The word “tensegrity” was coined by Buckminster Fuller (Wikipedia, 2015).

(Animation of the simplest of tensegrity structures by Cmglee from Wikipedia Commons)

This week I started on a long hoped for adventure: working towards a realistic tensegrity simulation of the structure of cytoplasm. Last March Steve introduced me to Vytas SunSpiral of NASA, who recently brought in Dorothea Blostein of Guelph University. Both have been developing tensegrity robots for exploring the terrain of bodies in the solar system (SunSpiral & Agogino, 2015), and doing computer simulations (Blostein, 2016) of how they move. We have much to teach each other, and then a lot of work to do to introduce biological phenomena into their software. We hope to reach the point where we can challenge biologists to do appropriate measurements to test how close we come to simulating real cytoplasm. Then on to nuclei, spindle apparatus, whole cells, tissues, and embryogenesis, all seen as a panoply of tensegrity phenomena. Well, maybe.


Saving Kemp’s Ridley Sea Turtles From Extinction

The Kemp’s Ridley (Lepidochelys kempii) sea turtle (also know as the Atlantic Ridley) is a small olive green to black looking sea turtles that reaches a maximum size of 58–70 cm (23–28 in) carapace length and weighing only 36–45 kg (79–99 lb).

One of the organizations I do occasional volunteer work for and with which I have a lot of personal familiarity is Gulf Specimen Marine Laboratory. This lab is one of the premier suppliers of ocean specimens to scientists around the world. They also do sea turtle rescue. And the sea turtle they most often rescue is juvenile Kemp’s Ridleys. GSML is located in a region famed for blue crabs and juvenile Ridleys eat a lot of crabs. So GSML is Florida’s juvenile Ridley headquarters.

Sea turtle rescue

In 2015 GSML joined with The Responsible Pier Initiative. This program is designed to educate fishermen and get juvenile Ridleys that have been accidentally caught on an angler’s hook into proper hook removal, care and then return to the wild. Without such care, getting hooked by a fisherman can be a death sentence. With the Responsible Pier Initiative, GSML had a 600% increase in the numbers of Kemp’s Ridleys they saved going from an average of 3 to 19 in the first year! GSML is a small outfit by turtle rescue standards but they get more Ridleys than any other turtle organization in Florida.

I met my first Kemp’s Ridley at Gulf Specimen Marine Lab in 2014. The little guy was a charming fellow named Spot. Spot was lucky. He got sick with pneumonia and was floating about the Gulf, near death, when a fisherman who happened to be passing by in his large boat spotted him. The sharp eyed fisherman netted Spot and took him on board. He called for help and diverted from his planned excursion in order to meet Jack Rudloe at a dock. He transferred Spot to Jack’s care and returned to his fishing. Jack took Spot to Norm Griggs, the vet who treats all the GSML sea turtles (without charge I might add). Spot required antibiotics, time and feeding to recover and he was eventually released ten months later.

2014 was a very bad year for juvenile Kemp’s Ridleys. 1200 of them washed ashore all up and down their range along the Atlantic coast swamping rescue facilities. The turtles were presumed to be suffering from “cold stun” which is what happens when the little fellow end up in colder water than they can function in. It commonly happens in small shallow bays. Low air temperatures in such shallow bays drop the water temperature down to the point that the turtles are stunned. When turtles are cold stunned they are susceptible to infections by a variety of organisms.

In 2014, there were so many sick Ridleys that hundreds had to be transferred to southern rescue aquariums in Florida and Texas. Things at these southern sea turtle rescuers are normally pretty quiet in winter. They are usually busiest in spring and early summer when the turtles migrate back to their nesting grounds. 2014 was not such a year. What made it even worse was the sheer number of turtles that were also very sick and required antibiotic treatment and an extended stay in the rescue facilities for rehabilitation. Cold stunned turtles can develop these secondary infections but normally if you catch them quickly and put them in warm water they can often be released into the wild as soon as it is warm enough.

Fortunately, the 2014/2015 cold stunning event has not happened this year. Unfortunately, we have to assume for every Ridley rescued, rehabilitated and returned to the sea, many many more were not lucky enough to be found by people and those Ridleys simply died. It could be that whatever the 2014 event was, it decimated the Ridley juvenile population. So what was the 2014 event? I am not a turtle biologist but I do have a lot of training in epidemiology. A review of the scientific literature yielded no specific clues. Most authorities seem to think that the cold stunning was just bad luck and the sickness came afterward. Spot, however, was found in Florida waters, not cold stunned but nonetheless very ill. His symptoms matched those of the cold stunned turtles from further north. It is impossible to know for certain, but I suspect the cold stunned turtles of the 2014 event were already ill with the same thing Spot had and the reason they ended up cold stunned was they were too sick to complete their southern migration. This is alarming.

If you measure Ridley population numbers by the numbers of nesting females, it is shocking to see how close these charming creatures came to extinction. Ridleys almost exclusively nest in one place, a 16-mile beach in the Mexican state of Tamaulipas. The number that nested in 1947 was 89,000. We can take this as a base number for what their numbers should be. In 1978 there were less than 200! A lot of care and effort went into helping them. Their nesting site was protected. Some of the hatchlings  were released from the nearby Padre Island in Texas. Baby sea turtles imprint on their birth beach when they dash over the sand to the water and the purpose of releasing them from San Padre was to try to establish a second nesting area. In 1996 there were six nests and that number has slowly increased so that San Padre reached a peak of 209 nests.


Nesting Sea Turtle Numbers from the Turtle Island Restoration Network

If we look at this graph of the Mexican nesting numbers, we can see that until 2010 the turtles were doing very well. If you think of the nesting numbers in mathematical terms, the population had begun to grow very rapidly entering an exponential growth phase starting about 2000. That was very good news for endangered Ridleys. However, you can see the exponential growth stopped and the numbers dropped abruptly in 2010. A lot of adult turtles did not nest after the Deepwater Horizon spill. It looks like about one third of the nesting females did not make it to the beach. We don’t know if they died or if they simply skipped nesting for one year. It looks like they died because if they had just skipped one year then the curve should have returned to its previous upward surge and it hasn’t. And in 2013 there was some other kind of hit. If we imagine what the curve should have been, it was a bad hit affecting about one half of the adult nesting sea turtles. What about 2014? The provisional number of nests is down again to a mere 118 in San Pedro, down from their highest point of 209. Similarly the 2014 numbers for Mexican nesting has dropped from 13,035 to 10,987, a terrifying 16% plunge in a population that was still reeling from the 2010 oil spill. I have not been able to find the numbers for 2015 but I am hoping the news will not be another drop.

So why have nesting numbers dropped so much? Again I don’t know for certain but my educated guess is this. When any population begins to enter the exponential growth curve, that population is in danger from epidemics. The population density reaches a high enough point that a disease can rapidly spread because individuals  have a very high probability of encountering one of their own while sick and passing he sickness along. It is an unfortunate side effect of success. So getting back to Spot and his pneumonia I can speculate that 2014 was one of those disease outbreak years. (Which is not to say that this sickness was not a delayed “hit” from some long term effect of the oil spill. It may well have been.) If you add in the hit that the population took in 2010 from the oil spill, it is easy to see how dangerous a string of multiple hits can be on a recovering population. In fact, Dick did a paper on the mathematics of multiple hits on a population and how this can cause extinction back in 1993. The take home message is that all our optimism about Kemp’s Ridleys coming back from the brink of extinction must be tempered with caution. They aren’t there yet!

So what can any one of us do about the situation? As it happens GSML is trying to expand the responsible pier initiative to increase the numbers of Juveniles they can save. But their facilities were bursting with healthy hooked Kemp’s Ridleys last year and they need more rehab space. So you can make a donation that will directly help Kemp’s Ridley sea turtles. And if giving to GSML doesn’t suit you, please consider giving to another sea turtle rescue organization. It is we humans who got the Kemp’s Ridleys into their current mess. We can get them out. We just have to decide to do it. You can see the GSML fund raising drive linked below. And I can personally assure you this bunch works largely on volunteer labor and there are no big salaried executives and administrators. Your donations will go directly to help the Kemp’s Ridley (and other sea turtles) back from the brink of extinction.

You can donate here. And Tilt does not deduct a single penny from what GSML gets and if you use your debit card, you aren’t charged anything either. And give or not, please share the message and pass the information on.

Shaped droplets, diatoms and the origin of life

A remarkable paper appeared online 09 December 2015:

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:, 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:

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:

Libbrecht2016 triangular.jpg

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:


Denkov&2015 Fig2b triangle.jpg

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.