Chirality rules

Handily enough.

 Ever wonder about the geometry behind hip and shoulder rotation?
 Rotation is related to supination and pronation, which has to do with chirality, or handedness.

Chirality (from the Greek cheir meaning hand) describes a geometric property of form in molecules and can be observed right up to the level of our bilaterally symmetrical human bodies.

Biological molecules are said to be chiral; it is their chirality that makes them recognisably organic and of life. Like gloves, chiral molecules are either left- or right-handed and can’t be superimposed on one another. Comparing this to asanas, the right side Trikonasana has a matching left side Trikonasana; they’re the same but opposite, like mirror images. Macromolecules like DNA are also chiral and are exclusively made of building blocks with the same handedness, or chirality,and are thus referred to as homochiral.

What we need to be clear on here is simply that chiral objects have a handedness. More examples: scissors, shoes, corkscrews, bicycle cranks, arms, and legs. As this is an anatomy for yoga blog, obviously we are less concerned with scissors and and even less so with shoes! We will be looking at how arms and legs are chiral objects and what this means for how we move our bodies in asana.

Although the term wasn’t commonly used until the 1960s,  Lord Kelvin coined the term “chirality” in 1884. The term enantiomorphous (in opposite shape) describes the macroscopic relationships between nonsuperimposable, mirror-image crystalline forms. The crystallographer René-Just Haüy (1743–1822) observed in 1801 that there were right- and left-handed quartz crystals, a phenomenon known as hemihedrism.

All these terms are relevant to organic chemistry, which is a field that examines the building blocks of life. Looking at how the really tiny shapes tend to form will help us to understand our experience of anatomy at the conscious level much further up the scale in our bodies in asana. Having a friendly acquaintance with the concept of chirality is really important because it is nature’s original system of cardinal direction, certainly for the vertebrates anyway! Less so for sponges.

Ever wonder about how your outstretched arms allow your hands to grasp a set of objects, for example the handlebars on your bicycle, and how lucky it is you’ve got a pair of arms to keep hold of your bike with your two hands wrapped in opposition in such a simple yet refined balance that you’re able to pedal the bicycle with two legs as your two mirror-image feet crank the machine along the pavement upright on skinny tyres for as long as you so fancy? We have bilateral symmetry, chirality, and gravity to thank for this miracle, friends.

The very experience of having a body is to appreciate chirality. The chiral nature of our tissues at the microscopic level gives rise to helical patterns as we scale up to the level of the limbs. The word helical refers to helix, which we can simplify for our purposes as a three-dimensional spiral. When we talk about “spiralling” as an instruction for what to do with your body parts in a yoga class, what we are really referring to is working with the helical tissue arrangements with respect to their chirality.

After many years of yoga practice, I’ve come to fully embrace the power of supination and pronation for keeping the more vulnerable connective tissues protected from the potential strain of performing dynamic asanas. For more about the practical aspects of pronation and supination in yoga, check out my practice blog coming soon: Pronate or Supinate?

 

 

The tetrahedron twists into a tetrahelix.

 

So from our study of biotensegrity, we know that geodesics will render form in the most efficient, minimal-energy, close-packed manner out of the Platonic solids. First the equilateral triangle, then the tetrahedron. Get a string of them together and match their faces up, and what appears? A helix. A tetrahelix.

As it turns out, the tetrahelix is an extremely simple, stable formation for organic molecules. I recently found this incredible patent for a Tetrahelical/curved bicycle crank arm/connecting rod for human/mechanical powered machines and the like that sounds absolutely brilliant. Their images gave me inspiration for the tetrahelix illustrations in this post as it seemed a nice way to connect the dots. Hope they don’t mind I stuck hands on their cranks!

Chirality begets the helix and vice versa

What does the chirality of molecules and the helix have to do with anatomy? As forms in nature spiral into existence, they do so near the smallest end of the scale in our protein molecules. The tetrahelix molecular structure embodies an intrinsic hierarchy of sub-helixes of complementary pitch and chirality that gives strength and viscoelasticity to biological structures. My understanding of the tetrahelix in biology owes a great deal to Graham Scarr and for a scholarly appraisal of the subject I would recommend heading over to his paper, FASCIAL HIERARCHIES AND THE RELEVANCE OF CROSSED-HELICAL ARRANGEMENTS OF COLLAGEN TO CHANGES IN THE SHAPE OF MUSCLES. 

Scaling up, we can see the entire human body exhibits bilateral symmetry as the left and right sides are mirror images of each other. So we can appreciate that chirality is a term applied to the tiniest particles, and yet is intrinsic to the bilateral symmetry characterising the entire body. Arms and legs pronate and supinate in their helical arrangement, and this movement is related to the natural joint rotations crucial for healthy movement.

One of the best papers I’ve seen on this concept is from engineers, Huijuan Zhu, et al, Mechanics of Fibrous Biological Materials With Hierarchical Chiralityfrom the Journal of Applied Mechanics. I got so excited I actually bought access to their paper, so I hope they don’t mind I’ve borrowed the image below. The researchers were looking at cellulose helices deformation showing up in lengths of paper to demonstrate a continuum mechanics model for understanding the bottom–up transfer of chirality in fibrous biological materials. As mechanical engineers, their interest is knowing how this transfer mechanism may provide a limit to the macroscopic size of biological materials through the accumulative contribution of twisting.

 

Fig. 1 Hierarchy of chirality in biological materials: (a) sugar unit, (b) cellulose molecule, (c) cellulose fibril, (d) single cell with helical winding of cellulose fibrils, (e) fiber bundle, (f) fiber network, (g) twisted belt, and (f) macroscopic helix

Their work shows how the chirality of constituent elements at the micro-scale can induce the twisting of higher-level structures. This transfer may in turn transfer into the macroscopic morphology, rendering the formation of hierarchically chiral structures in tissues or organs. It is true of fibrous tissues for paper-making, and it is true of mammals like you and I.

Biotensegrity is basically saying the same thing, that molecules form as tensegrity structures according to simple laws of geodesic minimal-energy and close-packing, and that from this tendency we can see the helix arising as a common motif in biology. As these helices are chiral and we are bilaterally symmetrical, and the language of biotensegrity is multi-scalar, we see this helical tendency from the molecules right up through embryology into the movement patterns of our adult limbs.

I’ll be looking more closely at the everyday implications of chirality in yoga practice in my next post!

 Links:

with special thanks to Graham Scarr at
http://www.tensegrityinbiology.co.uk/ 

http://iverson.cm.utexas.edu/courses/310M/Handouts/Handoutsfl05/stereohand.html

http://www.chemistryexplained.com/Ce-Co/Chirality.html

http://phys.org/news/2015-09-long-sought-chiral-anomaly-crystalline-material.html

http://chem.libretexts.org/Core/Organic_Chemistry/Chirality/Stereoisomers/Chirality_and_Symmetry

http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=2537145

http://www.phar.cam.ac.uk/research/vanveen/research

http://www.meru.org/Posters/TetrahelixSculpture.htmlhttp://bit-player.org/2013/tetrahedra-with-a-twist

http://bobwb.tripod.com/synergetics/photos/dblhelix.html#

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