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    Nature Loves A Straight Line: Geodesics In Biology
    By Stephanie Pulford | January 19th 2009 04:29 PM | 7 comments | Print | E-mail | Track Comments
    About Stephanie

    As engineering grad student at UCDavis, I am interested in the common ground between biology and machinery. Incidentally, my column's title refers...

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    My elementary school art teacher used to discourage the use of rulers, claiming that “there are no straight lines in nature”.  Mr. Dugan, your own cells are here to tell you it’s not true.  Systems of taut fibers and light struts— as straight as the bars and chains of a swingset—are omnipresent in biological forms.

    These organic analogs to popsicle sticks and rubber bands often occur in interwoven networks reminiscent of the geodesic domes that Buckminster Fuller promoted in the 1950’s.  Since form follows function, it’s hardly surprising that these natural geodesics offer the same benefits in nature that they do in architecture: high strength, dynamic stability, and material frugality.  

    Buckminster Fuller loved portmanteau words.  He referred to his domes’ structural strategy as “tensegrity”, the marriage of tension and structural integrity.  We often associate structural integrity with built-up, heavy structures intended to stand up to compressive loads, such as the massive concrete pillars that support the historic Fern Bridge.  Compare this to the spindly but no less stable design of the historic Folsom Truss bridge.  It’s easier to bend a thin metal bar than a concrete column, but the design of a truss eliminates any bending, shearing, or twisting forces.  This leaves thin metal members to do what they do best—resist forces that push and pull them in the direction of their length.  
    Left: The Fern Bridge, built in 1911 in the Eel River Valley, CA, uses concrete in a complex state of compression to maintain its stability. Image credit: sunnyfortuna.com.  Right: The Folsom Truss Bridge, built in 1895 in Folsom, CA, uses lightweight members exclusively in simple tension and compression. Image credit: myfolsom.com.

    The triangular network of the Folsom bridge is a common motif in both manmade and evolutionary engineering.  The reason for this pervasiveness is simply that the triangle is a very stable structure.  It’s a heck of a lot easier to build a house of cards out of triangles than rectangles. Geodesic structures, such as Bucky’s domes and the human spine, are a special set of trusses that create curved forms from straight line segments. Some, like the trabeculae of human bones, echo the rigid structure of a manmade truss in order to create lightweight stiffness.  But if frequency is any indication, nature’s best use for geodesic forms is in applications where stiffness is undesirable.

    In lieu of hard bones, soft invertebrates such as nematodes use a “hydrostatic” skeleton.  Muscles and skin contain their largely fluidic innards at a high pressure, like a water balloon.  But unlike a water balloon, nematodes change their shape.  They are capable of feats of extension, narrowing, and locomotion far more complex than their musculature dictates.   

    Recently in The Journal of Experimental Biology, Robert Shadwick discussed Clark and Cowey’s 1958 study revealing the role of inextensible collagen fibers in nemerteans and turbullarians.  Their musculature is complemented by a lattice-like helical network of fibers resembling the form of a Chinese finger trap in both form and function.   If a wormlike creature’s muscles contract its diameter, this fiber lattice reacts to extend the worm’s length. This breakthrough inspired a breadth of new discoveries in zoological morphology.  Similar fibrous networks are being found in a wide array of applications, including elephant trunks, fish skin, lizard tongues, and even the human penis. 

    Cells are also squishy things in need of structure, and their cytoskeleton includes a tensile network of actin fibers that looks suspiciously like Disneyland’s Spaceship Earth dome. Researchers such as Donald Ingber of MIT are showing that this geodesic array does more than reinforce the cell’s shape. Ingber’s work focuses on the coupling of the cell’s force sensors (“mechanotransducers”) to its tensile fiber network. 

    When an event causes a cell to adhere to its surroundings, force changes in the cytoskeleton delivers a message to the cell. We are just beginning to understand that the cell reacts to mechanical signals like in dramatic ways;  cellular forces dictate cell migration, instigate healing, and even trigger chromosomal events.  Researchers are betting that understanding the structural underpinnings of bodily cells might lead to breakthroughs in the treatment of cancer, athsma, osteoporosis, wounds, and other human maladies.  

    Though it never caught fire as a housing concept, “tensegrity” is experiencing its second coming as a scientific buzzword. Buckminster Fuller might be cheered today to know that  our every tissue represents a sprawling neighborhood of cellular geodesic dome-dwellers, showing nature’s endorsement of a great design strategy.      

    Levin, S.  The Tensegrity-Truss As A Model For Spine Mechanics: Biotensegrity.  Journal of Mechanics in Medicine and Biology, 2003.  2: 375-388

    Shadwick, RE.  Foundations of Animal Hydraulics: Geodesic Fibres Control The Shape Of Soft Bodied Animals.  J Exp Biol, 2008. 211: 289-291

    Kier, W.M. and Smith, K.K. Tongues, tentacles and trunks: The biomechanics of movement in muscular-hydrostats. Zoological Journal of the Linnean Society , 1985. 83: 307-324.

    Hebrank, MR. Mechanical properties and locomoter functions of eel skin.  Biology Bulletin, 1980.  158:56-58.

    Kelly, D. Penises as variable-volume hydrostatic skeletons. Annals of the New York Academy of Sciences, Reproductive Biomechanics, 2007. 1101(1), 453-463.

    Ingber, DE. Tensegrity I. Cell structure and hierarchical systems biology. Journal of  Cell Science, 2003. 116: 1157-1173 (2003).

    Ingber DE. Tensegrity and mechanotransduction. Journal of Bodywork and Movement Therapies, 2008. 12(3) 198-200.


    Great article. Relating cellular structures to bridges is a nice way to make your point.

    There is a lot of talk about applying engineering principles to biology, but, at least at the universities where I've worked, traditional biologists and engineers don't get much of a chance to talk to each other. I'm looking forward to hearing more.
    Stephanie Pulford
    Thanks, Michael!  I'm also hoping that the invisible wall between life sciences and engineering is going to be eroded soon.  It seems to me that the two fields could learn a lot from one another.  Thankfully, my university (UCDavis) does a pretty good job of promoting biology/physics cross-talk (which is partly why I chose it). 
    BIOMIMETICS is up and jumping at the University of Bath.  Their research is headed by Julian Vincent, whom we used to know at Reading, until he went to Bath about fifteen years ago (reminds me of Jane Austen's Persuasion!)

    He is an example of biology and engineering in one person, and my own encounter with him was when he came over to our group to use our Differential Scanning Calorimeter to study the self-tanning of insect cuticle.  To be more precise, as it turns into a pupa, proteins in the soft skin of the maggot crosslink with tannic acids, a bit like the curing of an epoxy resin.

    Biomimetics is forging ahead, and you can see some of things they are now getting up to at Bath.

    For background to the subject, I recommend Julian Vincent's book Structural Biomaterials.
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Stephanie Pulford
    That's some interesting research!  How did he and your group use a differential scanning calorimeter in that study?
    Thanks for the links and the book recommendation, Robert.  Being sort of a structures nerd, I'll definitely check out the book.  
    How did he and your group use a differential scanning calorimeter in that study?
    He was looking at the freezing point of water in the system, as a function of tanning.  Here is probably the most up-to-date paper on this work (our library doesn't take either of the references I'm about to cite.)

    Author(s): VINCENT JFV, ABLETT S
    Source: JOURNAL OF INSECT PHYSIOLOGY    Volume: 33    Issue: 12    Pages: 973-979    Published: 1987  

    No abstract, I'm afraid.  This much more recent one looks interesting:

    Deconstructing the design of a biological material
    Author(s): Vincent JFV
    Department of Mechanical Engineering, Centre for Biomimetic and Natural Technologies, The University of Bath, Claverton Down, Bath, BA2 7AY, UK
    Source: JOURNAL OF THEORETICAL BIOLOGY    Volume: 236    Issue: 1    Pages: 73-78    Published: SEP 7 2005  

    Abstract : By identifying the functional conflicts in its design, the cuticle of arthropods can be shown to cope with IR and UV irradiation in the same manner as our technology—by controlling spectral properties (transmission and reflection). However, the skeletal properties of cuticle are integrated with demands for sensory transmission, movement, etc, by controlling the local properties of the material rather than by changing global parameters (which would be the technical solution). On the basis of this study, the biomimetic similarity of cuticle with technology is only about 20%, suggesting that we can learn from the design of arthropod cuticle.

    1. Introduction
    2. Conflict resolution
    3. Functions of arthropod cuticle: 3.1. Stiff skeleton: 3.2. Waterproofing: 3.3. Protection from heat/radiation
    4. Discussion

    (which is as much as I have access to.)

    Here, however, are three papers of his in Nature:

     1.     Title: How pine cones open
    Author(s): Dawson J, Vincent JFV, Rocca AM
    Source: NATURE   Volume: 390   Issue: 6661   Pages: 668-668   Published: DEC 25 1997
     2.     Title: CUTICLE UNDER ATTACK
    Author(s): VINCENT JFV
    Source: NATURE   Volume: 273   Issue: 5661   Pages: 339-340   Published: 1978
    Author(s): VINCENT JFV, WOOD SDE
    Source: NATURE   Volume: 235   Issue: 5334   Pages: 167-&   Published: 1972
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    I had a highschool teacher say a similar thing, "There are no straight lines in nature." HA! Any common quartz xtal reveals the lie of such statements. Must be why I became a geologist.

    Geodesics are curved on a curved surface, such as the sphere and the hypersphere in the picture below.  See how the angles of the triangles on the sphere add up to >180°, and <180° on the hyperbolic plane.

    (adapted from Wikipedia "geodesic" and "hyperbolic geometry".)

    They're also curved in curved space, which with why people do all those "bent basketball net" pictures to illustrate black holes.
    Robert H. Olley / Quondam Physics Department / University of Reading / England