Tensegrity in Biology

This is the work of Graham Scarr D.O.  It is such a great piece of work that I had to include it this blog.  Although I try to stick to "original" work, this one is absolutely fabulous.  Very long, but worth every minute.  Enjoy! 

 
Biology

BIO-TENSEGRITY is a structural system that maintains stability by distributing mechanical forces through components that interact in just one of two different ways - attraction (tension) or repulsion (compression). Such simplicity is due to some basic laws of physics and because it is energetically efficient is likely to have developed throughout evolution to produce biological organisms of great complexity. Tensegrity systems eliminate the need for bulky elements and are lightweight structures with a high resiliency that depends on the integration of every part. It seems to be pervasive in biology and is described in the human body through molecules, cells, the extra-cellular matrix, vascular system and entire musculo-skeletal-fascial system.

Many examples of tensegrity in biology can be found but they often occur in obscure journals or are written in complicated scientific language; they are described here in the hope of making them more accessible. Most experimental work has been carried out on cells, which are essentially complete organisms, while generalizations from a 'whole-body' perspective have been reasoned from first principles or inferred from models and observation. Because tensegrity describes biological systems more thoroughly it is only a matter of time before it becomes the standard approach to bio-mechanics.

CONTENTS:

Structural hierarchies; Cellular cytoskeleton and morphogenesis; Cell cortex; Helix; Collagen; Fascial system; Cranal vault; Spider silk; Shoulder joint, elbow and pelvis; Respiratory system of the bird; Mammalian lung; Central nervous system; DNA nanostructures.

Biological structures appear to be very different to the simple tensegrity models that we make with sticks and bits of string, but they conform to the same simple rules of geodesic geometry, close-packing and symmetry, to build more complex structures (the basic principles and construction of a tensegrity structure are given on the geodesics and models pages). Physical models are usually built with components on the same size scale but the essence of bio-tensegrity is structural and functional interdependency between components at multiple size scales. One particular aspect that is often not appreciated in simple models is structural hierarchies and an example of one is shown here.

STRUCTURAL HIERARCHIES

Hierarchies are ubiquitous in biology and an inherent capability of tensegrity configurations. They provide a mechanism for efficient packing of components, the dissipation of potentially damaging stresses, and a functional connection at every level, from the simplest to the most complex, with the entire system acting as a unit. Each component in a hierarchy is made from smaller components, with each of these made from smaller still, often repeating in a fractal-like manner.

Tensegrity hierarchies achieve a significant reduction in mass and as tension always tries to reduce itself they automatically balance in the most energy-efficient configuration. Because every part influences every other part forces are distributed throughout the network and stress concentrations avoided.

The separation of tension and compression into separate components means that material properties can be optimized and these forces transferred down to a smaller scale with the elimination of damaging shear-stresses and bending moments. At atomic and molecular levels they automatically balance in the most energetically efficient configuration to form crystals and molecules which are, therefore, tensegrity structures in their own right. The forces of tension and compression always act in straight lines, but components arranged in hierarchies can give the appearance of curves at larger scales, and curves are common in biology (see definitions page).

The helix is a common motif in protein structure and a general model for coiled winding at multiple size scales throughout the body; its functional value has been demonstrated in a diverse group of organisms and is also described in relation to tensegrity (also see geodesics and helix pages).

The hierarchical arrangement of helixes in muscle shows this scaling up and links with the close-packing geometry of a myofibril.

At the nano level, tensegrity helixes describe the mechanical behaviour of the cellular cytoskeleton - a semi-autonomous structural system amenable to such analysis because of its size.

CELLULAR CYTOSKELETON AND MORPHOGENESIS

Ingber showed how the cytoskeleton behaves as a multi-functional tensegrity structure that influences cell shape and activates multiple intra-cellular signalling cascades. Within the cell, microtubules under compression are balanced by microfilaments of actin under tension with bundles of actin and spectrin fibres playing similar respective roles in the cell cortex. Intermediate filaments link them all together from the nucleus to the cell membrane so that any change in force at one part of the structure causes the entire cytoskeleton to alter cell shape. Tension is generated through the action of actomyosin motors and polymerization of microtubules.

Many enzymes and substrates are immobilized on the cytoskeletal lattice and mediate critical metabolic functions including glycolysis, protein synthesis and messenger RNA transcription. DNA replication and transcription are also carried out on nuclear scaffolds that are continuous with the rest of the cytoskeleton. Changes in the cytoskeleton and cell shape thus alter cellular biochemistry leading to a switch between different functional states such as growth, differentiation or apoptosis.

Experiments that allowed individual cells to assume certain shapes showed that those able to distort or spread had the highest rates of growth; rounded cells became apoptotic (died) while those intermediate in shape became quiescent and differentiated. Cells also tend to extend new motile processes (lamellipodia and filopodia) on sharp corners rather than blunt ones and this is linked with the cytoskeleton.

The cytoskeleton connects to the extracellular matrix (ECM) and other cells through adhesion molecules such as integrins and cadherins, respectively. These transmembrane proteins create a mechanical coupling that transfers tension generated within the cytoskeleton to the ECM and adjacent cells. Because a prestressed state of tension exists between them, so a change in ECM tension also causes a realignment of structures within the cytoplasm and a change in cell function; this process is known as mechanotransduction.

Integrins act as strain gauges that respond to changes in tension on both sides of the membrane and their ativation promotes the binding of proteins such as talin, vinculin, alpha-actinin, paxillin and zyxin. These physically link them to contractile actin bundles ('stress fibres') in the cytoskeleton and form part of a specialized complex called a 'focal adhesion'.

The transfer of tension from the ECM stimulates actomyosin tension generation, causing an increase in integrin binding and clustering, and the recruitment of more focal adhesion proteins that balance the ECM tension. Force transfer is also transmitted via the cytoskeleton to other focal adhesions and integrins, stress-sensitive ion channels, cadherins, caveolae, primary cilia and nuclear structures etc.

The attachment of fibronectin molecules (ECM) to the outside of certain integrins (alpha-5-beta-1) is what stimulates a reorganization of actin in the cytoskeleton and the accumulation of focal adhesions to the area. Changes in tension then feed back to cause unfolding of the fibronectin molecule and exposure of cryptic sites within it that lead to fibrillogenesis of itself and ultimately of collagen. The spacing of fibronectin nanofibrils on the outside of the membrane is proportional to the spacing of cross-linked actin bundles in the cytoskeleton and the cell is thus able to maintain tight regulatory control over collagen morphogenesis.

During embryogenesis, tension generated in the cytoskeleton is transferable to the ECM, and changes in matrix tension cause a realignment of structures within the cytoplasm and a change in cell function. Consequently changes in enzymatic activity produce local and regional variations in the compliance of the basal membrane and cells adhering to these regions then distort more than neighbouring cells. Mitogen stimulation can then lead to the development of more complex tissue patterns such as budding, branching (alveoli) and tubular structures (capillaries) or produce motile cells that are able to migrate(epithelial-mesenchymal transition).

Branching can create a pattern similar to the 'Koch snowflake' fractal and it has been suggested that the position of coronary artery lesions around the heart follows a pattern related to the Fibonacci sequence and Golden Mean, maximising perfusion of the myocardial bed.Gibson Simple geometry seems to get everywhere.



If the reciprocal transfer of mechanical forces between the cytoskeleton and extracellular matrix orchestrates cellular growth and expansion, it is likely that complex multi-cellular tissue patterns can emerge based on the same principles, and continuity of the extracellular matrix with the fascia could extend this throughout the entire body. Levin and Ingber have both proposed this as a tensegrity configuration but it is not universally accepted as yet; however, new developments in computer modelling confirm the relevance of tensegrity to the cytoskeleton  and multi-cellular systems.

CELL CORTEX


The cellular cortex (cortical cytoskeleton) lying just beneath the cell membrane can be considered as many tensegrity units within a geodesic dome and has been modelled around an icosahedron. It is essentially made from triangulated hexagons of the helical protein spectrin (tension) coupled to underlying bundles of the helical protein actin (which in this case are under compression). The network is organized into ~33,000 repeating units, each with a short central actin protofilament, linked by 6 spectrin filaments to a lipid-bound suspension complex (model). About 85% of these units appear as hexagons, with ~3% pentagons and ~8% heptagons, which suggests that the hexagonal arrangement is a biological preference (see the geodesic page).

The erythrocyte with a diameter of 8um has a composite membrane that distorts as it flows through smaller capillaries but allows the cell to recover its biconcave shape. Deformation of the membrane network may cause turbining of the actin protofilaments through the suspension mechanism thereby facilitating oxygen transfer from one side of the membrane to the other. The membrane is itself a bilayered structure of phospholipid molecules with outer heads under tension separated by hydrophobic tails under compression (see 'spheres' on the geodesics page).

THE HELIX

The helix is a common motif in protein construction and creates a general model for coiled winding in many other structures throughout the body; it has links to tensegrity through a common origin in the geodesic geometry of the platonic solids (see geodesic and helix pages). Helical molecules behave as tensegrity structures in their own right as they naturally stabilize through a balance between the forces of attraction (tension) and repulsion (compression). Globular proteins contain multiple helical domains and can themselves polymerize into larger helixes such as those in the cytoskeleton. Similar helixes can form hierarchies as they wind around each other to form coiled-coils (eg. spectrin) or assemble into mechanically rigid rods or filaments, or further combine into more complex structures with specialized functions (eg. collagens). Collagens are major structural proteins that consist of several hierachical levels of helixes within bone, tendon, ligaments and fascia.

Axial stretching or compression of a helix initiates rotation in a direction that depends on the direction of twist or chirality. Linking it to another one surrounding it with opposite chirality causes resistance as each helical layer counteracts the rotation of the other. Crossed-fibres of collagen scale up to form tubular helixes in the walls of blood vessels, the urinary system and intestinal tract and influence their mechanical properties. Elastic arteries such as the aorta have walls organized into lamellar units with collagen reinforcement and smooth muscle cells that form crossed-helixes with an orientation of 55o. It is likely that wall components under tension contain sub-structures under compression at a different hierarchical level, and vice versa.

Capillary formation results from tension-dependent interactions between endothelial cells and an extra-cellular scaffold of their own construction and these cells form a selective barrier that allows vascular contents to pass out between capillary walls. The internal cellular cytoskeleton determines cell shape and orientation through tensegrity, is affected by signalling mechanisms and variations in fluid flow, and alters the tension between cells through adherens junctions, ultimately affecting tube permeability. This compares with the wall of a helical tensegrity model that has many gaps but if the struts could be expanded into plates that just touched each other they could be made to 'seal' the internal space; just like the capillary cells.

An optimum helical angle of ~55o balances longitudinal and circumferential stresses and helical fibre arrays allow pressurized tubes to bend smoothly without kinking and resist torsional deformation. Cardiac muscle fibre orientation varies linearly between inner and outer walls, from 55o in one direction to 55o in the other, with tangential spiralling in a transverse plane. The heart is a helical coil of muscle that contracts with left and right-handed twisting motions, and a simple tensegrity pump that may have relevance to cardiac dynamics has also been described using the 'jitterbug' mechanism.

Similar helixes form hierarchical 'tubes within tubes' in fascia and permeate and surround the muscles, limbs and body walls of a huge variety of species, all considered through tensegrity (see helix page). Tubular organs that maintain constant volume throughout changes in shape have been described in the tongues of mammals and lizards, the arms and tentacles of cephalopods and the trunks of elephants. The arrangement of scales in the pangolin and snake illustrate the helix at the macro level although notice how the orientations of left and right-handed helixes on the body are different in the limbs; the pattern in the limbs may be related to the Fibonacci sequence (see geodesics page). The thoraco-lumbar and abdominal fasciae also have a spiral appearance, if only in part, and helical fascial sheaths that transfer tensional forces within and between themselves have been described in controlling movement in a way that the nervous system is incapable of. Fascial tissues are also reinforced by two helical crossed-ply sets of collagen with the 'ideal' resting fibre orientation of 55o (axial) that varies with changing muscle length.

COLLAGEN


Bones, tendons, ligaments and fascia are all arranged in hierarchies with collagen the most widespread of all structural proteins appearing at several different levels. In collagen type I repeating sequences of amino acids spontaneously form a left-handed helix of procollagen with three of these combining to form a right-handed tropocollagen molecule. Five tropocollagen molecules then coil in a staggered helical array, that lengthens longitudinally by the addition of more tropocollagen to form a microfibril, and pack radially to form a fibril; with higher arrangements forming fibres and then fascicles. (see helix page).

The collagen molecule exists in many different configurations and is a major component of the extracellular matrix (ECM) that surrounds virtually every cell. The matrix attaches to the cellular cytoskeleton through adhesion molecules in the cell membrane and forms a structural framework that extends through the fascia to every level in the body.

FASCIAL SYSTEM

Traditionally considered as mere packing tissue fascia has been show to exert considerable influence over muscle generated force transmission. It naturally develops into compartments, or 'tubes within tubes', particularly noticeable in cross-sections of the limbs. Within muscle a delicate network of endomysium surrounds individual muscle fibres and is continuous with the perimysium ensheathing groups of fibres in parallel bundles, or fasciculi. Perimysial septa are themselves inward extensions of the epimysium, which covers the muscle and is continuous with the fascia investing whole muscle groups. These fascial tissues are reinforced by two helical crossed-ply sets of collagen with the 'ideal' resting fibre orientation of 55o (axial) that varies with changing muscle length (see helix page).

The fascial system has been described as a tensegrity system which might seem rather strange initially because there dont appear to be any compression struts. The extracellular matrix/fascial system is a complex biological hierarchy which means that it is likely to be different to simple models. As tension and compression always occur together it must have structures under tension and others under compression.

Considering a sheet of tensioned fascia between two bones, or even both ends of the same bone, any two points along that tension line (x,y) will be separated by a pull from either end. The points are held apart by tension but as one of the functions of a 'strut' is to hold two points apart (nodes) the tissue between them is behaving as such to other parts lower down in a tensegrity hierarchy. Collagen and proteoglycans probably interact in a tensegrity way at the nano level. Fascia could thus be considered as a network of tensioned cables and [virtual] 'struts' but only if it is part of a larger tensegrity system that includes 'real' struts such as bones at a higher level. The basic tensegrity principles remain the same but the description starts to become a bit more complex (see definitions page).

At the macro level,bones (struts) are compressed by muscles and fascia under tension. Muscles are cables that generate axial tension on contraction, but the resulting changes in their diameter also make them variable length compression struts perpendicular to this, which probably contributes to the tension in associated fascia and force appearing at tendons. The balance of ‘agonist/antagonist’ muscle tensions has also been shown to reduce stress concentrations in long bones (bending stresses) making them compatible with the resiliency required of tensegrity struts.

Guimberteau described a 'microvacuolar' system that allows sliding between different tissues throughout the body as the basic network of tissue organization. These microvacuoles are collagen envlopes containing proteoglycans and "histological continuum without any clear separation" was observed between fascia, skin, muscles and vasculature; sounds remarkably like a tensegrity.

THE HUMAN CRANIUM

Many aspects of normal cranial development are poorly understood, with some previously held views now outdated, but a tensegrity model can explain some of these and improve understanding of normal and abnormal development. A more detailed explanation is given on the cranial vault page.

The skull is generally considered to be a solid box but is actually made up of 22 bones most of which remain distinct throughout life; several of these bones contribute to the cranial vault that covers and protects the brain. The sutural spaces between the bones are filled with fibrous tissue and are important to the mechanism that allows the cranium to grow larger and accommodate the developing brain. A tough membrane called the dura mater lines the internal surface of the bones. Until recently the general opinion was that the growing brain pushes the bones outwards but this is now known not to be the case; an increase in dural mater tension does stimulate bone growth but the mechanism is much more complex than previously thought and better explained through tensegrity.



The geodesic dome (icosahedron) is developed into a tensegrity model (T6-sphere) with the struts connecting opposite vertices. The straight struts are then replaced with curved struts and these are replaced with curved plates (not shown) to produce the model skull with bones that surround a central space. The bones of the cranial vault are tensioned by the dura mater (elastic cord in model) and configured as a tensegrity structure. The curved struts are at the top of a bone hierarchy (at least seven different levels within bone) that extends down to the molecular level (see definitions page).



Adult bones are separated by a sutural gap of about 100 microns and have curved outlines with a fractal relationship between them. Dural membrane (tension cords) attached to the peaks of bone convexities, and the alignment of collagen fibres in sutures, cause adjacent bones to be pushed apart as they form the tensegrity structure. (see definitions page).



The vault bones develop totally within membrane which they separate into an outer periosteum and inner dura mater membrane as they grow around their edges (bone fronts). Tension in the dural membrane beneath the sutures, combined with chemical signals from the osteoblasts (bone-making cells) at the bone fronts, influence the cytoskeleton of epithelial cells in the membrane beneath the suture through the process of mechanotransduction, and change cell activity that results in further bone growth. It is a cyclic mechanism that regulates bone growth and maintains sutural patency up until at least seven years of age (when the brain stops growing). Even after this age the sutures should remain patent and may contribute to the small amounts of bone mobility recognized by 'cranial' osteopaths and 'cranio-sacral' therapists.



The bones form a dome that provides protection to the brain, compression struts of a tensegrity structure that maintains sutural flexibility and accomodates brain growth, and a microstructure that transfers external forces down through a hierarchy to the nano-scale. The centre of the bone is a honeycomb like structure made from collagen and mineral reinforcement. Curved-strut plates are still compatible with tensegrity when considered in terms of hierarchies because the forces of tension and compression ultimately act in straight lines at some smaller scale.

A tensegrity configuration allows the skull to enlarge and remain one step in front of the growing brain rather than being pushed out by it. It also allows the skull to respond to the mechanical demands of external muscular and fascial structures and integrates the entire cranium. The dural membrane also reduplicates into four sheets that penetrate the cranial cavity (falx cerebri and cerebellum and two halves of the tentorium cerebelli). Abnormalities in the cranial base may alter the tension pattern in these sheets and cause the sutural/dural mechanism to behave differently, leading to premature sutural fusion in babies (craniosynostosis) and malformation in head shape (plagiocephaly).



SPIDER SILK

Spider silk can be considered as a tensegrity structure with some similarities to fascia. It is a composite material with a hierarchical structure composed mainly of the proteins Spidroin I and II. Spidroin I consists of poly-alanine chains in anti-parallel beta-sheet conformation packed into an orthorhombic crystallite unit. These crystallites are interconnected by helical oligopeptides rich in glycine that form a polypeptide chain network within an amorphous glycine-rich matrix. The overall network shape is circular segments (40-80 nm diameters) interconnecting in series to form a silk fibril with many of these arranged laterally to form the silk thread with a diameter of 4-5 microns. It is the regular spacing and orientation of these crystallite units and hierarchical structure that suggests that it is a tensegrity structure.

An analogy can be made between a spiders web and the spoked bicycle wheel where cable tension is balanced by compression within the rim and central hub. If the cables were relatively elastic the central hub could be moved around always returning to the same position of stable equilibrium. The multiple hubs in the second model could also be reduced so that they looked like single nodes between crossing cables (although under a microscope they would appear unchanged). The common spider web is made from silk woven into a configuration of radial and spiral tension cables attached to a gate post and tree. These latter form a single compression element connected through the ground like the rim of the bicycle wheel. Each of the connecting nodes between cables represents one of many ‘hubs’ that can be displaced within the elastic tension network but that always returns to the same position of stable equilibrium, one of the conditions of tensegrity. However these examples of the bicycle wheel and spiders web should probably be considered as on the limit of 'tensegrity' (see definitions page).

THE BICYCLE WHEEL AND SHOULDER JOINT

Levin was the first to describe the higher complexities of the human body in terms of tensegrity using the analogy of a bicycle wheel. Here the outer rim and central hub are considered as compression elements held in place by a network of wire spokes in reciprocal tension. This type of wheel is a self-contained entity maintained in perfect balance throughout with no bending moments or torque, no fulcrum of action, and no levers. He suggested that the scapula functions as the hub of such a wheel, in effect as a sesamoid bone, and transfers its load to the axial skeleton through muscular and fascial attachments. The sterno-clavicular joint is not really in a position to accept much compressional load and the transfer of axial compression across the gleno-humeral joint is at maximum only when loaded at 90o abduction. The joint is essentially a frictionless inclined plane which means that it must rely heavily on ligamentous and muscular tension in all other positions. The humerus as a hub model would function equally well with the arm in any position. Interestingly, different parts of the gleno-humeral capsule that transfer specific tensional stresses can only do so if the capsule is intact, even if those stresses do not apparently pass through the missing parts (this would make sense if the capsule is a tensegrity sheet at a microscopic level).

In a similar way the ulna could be likened to a hub within the distal humeral ‘rim’ of muscle attachments, where load bearing across the joint may be significantly tensional and allow compressional forces to be distributed through a tensioned network and the hand to lift loads much larger than would otherwise be the case (see the elbow page).

The pelvis is also like a wheel, with the iliac crests, anterior spines, pubis and ischia representing the outer rim and the sacrum representing the hub tied in with strong sacro-iliac, sacro-tuberous and sacro-spinous ligaments. Similarly the femoral heads may act like hubs within the ‘spokes’ of the ilio-femoral, pubo-femoral and ischio-femoral ligaments.

'Hinge' joints in the skeleton are very different to those in man-made structures. A standard door hinge has metal plates screwed to the door and fram, with one side of each plate bending around a central metal rod. The rod holds the door part of the hinge to the frame part and is compressed between them as the door swings. Most skeletal joint movements display helicoid motion around a variable fulcrum and in the knee joint it has been shown that there is no continuous compression between bones and cartilage, even when they are pushed together.  A tensegrity ‘hinge’ joint in a biological context doesn’t need a single compression element to carry the entire load and the tensegrity arm models clearly shows these features (see the elbow page for more anatomical details).



The body is made of many joints and they are all linked together through the fascial system. Theo Janssen is a Dutch artist who has linked multiple joint units so that they can walk; a comparison with the human locomotor system seems inevitable. A Janssen mechanism is a structure made of parts with specific lengths according to a precise formula so that they can move as a single entity.

The second model is a multi-joint tensegrity based on the same mechanism with each joint modelled with the six struts of a T6-sphere. Some of the struts are elongated so that they become parts of two of these joints. The rotation then produces the same relative motion and interactions although it needs a bit more head scratching to work out which parts are pushing and pulling during the movement. The long thin struts between the 'joints' are substructures in a hierarchy where the next level above is comparable to the metal plates of the original TJ mechanism. Apart from the fixings to the wooden block there are no fixed fulcrums, levers, or moments of inertia in this model. This model shows how the movement of a tensegrity joint can cause other joints to move passively at a basic level and that muscles just refine that movement further down the chain as a higher active level of control. We can separate passive and active components in models but in biology they are often inseparable. This model still has a long way to go but it is one more step.

According to Wolff’s law, tensional forces remodel the bony contours and alter the positions and orientations of their attachments, contributing to the complexity of shapes apparent in the skeleton. As part of a tensegrity structure each attachment would influence all the others, distributing forces throughout the system and avoiding points of potential weakness, in contrast to a rod or truss which is vulnerable to buckling. Such a mechanism would be an advantage in long-necked animals such as giraffes, camels and dinosaurs, where the load from the head is distributed throughout the neck, as opposed to a stress-ridden cantilever system such as the Forth Bridge.

The erect spine and bipedal weight bearing capability of humans has traditionally been viewed as a tower of bricks and compressed disc joints that transfer the body weight down through each segment until it reaches the sacrum; but a vertical spine is a relatively rarity amongst vertebrates. Most other species have little or no use for a compressive vertebral column which is frequently portrayed as a horizontal truss and cantilever support system. As the main difference in vertebrate anatomies is in the detail it seems reasonable to suppose that they have some structural properties in common. Tensegrities are omni-directional ie. they are stable irrespective of the direction of loading, and the spine, pelvis and shoulder all demonstrate this property (within physiological limits), enabling dancers to tip-toe on one leg and acrobats to balance on one hand.

RESPIRATORY SYSTEM OF THE BIRD

The respiratory system of the bird differs substantially from the mammalian lung; it is an exceptionally efficient gas exchanger that processes the large amounts of oxygen required to sustain flight. Some of the reasons for this are considered to be its geodesic design and hierarchical tensegrity arrangement that mechanically couples each part into a functionally unified structure. The volume of the bird lung is about 27% less than that of a mammal of similar body mass although the respiratory surface area is about 15% greater. The lung is attached to a rigid ribcage and its volume changes relatively little during a respiratory cycle (1.4%); instead, separate air sacs act like bellows and cause unidirectional and continuous ventilation. The air passages of the lung have a hierarchical arrangement with two-thirds of the lung volume taken up with several hundred parabronchi; their polygonal atrial openings each give rise to several funnel shape ducts (infundibulae) that terminate in numerous air capillaries, the terminal respiratory units (fig. ?). Both blood and air capillaries anastomose and interdigitate to form a tightly packaged three-dimensional network.

The parabronchi develop from epithelial cells that are compressed due to space restraint and naturally form hexagons with lumens that enlarge during development (fig. ?). This geodesic packing arrangement persists into the adult and makes the most economical utilization of space, thus maximizing the potential respiratory surface area. The constitutive parts of the parabronchus act together to function as an integrated unit that prevents the air capillaries from collapsing under compression and blood capillaries from distending with over-perfusion; mechanically, it is rather similar to the tensegrity bicycle wheel described in chapter 2.

Intertwined smooth muscle bundles and collagenous tissue surround the atrial openings into the central lumen and form a complex helical arrangement. The collagen forms an intricate system of longitudinal, transverse and oblique fibres that connect to elastic fibres in the interatrial septa and floor of each atrium, and continue as the interfundibula septa that eventually becomes the basement membrane surrounding the exchange tissues. The smooth muscle, collagen and elastic fibres surrounding the atrial openings form an internal parabronchial column that lies next to the lumen (fig. ?). The collagenous septa and exchange tissues are also continuous with the interparabronchial septa that enclose the walls of larger blood vessels and form an external parabronchial column. The exchange tissues and associated septa are thus suspended between the internal and external parabronchial columns like the spokes in a bicycle wheel.

Contraction of smooth muscles around the atrium tenses the interatrial and interfundibula septae and stretches the elastic fibres, with collagen limiting their stretchability; the elastic fibres then act as energy-storage elements and recoil when the muscles relax. The interatrial, interfundibula and interparabronchial septa thus balance the centripetal force produced by contraction of the smooth muscle. An outward centrifugal force is also produced, by surface tension generated within the air capillaries and the prevailing intramural pressure in the interparabronchial arteries, and this is balanced by the elastic and inflexible collagen fibres. The parabronchus thus exists in a dynamically tensed state, with the inward pull of the atrial smooth muscles (internal column/wheel hub) ultimately counterbalanced by the interparabronchial septa (external column/wheel rim) and surrounding parabronchi. The morphology of the parabronchus and its constitutive parts thus fits every definition of a tensegrity structure.



MAMMALIAN LUNG ALVEOLI

The matrix surrounding alveoli is considered to be a tensegrity structure. “The septa between alveoli are very thin and contain a single dense capillary network. They are supported by a fine network of fibres that are interwoven with the capillaries and anchored at both ends in axial fibres that form the network of alveolar entrance rings in the wall of alveolar ducts; and peripheral fibres that extend through interlobular septa towards the pleura. This allows the spreading of the capillaries by mechanical tension on the fibres. Because of this disposition of capillaries and fibres, alveoli in the mature lung are not structural units that can be separated: each of their walls is shared by two adjoining alveoli, both in terms of gas exchange with the capillary and with respect to mechanical support. Even the epithelial lining is shared by two adjacent alveoli as it extends through the pores of Kohn... This disposition of the fibre system makes the lung a tensegrity structure, which means that, in terms of mechanics, the integrity of lung parenchymal structure is exclusively ensured by the tension of the fibre continuum that supports alveolar walls and their capillaries. If one fibre is cut, this causes collapse of the septum followed by rearrangement of the adjacent parts, as occurs in emphysema.

THE CENTRAL NERVOUS SYSTEM

It may be that a tensegrity mechanism is responsible for morphogenesis of the central nervous system, based on some particular characteristics of developing neurites and anatomy of the cerebral cortex. Tension along axons in the white matter is considered to be the primary driving force for cortical folding and is counterbalanced by hydrostatic and growth-generated pressures.

When neurites are transiently stretched, their length increases in proportion to the applied tension, indicating simple elastic behaviour. Under sustained stretching, however, they display visco-elastic properties as the initially elevated tension passively relaxes to a lower level over a period of minutes. Active elongation occurs when tension is maintained above a threshold level and active retraction occurs when tension is fully released. Collectively these passive and active mechanical properties allow neurites to adjust their length by a negative feedback mechanism that tends to maintain a steady tension, much as a fishing line is reeled in or out to regulate tension on the line.

Early in development, neurons migrate to the cortical plate along radial glial cells, differentiate and emanate axons that reach specific target structures. Many structures have pronounced anisotropies in the orientation of axons, dendrites and glial processes; and are under tension. Consequently tissue elasticity will vary in different directions and expansion will occur preferentially in the direction with the greatest compliance, generally perpendicular to the main fibre axis.

The trajectories of long-distance processes arising or terminating in a given region of the cerebral cortex are biased towards one side as they enter and leave exclusively through the underlying white matter. During cerebral growth collective axon tension pulls strongly interconnected regions towards one another (conjoining arrows), forming outward folds (gyri) and allowing weakly connected regions to drift apart and form inward folds (sulci). Consequently cortical cell layers vary in thickness beneath gyri and sulci (similar to the effect of folding a paperback book).

DNA NANOSTRUCTURES

The self-assembly of three-dimensional tensegrity nanostructures of the simplest 3-strut tensegrity model and platonic solids is now possible using single and double strands of synthetic DNA. They confirm that the tensegrity concept can realistically be applied to the evolutionary development of biological structures.