Rotating locomotion in living systems

A wagon wheel
A passive wheel

Rotating locomotion encompasses two distinct modes of locomotion: simple rolling, and spinning relative to a fixed axle or body, in the manner of a wheel or propeller. Several organisms move by rolling, however, despite the integral role that the wheel has played in locomotion of vehicles designed by humans, true wheels do not appear to play any role in the locomotion of biological systems. The reasons for this apparent lack of biological wheels have been expounded on by biologists,[1][2] and wheeled creatures have appeared in numerous works of speculative fiction.[3][4]

Given the apparent utility of the wheel in human technology, and the existence of biological analogues of many other human technologies (such as wings and lenses), it might seem odd that a true wheel has never evolved naturally, but this lack of biological wheels is typically explained by two main factors: first, there are several developmental and evolutionary obstacles to the evolution of a wheel by natural selection, and secondly, wheels often do not carry a competitive advantage over other means of propulsion (such as walking, running, or slithering) in the environments in which ambulatory species have evolved.[5] (The latter factor also explains why wheels have not found use in some human civilizations, despite those civilizations' awareness of the wheel.)[6]

This article begins by examining existing instances of rolling and wheel-like motion in natural biology. Next, the constraints on wheeled motion imposed by evolution and by the nature of biological development are discussed, addressing the question, "Why can't a true wheel evolve?" This is followed by a summary of the disadvantages of wheels when compared with limbed locomotion, addressing the question, "If wheels could evolve, why would they be unlikely to do so?" Finally, examples of rotating locomotion in fiction and legend are presented.

Rotation in biology

Rolling

A curled-up pangolin
The pangolin Manis temminckii in a defensive position

Some organisms use rolling as a means of locomotion. These examples do not constitute the use of a wheel, as the entire organism rotates itself, with no fixed axle.[7][8]

Several species of elongate organisms will form their body into a loop in order to roll, including caterpillars, myriapods, mantis shrimp, and salamanders,[5][7][9] while other species adopt more spherical postures, as in pangolins, hedgehogs, armadillos, the armadillo Lizard, isopods, the wheel spider, and fossilized trilobites.[9][10] These species may roll passively (under the influence of gravity or wind) or actively, typically by altering their shape to generate a propulsive force.[9]

Alternatives to whole-body rolling include the tumbleweed, which breaks off the above-ground portion of the plant and uses wind-powered rolling to distribute the seeds, and "roller" dung beetles. Dung beetles are unique in that the ball of fecal matter rolls, rather than the beetle itself, though it still faces many of the same mechanical difficulties.[9]

Keratinocytes, a type of skin cell, migrate with a rolling motion during the process of wound healing.[11][12]

Although their Latin name means "wheel-bearer", rotifers do not actually possess any rotating structures, but rather a ring of rhythmically beating cilia used for feeding and propulsion.[13]

Wheel-like rotation

Though no known multicellular organism is able to spin part of its body freely relative to another part of its body, there are two known examples of rotating molecular structures used by living cells.[14] ATP synthase is an enzyme used in the process of energy storage and transfer, notably in photosynthesis and oxidative phosphorylation.[15] It bears some similarity to flagellar motors.[16] The evolution of ATP synthase is thought to be an example of modular evolution, in which two subunits with their own functions have become associated and gained a new functionality.[17]

Diagram of a bacterial flagellum
Bacterial flagellum

The only known example of a biological "wheel", a system capable of providing continuous propulsive torque about a fixed body, is the flagellum, a propeller-like tail used by single-celled prokaryotes for propulsion. The bacterial flagellum is the best known example.[6][18] About half of all known bacteria have at least one flagellum, indicating that rotation may in fact be the most common form of locomotion in living systems.[19]

At the base of the bacterial flagellum, where it enters the cell membrane, a motor protein acts as a rotary engine. The engine is powered by proton motive force, i.e., by the flow of protons (hydrogen ions) across the bacterial cell membrane due to a concentration gradient set up by the cell's metabolism. (In species of the genus Vibrio, there are two kinds of flagella, lateral and polar, and some are driven by a sodium ion pump rather than a proton pump.)[20] Flagella are quite efficient, allowing bacteria to move at speeds up to 60 cell lengths per second. The rotary motor at the base of the flagellum is similar in structure to that of ATP synthase.[14] Spirillum bacteria have helically-shaped bodies with flagella at either end, and spin about the central axis of their helical body as they move through the water.[21]

Archaea, a group of prokaryotes distinct from bacteria, also feature flagella driven by rotary motor proteins, though they are structurally and evolutionarily distinct from bacterial flagella. Whereas bacterial flagella evolved from the bacterial Type III secretion system, archaeal flagella appear to have evolved from Type IV pili.[22] Some eukaryotic cells, such as the protist Euglena, also have a flagellum, but eukaryotic flagella do not rotate at the base; rather, they bend in such a way that the tip of the flagellum whips in a circle. The eukaryotic flagellum, also called a cilium or undulipodium, is structurally and evolutionarily distinct from prokaryotic flagella.[23]

Biological barriers to wheeled organisms

Evolutionary constraints

Sketch of a fitness landscape
Sketch of a fitness landscape. The arrows indicate the preferred flow of a population on the landscape, and the points A, B, and C are local optima. Potentially beneficial changes that require descent into a fitness valley (such as movement from point A to point B) are foreclosed to populations that evolve by natural selection.

The processes of evolution, as they are presently understood, can help explain why wheeled locomotion has not evolved in multicellular organisms; simply put, a complex structure or system will not evolve if its incomplete form provides no benefit to an organism.[1][2]

According to the modern evolutionary synthesis, adaptations are produced incrementally through natural selection, so major genetic changes will usually spread within populations only if they do not decrease the fitness of individuals.[1] Although neutral changes that provide no benefit can spread through genetic drift,[24] and detrimental changes can spread under some circumstances,[25] large changes that require multiple steps will occur only if the intermediate stages increase fitness. Richard Dawkins describes this situation as follows: "The wheel may be one of those cases where the engineering solution can be seen in plain view, yet be unattainable in evolution because it lies [on] the other side of a deep valley, cutting unbridgeably across the massif of Mount Improbable."[1] In such a fitness landscape, wheels might be a highly beneficial "peak", but the valley around such a peak is too low or wide for the gene pool to move across by genetic drift or natural selection. Stephen Gould notes that biological adaptation is limited to working with available components, saying "wheels work well, but animals are debarred from building them by structural constraints inherited as an evolutionary legacy."[2]

Natural selection therefore explains why wheels have not appeared, as a wheel missing one or more of its key components would probably not impart an advantage to an organism. The same cannot, however, be said of the flagellum, the only known example of a freely rotating propulsive system in biology. In the evolution of flagella, individual components were recruited from other structures, where they performed tasks unrelated to propulsion. The basal body that is now the rotary motor might have evolved from a structure used by the bacterium to inject toxins into other cells.[26][27][28] The recruitment in evolution of existing structures to serve new functions is called exaptation.[29]

Molecular biologist Robin Holliday has written that the apparent lack of biological wheels argues against creationist or intelligent design accounts of the diversity of life—for, free of the limitations imposed by evolution, an intelligent creator would be expected to deploy wheels wherever they would be of use.[30]

Developmental and anatomical constraints

Using human manufacturing processes, wheeled systems of varying complexity have proven fairly simple to construct, and issues of power transmission and friction have proven tractable. It is not clear, however, that the vastly different processes of embryonic development are suited to—or even capable of—producing a functioning wheel, for reasons outlined below.1

The greatest anatomical impediment to wheeled multicellular organisms is the interface between the static and rotating components of the wheel. In either a passive or driven case, the wheel, or wheel and axle, must be able to rotate freely relative to the rest of the machine or organism. Unlike animal joints, which have a limited range of motion, a wheel must be able to rotate through an arbitrary angle without ever having to be "unwound". As such, a wheel cannot be permanently attached to the axle or shaft about which it rotates (or if the axle and wheel are fixed together, the axle cannot be affixed to the rest of the machine or organism).[2] No true multicellular organism is known to grow tissue or organ structures that are not attached in some way to the rest of the organism.

Power transmission

Drawing of human arm muscles
Skeletal muscle

In the case of a driven wheel, some type of torque must be applied to the axle to generate the locomotive force.2 For human-made technology, this torque is generally provided by an engine, which may be electric, turbine-driven, combustion-driven, pneumatic, hydraulic, etc. (Torque may also be provided by human power, as in the case of a bicycle.) In animals, motion is achieved by the use of skeletal muscles, which derive their energy from the metabolism of nutrients from food. Because these muscles are attached with connective tissue to both of the components which must move relative to each other, they would not be an effective means of directly driving a biological wheel. In addition, animals suffer degraded energy efficiency because their propulsive cycles employ only periodic accelerations (repeated flexion and extension of joints). Large animals cannot produce high rates of acceleration, because as animal size increases, it becomes more difficult for muscles to quickly generate high enough stress to overcome relative inertia.[31]

Friction

In typical mechanical systems, some sort of bearing and/or lubricant must be used to reduce friction at the interface between two components. Reducing friction is vital for minimizing wear on components, and preventing overheating. As the relative speed of the components increases, and as the force of contact between the components increases, the importance of friction mitigation increases as well. In biological joints such as the human knee, friction is reduced by means of cartilage with a very low friction coefficient, as well as a lubricant called synovial fluid, which has very low viscosity. Gerhard Scholtz, professor at the Institut für Biologie Vergleichende Zoologie ("Institute for Biology and Comparative Zoology") at Humboldt University of Berlin, asserts that a similar excreted lubricant or dead cellular material could allow a biological wheel to rotate freely, though such a mechanism has not been found in nature.[9] In addition, even a small imperfection, scar tissue or injury would cause the wheel to no longer rotate optimally along its axle, with the injury compounding itself with further use. In a bipedal organism injury to extremities can be overcome by adjusting body positioning, gait, etc. In a wheeled organism (if the number of wheels is limited) there is no such flexibility of adjustment and adaptability, especially if the wheel is the primary limb of propulsion.

Nutrient and waste transfer

Another potential problem that arises at the interface between wheel and axle is the ability of an organism to transfer materials across this interface. If the tissues that make up a wheel are living, they will need to be supplied with oxygen and nutrients and have wastes removed in order to sustain metabolism. A typical animal circulatory system, composed of blood vessels, would not be able to provide transportation across the interface.[1][32] In the absence of circulation, oxygen and nutrients would need to diffuse across the interface, a process that would be greatly limited by the available partial pressure and surface area, in accordance with Fick's law of diffusion.[2] For large multicellular animals, diffusion would be insufficient.[6] Alternately, a wheel could be composed of excreted, nonliving material, such as keratin, of which hair and nails are composed.[6][9], yet these are always secreted from living tissue, which would need to be in contact with circulation, oxygen, nutrients, etc.

Disadvantages of wheels

Wheels incur mechanical and other disadvantages in certain environments and situations, which would represent a decreased fitness when compared with limbed locomotion.[1] These disadvantages suggest that, even barring the biological constraints discussed above, the absence of wheels in multicellular life may not, in fact, be the "missed opportunity" of biology that it first seems. On the contrary, given the mechanical disadvantages and restricted usefulness of wheels compared with limbs, the central question can be reversed: not "Why doesn't nature produce wheels?", but rather, "Why don't human vehicles make more use of limbs?"[6] The use of wheels, rather than limbs, in many engineered vehicles can likely be attributed to the complexity of design required to construct and control limbs, rather than to a consistent functional advantage of wheels over limbs.[33][34]

Efficiency

Rolling resistance

diagram of the forces acting on a wheel
A hard wheel rolling over—and deforming—a soft surface, resulting in the reaction force from the surface having a component that opposes the motion

Though stiff wheels are more energy efficient than other means of locomotion when traveling over hard, level terrain (such as paved roads), wheels are not especially efficient on soft terrain such as soils, because they are vulnerable to rolling resistance. In rolling resistance, the wheel is robbed of energy by the deformation of the wheel and the surface on which it is rolling. Smaller wheels are especially susceptible to rolling resistance.[32] Softer surfaces deform more and recover less than firm surfaces, resulting in greater resistance. Compared with rolling on concrete, resistance on medium-hard soil can be five to eight times greater, and on sand can be 10 to 15 times greater.[6]

Rolling resistance is also the reason wheels are not seen in certain human civilizations. During the Roman Empire, wheeled chariots were common in the Middle East and North Africa, yet when the Roman Empire collapsed, wheels fell out of favor with the local populations, who turned to camels to transport goods in the sandy desert climate. Stephen Jay Gould discusses this curiosity of history in his book Hen's Teeth and Horse's Toes, asserting that in the absence of maintained roads, camels required less manpower and water than a cart pulled by oxen.[35]

Efficiency of aquatic locomotion

With regard to aquatic locomotion, rotating systems carry an efficiency advantage only at extremely low Reynolds numbers (viscosity-dominated flows), such as those experienced by bacterial flagella, whereas oscillating systems have the advantage at higher (inertia-dominated) Reynolds numbers. Whereas ship propellers typically have efficiencies around 60%, and aircraft propellers up to around 80% (achieving 88% in the human-powered Gossamer Condor), much higher efficiencies, in the range of 96%–98%, can be achieved with an oscillating flexible foil, like a fish tail or bird wing.[6][32]

Traction

Wheels are prone to slipping—an inability to generate traction—on loose or slippery terrain. Slipping wastes energy, and can potentially lead to a loss of control or becoming stuck, as with an automobile on mud, ice, or snow. This disadvantage of wheels is apparent in the realm of human technology; in an example of biologically inspired engineering, legged vehicles find use in the logging industry, where they allow access to more challenging terrain than wheeled vehicles can navigate.[36] Tracked vehicles suffer less from slipping than wheeled vehicles, due to their larger contact area with the ground, but they tend to have larger turning radii than wheeled vehicles, and are less efficient and more mechanically complex.[37]

Obstacle navigation

Mountain goat
A mountain goat navigating a rocky landscape. Mountain goats provide an example of the versatility of legs for dealing with challenging terrain.

Work by engineer Mieczysław G. Bekker implies that the distribution of irregularities in natural terrains is log-normal, i.e., small obstacles are far more common than larger ones. Thus, obstacle navigation presents a challenge to wheeled locomotion in natural terrains at all size scales.[32]

Going around obstacles

Standard methods of steering, which do not provide individual wheel articulation, are limited in their achievable turning radius, thus limiting the ability of such vehicles to navigate an environment with a high obstacle frequency.[38]

Michael LaBarbera illustrates the poor maneuverability of wheels by comparing the turning radii of walking and wheelchair-bound humans.[32] As Jared Diamond points out, most biological examples of rolling are found in wide open, hard-packed terrain, including the use of rolling by dung beetles and tumbleweeds.[6]

Going over obstacles

Wheels are poor at dealing with vertical obstacles, especially obstacles on the same scale as the wheel itself. Assuming a vehicle or animal can shift its center of mass, the limiting height of vertical obstacles for a passive wheel is one radius.[6] If the center of mass cannot be shifted, the highest obstacle a vehicle can surmount is one quarter to one half the radius of the wheel. Because of these limitations, wheels intended for rough terrain require a larger diameter.[32]

In addition, without articulation, a wheeled vehicle can become stuck on top of an obstacle, with the obstacle between the wheels, preventing them from contacting the ground.[39] Limbs, in contrast, are useful for climbing, and equipped to deal with uneven terrain.[32]

For unarticulated wheels, climbing obstacles will cause the body of the vehicle to rotate. If the vehicle's center of mass moves outside of the wheelbase or axle track, the vehicle will become statically unstable and tip over.[40] At high speeds, a vehicle can become dynamically unstable, meaning that it can be tipped over by an obstacle smaller than its static stability limit, or by excessive acceleration or tight turning.[41] Without articulation, this can be an impossible position from which to recover.

Versatility

Articulated limbs used by animals for locomotion over terrain are frequently also used for other purposes, such as grasping, climbing, branch-swinging, swimming, digging, jumping (as across gaps), and kicking. With a lack of articulation, wheels would not be as useful as limbs in these roles.[32]

Rolling and wheeled creatures in fiction and legend

Escher's "Curl-up"
Escher's Curl-up

Rolling

The hoop snake is a creature of legend in the United States and Australia.[5] The snake is said to grasp its tail in its mouth and roll like a wheel towards its prey. The Japanese Tsuchinoko is a similar mythical creature.[42]

The 1944 science fiction short story "Arena", by Fredric Brown, features a telepathic, alien creature called an "Outsider", which is roughly spherical and moves by rolling.[43] The story was the basis for the 1967 Star Trek episode of the same name, and a 1964 episode of The Outer Limits entitled "Fun and Games".[44]

The Dutch graphic artist M. C. Escher invented a creature he called Pedalternorotandomovens centroculatus articulosus, which was capable of rolling itself forward like a wheel. He illustrated this creature in his 1951 lithograph Wentelteefje (also called by the English title Curl-up).[9][45]

Tuf Voyaging, a science fiction novel by George R. R. Martin, first published in 1986, features an alien species called the "Rolleram", which kills its prey by rolling over it.[46][47]

In the Sonic the Hedgehog video game series, which first appeared in 1991, the eponymous Sonic and his sidekick Tails move by rolling.[48][49]

The 1995 short story "Microbe", by Kenyon College biologist and feminist science fiction writer Joan Slonczewski, describes an exploratory expedition to an alien world, whose plant and animal life consists entirely of doughnut-shaped organisms.[50]

Wheeled

L. Frank Baum's 1907 children's book Ozma of Oz features humanoid creatures with wheels instead of hands and feet, called "Wheelers".[3]

The 1968 novel The Goblin Reservation by Clifford D. Simak features an intelligent alien race that uses biological wheels.[51]

Piers Anthony's 1977 book Cluster and its sequels feature members of an alien species called Polarians, which locomote by gripping and balancing atop a large ball. The ball is a living, though temporarily separable, portion of the Polarian's body.[52]

David Brin's Uplift Universe includes a wheeled species called the G'Kek, which are described in some detail in the 1995 novel Brightness Reef. In the 1996 novel Infinity's Shore, the G'Kek are described as looking like "a squid in a wheelchair." They suffer from arthritic axles in their old age, particularly when living in a high gravity environment.[53][54]

A 1997 novel in the Animorphs series, The Andalite Chronicles, includes a species called Mortrons, composed of two separate entities, a yellow and black bottom half with four wheels, and a red elongated head with razor-sharp teeth and concealed wings.[55]

The 2000 novel The Amber Spyglass, by English author Philip Pullman, features an alien race known as the Mulefa, which have diamond-shaped bodies with one leg at the front and back and one on each side. The Mulefa use large, disc-shaped seed pods as wheels. They mount the pods on bone axles on their front and back legs, while propelling themselves with their side legs. The Mulefa have a symbiotic relationship with the seed pod trees, which depend on the rolling action to crack open the pods and allow the seeds to emerge.[4]

In the 2000 novel Wheelers, by English mathematician Ian Stewart and reproductive biologist Jack Cohen, an alien species called "blimps" has developed the ability to biologically produce machines called "wheelers", which use wheels for locomotion.[56][57]

See also

Notes

1.^ Although evolutionary and developmental constraints preclude the possibility of a wheel as part of an organism, they do not preclude the use of foreign objects as "wheels", either instinctually (as in the case of the dung beetles discussed above), or through intelligently directed tool use (as in human technology).
2.^ Wheels can be considered to fall into two types: passive and driven. A passive wheel simply rolls freely over a surface, reducing friction when compared with dragging. A driven wheel is powered, and transmits energy to the surface as a means of achieving locomotion.

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