Mechanics of cuticular elastic energy storage in leg joints lacking extensor muscles in arachnids
Department of Entomology, University of Maryland, College Park, MD 20742, USA
* Author for correspondence (e-mail: sensenig{at}wam.umd.edu)
Accepted 29 November 2002
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Summary |
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The efficiency of elastic energy storage (resilience) in the absence of internal fluid pressure was 70-90% for joints with well-developed transarticular sclerites, and the magnitude of torque was similar to those produced by different joint extension mechanisms in other arthropods. Increased internal fluid pressure acted synergistically with transarticular sclerites in some joints but had little or no effect in others. Joints that lacked both extensor muscles and transarticular sclerites appeared to be specialized for hydraulic extension, and joints operated by antagonistic muscles lacked apparent specializations for either elastic or hydraulic extension. It is well known that elastic energy storage is a significant contributor to propulsion in running vertebrates and certain arthropods, where elastic elements are loaded as the center of mass falls during one phase of the locomotor cycle. However, transarticular sclerites are apparently loaded by contraction of flexor muscles when the leg is not in contact with the substratum. Hence the mechanism of a transarticular sclerite is more similar to the flight and jumping mechanisms of other arthropods than to running vertebrates. The evolutionary significance and potential mechanical advantages of the transarticular elastic mechanism are discussed.
Key words: leg joint, extensor muscle, arachnid, transarticular sclerite, arthropod, elastic energy storage, resilience
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Introduction |
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We examined the functional roles of elastic and hydraulic mechanisms in selected joints from the fourth walking leg of several arachnid groups, including scorpions (Scorpiones), tarantulas (Araneae), whipscorpions (Uropygi), sun-spiders (Solifugae) and harvestmen (Opiliones). Measurements were taken by recording forces exerted by each joint during mechanically induced joint movements approximating those used by walking animals. These organisms exhibit a diverse range of leg adaptations for extension and were expected to differ significantly in mechanics. For example, scorpions have evolved a muscle that functions in extension of major leg joints, and tarantulas and whipscorpions are known to make wide use of hydraulic pressure. Sun-spiders have large transarticular sclerites on two important leg joints, while in harvestmen these are found on only one leg joint.
The magnitude of the torque generated by an elastic mechanism was measured to evaluate the degree to which the animal relies on elastic extension as the sole or primary extensor of a joint. Torque generated by hydraulic pressure was compared with that generated by elastic extension mechanisms, and changes in internal joint volume with joint angle were used to indicate the possible use of hydraulic pressure. The dynamic context of locomotion required examination of frequency effects on both resilience and torque. Finally, the energy contribution by elastic extension to propulsion in the arachnids used in this study can be compared with muscular extension in a commonly studied arthropod, the cockroach Blaberus discoidalis.
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Materials and methods |
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The study was conducted on selected joints of the fourth (most posterior) walking leg (Fig. 1). This leg functions primarily in pushing the animal forward by joint extension. We focused on bicondylar hinge joints (one axis of movement), which undergo substantial angular excursions during locomotion, rather than monocondylar joints (multiple axes of movement) or joints that show little movement during locomotion. Based on these criteria, we examined the femurpatella joints in scorpions, Mastigoproctus and Aphonopelma; the patellatibia joints in scorpions, Eremopus and Mastigoproctus; the tibiabasitarsus joint in all taxa; and the basitarsustelotarsus joint in Aphonopelma. Elasticity appeared in some other distal joints but movement was complex, limited in range, or did not occur in forward locomotion and thus these joints were examined superficially.
Kinematic analysis
Each animal was videotaped as it walked on a variable-speed treadmill
(treadmill dimensions, 50 cmx20 cm lengthxwidth, speed resolution,
5 mm s-1). Images of walking animals were captured using two
gen-locked Peak Performance High Speed cameras (60 fields s-1 for
Eremopus and Leiobunum and 60 or 120 fields s-1
for Aphonopelma, Hadrurus, Heterometrus and Mastigoproctus),
positioned so as to obtain lateral and dorsal perspectives of the animal. The
angle between the cameras ranged from 60-90°. The videotapes were
synchronized using the Peak Performance manually operated event marker. A
calibration frame (4 cmx4 cmx4 cm or 25 mmx15 mmx11
mm) was videotaped by both cameras. The larger frame consisted of 12
non-coplanar points and the smaller frame 6 non-coplanar points. The smaller
calibration frame was used for smaller animals. The resolution of points of
the calibration frames was approx. 0.5 mm. Using the larger calibration
object, points in space could be located with mean-squared errors of 0.09 mm,
0.23 mm and 0.35 mm for the x, y and z positions,
respectively, yielding a 0.43 mm mean-squared error for position. Using the
smaller calibration object, points in space could be located with mean-squared
errors of 0.023 mm, 0.136 mm and 0.103 mm for the x, y and z
positions, respectively, yielding a 0.172 mm mean-squared error for position.
Paint was used to mark the articulations of the fourth leg to facilitate
subsequent digitization.
Videotapes of walking animals were analyzed to determine the natural range
of motion at each joint using a computerized motion analysis system (Motus,
Peak Performance Technologies, Inc., version 6.0). Video images were digitized
manually. Data were filtered using a low-pass, fourth-order, zero-phase-shift
Butterworth digital filter with a cut-off frequency of 10 Hz, a frequency that
minimized distortion and noise (Biewener
and Full, 1992). Data from both camera views were filtered before
direct linear transformation to three-dimensional coordinates in Motus.
Mechanically controlled joint movement and kinetic analysis
A computer-controlled stepper motor (Arrick Robotics, Model MD-2, angular
resolution of motor 0.9° step-1, angular resolution of plate
shaft achieved through gearing 0.75° step-1) was used to belt
drive a shaft terminating with a flat circular plate equipped with a specimen
clamp (Fig. 2A). The stepper
motor was programmed to rotate the plate through angular excursions and
velocities approximating those observed during locomotion (position
versus time was linear, i.e. a saw-tooth wave). A rotary
variable-inductance transducer (Schaevitz, Model RVIT-15-60, linearity error
0.25% full-scale output) was mounted on the same shaft as the plate and used
to record the instantaneous angle. The stepper motor, belt, gears, plate and
rotary transducer were mounted together in a stiff steel frame. A force
transducer (Aurora Scientific Inc, Model 404A, range 100 mN, resolution 2000
nN) was attached to a separate laboratory stand and the transducer input tube
was brought into contact with the free end of a clamped and mounted joint
specimen (Fig. 2A). The
transducer measured the force exerted at the free end of the joint during
mechanically induced flexion and extension. Force and angular position data
were collected using an Analog/Digital Interface Unit and Motus 6.0 software
(Peak Performance Technologies) at a sampling rate of 600 Hz. Joints were
rotated through 0.5, 1, 2, 3.3, 5 and 10 Hz. Force data were filtered in the
Motus program using a Butterworth filter (cutoff frequency 6-12 Hz). The
cutoff frequency for each trial was chosen so that approximately equivalent
noise reduction occurred among trials of different rotation frequencies.
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Joint preparation
Each joint was prepared by thawing an animal from -80° C, amputating a
fourth leg, isolating the experimental joint by cutting away portions of the
leg segments proximal and distal to the joint, removing all muscles and
tendons, and mounting one end of the joint specimen at the end of a stainless
steel tube (5 mm diameter, 6 cm length)
(Fig. 2A). Epoxy resin was used
to seal the specimentube interface and the free end of the joint
specimen was also sealed with epoxy. The epoxy was allowed to dry for approx.
30 min, and the joint and tube were filled with Ringer's solution
(Ingham and Jowett, 1997). A
long micropipette was inserted into the steel tube and used to inject the
solution, a procedure intended to ensure that the specimen was filled and that
air bubbles in the joint and tube were minimized.
The stainless steel tube was clamped to the plate so that the joint axis
could be aligned with the shaft axis by eye
(Fig. 2A). Adjustments were
made using the clamp screws to ensure that joint movement was in a plane
parallel to the plate surface. The force transducer input tube was brought
into direct contact with the joint at a right-angle to the free end of the
joint specimen. The point of contact between the specimen and transducer was
improved when necessary by scraping off setae or applying a drop of melted
paraffin. A protractor next to the plate allowed positioning of the joint
angle by eye (resolution approximately 5°), the stepper motor was turned
on and locked at this angle, and all angular excursions were then based on
this start position. Errors in torque measurement were caused primarily by
misalignment of the joint and shaft axes, and secondarily by precision in
positioning the starting joint angle. The stainless steel mounting tube was
then attached through rubber tubing to a graduated titration cylinder (length
50 cm) to which Ringer's solution was added. Fluid pressure was varied by
changing the vertical placement of the cylinder relative to the joint
specimen. The arthrodial membrane was observed prior to cycling to ensure that
fluid was filling the specimen. Internal fluid pressures of 0, 2.5, 4.9 and
9.8 kPa were applied to encompass the range of pressures typically measured in
walking and resting arachnids, although much higher pressures have been
measured in startled and restrained animals (for example, see
Alexander, 1967;
Stewart and Martin, 1974
;
Anderson and Prestwich, 1975
;
Blickhan and Barth, 1985
;
Shultz, 1991
). To ensure that
bubbles trapped in joints with transarticular sclerites were not the main
mechanism generating elastic properties, torque generated by empty joints
(joints with muscles removed but not yet connected to flexible tubing and
filled with solution) was measured and was found to be essentially the same as
those filled with solution. While drying of the arthrodial membrane will
eventually result in an empty joint becoming completely stiff, increased
stiffness of empty joints was not apparent until several hours had
elapsed.
Measurement of changes in joint volumes
Use of internal pressure for joint extension should be correlated with an
increase in joint volume during extension
(Blickhan and Barth, 1985);
absence of volume increase indicates the absence of hydraulically mediated
extension. Changes in joint volume during flexion and extension were measured
by observing fluid movement in a micropipette attached to the joint mounting
tube. A 50 µl micropipette was marked with 1 µl increments and glued to
a 3 cm piece of flexible tubing. The flexible tubing was then attached to the
steel mounting tube. Filling and assembly of components were performed in a
pan of saline to minimize the presence of air bubbles. The joint specimen was
held lower than the micropipette so as to increase the pressure in the joint
by approx. 2.5 kPa (18 mmHg) and the joint was flexed and extended by hand.
The precision of this technique was approx. 0.5 µl.
Calculations of torque and efficiency of elastic energy storage
Data sets were imported to a spreadsheet program (Microsoft Excel 97).
Scaled (or relative) torque (s) of a joint was calculated
according to Evans and Forsythe
(1984
):
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Elastic energy storage was measured by flexing and extending individual joints under zero internal fluid pressure while recording the input and output impulse. Input impulse was calculated as the area under the loading curve (flexion) in the torqueangle graph (Fig. 2B,C), while output impulse due to elastic recoil was the area under the unloading curve (extension). Areas under these curves were calculated using a Visual Basic program in Microsoft Excel 97 that summed all torque values between a minimum and a maximum in the loading curve (sampling frequency 600 Hz). The percentage efficiency of elastic energy storage (or resilience) was calculated as (output impulse/input impulse)x100. The curves obtained by manipulating joints under zero internal pressure were compared to those obtained with the joint under various positive fluid pressures, but the resilience obtained under these conditions represented the relative effectiveness with which the joint transduced internal fluid pressure into kinetic energy during flexion and extension in addition to resilience.
Calculation of potential contribution of elastic recoil to
propulsion
The potential propulsive work contributed by elastic recoil of a joint was
calculated from kinematic data obtained by video analysis of walking animals
and kinetic data from force measurements on isolated joints under zero
internal fluid pressure. Potential work (W) directly contributed by
recoil to forward motion of the animal's center of mass during one propulsive
stroke was calculated using the following equation:
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Results |
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Patellatibia joints of Eremopus (N=4, mass=1.4±0.4 g) were rotated through approximately 60-120° (Fig. 3). Elastic extension over the range measured by motion analysis occurred at 0 kPa. Torque increased with pressure, and pressurizing the patellatibia joint (Fig. 4) to 4.9 kPa (37 mmHg) approximately doubled the extension torque at any angle. Torque at midrange (90°) generated by the patellatibia joint was 6.4±2.4 mN mm at 0 kPa, 9.3±3.5 mN mm at 2.5 kPa, 12.3±5.1 mN mm at 4.9 kPa and 18±7.9 mN mm at 9.8 kPa. Scaled torques at midrange angles are shown in Fig. 5. Scaled midrange torque generated solely by the elastic mechanism of this joint was equivalent to that generated by Aphonopelma femurpatella joints at 2.5 and 4.9 kPa and by Mastigoproctus femurpatella joints at 9.8 kPa (Table 1, Fig. 5).
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Tibiabasitarsus joints of Eremopus (N=4, mass=1.3±0.48 g) were moved through ranges indicated by motion analysis (150-170°) (Fig. 3). Induced flexion of this joint could occur to angles of approx. 100° and therefore joints were also flexed to this angle, although this degree of flexion is substantially greater than that observed during locomotion. Elastic extension at 0 kPa occurred not only over the range measured in walking animals but also after much greater flexion. Pressurizing the tibiabasitarsus joint (Fig. 4) to 4.9 kPa (37 mmHg) increased the torque by approx. 20%. Torque at midrange (160°) generated by the tibiabasitarsus joint was 6.7±1.5 mN mm at 0 kPa, 8.2±1.9 mN mm at 2.5 kPa, 8.4±2.1 mN mm at 4.9 kPa and 13±2.2 mN mm at 9.8 kPa. Scaled midrange torque generated solely by the elastic mechanism of this joint was equivalent to that generated by Aphonopelma tibiabasitarsus joint at 4.9 kPa (Table 1, Fig. 5).
The tibiabasitarsus joints of Leiobunum (N=4, mass=71±6 mg) were rotated through 100-150° (Fig. 3). Joints were also rotated through ranges as great as 90-170°. Elastic extension occurred over the entire range measured by motion analysis. Pressurizing the joint to 9.8 kPa (74 mmHg) raised peak torque by approx. 15% (Fig. 4). Torque generated by the tibiabasitarsus joint at midrange (125°) was 0.45±0.05 mN mm at 0 kPa, 0.47±0.05 mN mm at 4.9 kPa and 0.50±0.06 mN mm at 9.8 kPa. Scaled midrange torque generated by the elastic mechanism of this joint was equivalent to that generated by hydraulic pressure in Aphonopelma tibiabasitarsus joint at 2.5 kPa but less than that generated by the elastic mechanism of Eremopus tibiabasitarsus joints (Table 1).
Narrow strips of sclerotization span the arthrodial membrane of the patellatibia joint of Mastigoproctus and this structure appeared to store and release some energy by folding. The patellatibia joint of Mastigoproctus (N=3, mass=6±2 g) was elastic over the range used by walking animals, with resilience as great as 80% (Fig. 6). Excursion of this joint was small, and the lack of resolution in determining joint angle made accurate simulation of the walking range difficult. The maximum torque measured at this joint was high, with one specimen generating torque up to approx. 300 mN mm within the walking range. Torque generated by the patellatibia joint at midrange (155°) was 13±6 mN mm at 0 kPa, 15±5 mN mm at 2.5 kPa, 19±2 mN mm at 4.9 kPa and 24±6 mN mm at 9.8 kPa. Variance of scaled midrange torque among individuals was high.
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The tibiabasitarsus joints of both scorpion species were compliant and resilient when flexed over the inducible range of approximately 160-185° (Fig. 7). Scorpions typically rested with this joint hyperextended (approximately 200°), and when flexed, the elastic mechanism exerted a torque that resisted flexion and stored energy. The tibiabasitarsus joint appeared to be the only leg joint in scorpions with some sclerotization of the arthrodial membrane. Movement of the tibiabasitarsus joint was difficult to resolve by video recordings due to a small excursion range. Observations of slow walking suggested that the elastic mechanism of this joint is loaded during the propulsive stroke. The tibiabasitarsus joint flexes during propulsion, but only to approx. 180°. Over the induced range, maximum torque generation was approx. 120 mN mm (Fig. 7) and resilience was approx. 70%.
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Magnitude of torque generated by joints without transarticular
sclerites
Joints without transarticular sclerites never extended elastically over any
significant excursion range. These joints were the femurpatella and
patellatibia joints of scorpions, and the femurpatella and
tibiabasitarsus joints of Aphonopelma. The femurpatella
and tibiabasitarsus joints of Mastigoproctus, while weakly
sclerotized, were also very limited in elastic extension.
Induced flexion of the femurpatella and patellatibia joints of both scorpion species was achieved by torque lower than 10 mN mm over this range, and little extension occurred when the joint was moved away from the transducer's input tube (Fig. 7). Pressure of 9.8 kPa (74 mmHg) in both these joints resulted in limited extension, much less than that observed in walking. The patellatibia joints of Heterometrus and the femurpatella and patellatibia joints of Hadrurus produced no torque at midrange angles at pressures up to 9.8 kPa. Torque generated by the femurpatella joint of Heterometrus at midrange (100°) was 1.3±0.58 mN mm at 9.8 kPa. Scaled midrange torque in the femurpatella and patellatibia joints of scorpions generated by hydraulic pressure of 9.8 kPa was significantly lower than that generated in the femurpatella and patellatibia joints of all other species at the same pressure.
The femurpatella and tibiabasitarsus joints of Aphonopelma (N=4, mass=16±5 g) did not extend elastically over the range observed in locomotion, but an internal pressure of 4.9 kPa (37 mmHg) was usually sufficient to induce full extension. Pressurization readily induced higher torque in all these joints. Torque generated by the femurpatella joint at midrange (120°) was 28±14 mN mm at 25 kPa, 52±16 mN mm at 4.9 kPa and 98±34 mN mm at 9.8 kPa. Torque generated by the tibiabasitarsus joint at midrange (140°) was 14±7 mN mm at 25 kPa, 29±7 mN mm at 4.9 kPa and 60±18 mN mm at 9.8 kPa.
The femurpatella joint of Mastigoproctus (N=4, mass=6±1.4 g) resisted loading at maximum induced flexion, but resilience was low (approx. 18%) and could not extend the joint beyond approx. 10°. Pressure lower than 4.9 kPa (37 mmHg) was never sufficient to cause the degree of extension observed in walking (Fig. 6). Torque generated by the femurpatella joint at midrange (105°) was 2±1.7 mN mm at 25 kPa, 4±2.4 mN mm at 4.9 kPa and 10±5.8 mN mm at 9.8 kPa.
The tibiabasitarsus joints of Mastigoproctus were elastic only over the lower range of angles used in walking (Fig. 6). However, flexion beyond this walking range resulted in elastic extension, and resilience as high as 80% was measured. At this high degree of flexion, pressure of 49 kPa (37 mmHg) raised peak torque by approx. 25%.
Time-dependent effects on resilience and torque
The resilience of joints with obvious elastic properties was measured at
different frequencies. Patellatibia joints of Eremopus
operated with resilience of 83±6% over frequencies of 0.5 to 5 Hz, and
the changes in resilience and torque at different frequencies were smaller
than typical experimental variation and displayed no consistent trends. The
frequency of 10 Hz resulted in substantial vibration in the joint and noise in
the data, and resilience appeared to decrease. However, resilience was never
observed to be lower than 70%. Measurement of Eremopus
tibiabasitarsus joints and Leiobunum tibiabasitarsus
joints produced similar results with Eremopus operating with
resilience of 85±11% and Leiobunum with resilience of
82±9% (Fig. 4) across
frequencies of 0.5 to 5 Hz. No consistent dependence on frequency or angular
excursion was apparent.
While no timedependent properties were measured during constant cycling, the recoil force of Eremopus elastic joints held at a constant angle decayed after loading, with the initial loss of force being especially rapid (Fig. 8). When flexed to an angle normally seen in locomotion, the extension force of the patellatibia joint of Eremopus dropped by approx. 30% of its original magnitude after 0.4 s and then underwent a slower decay for many seconds thereafter. When flexed and held at angles used in locomotion and greater, the force exerted by the tibiabasitarsus joint decayed by 10-15% after 0.3 s. After 13 s the extension force was at least 80% of its original magnitude (Fig. 8). The decay in recoil force of the tibiatarsus joint of Leiobunum at maximum flexion tended to be greater than that of the patellatibia joint of Eremopus, with the fast (0.5 s) initial loss in force being 30-50% (Fig. 8).
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Centrifugal forces involved in motion of the steel tube prevented reliable
measurement of torque and resilience at high frequencies (5 Hz) in joints
that extended only under hydraulic pressure (e.g. tibiabasitarsus and
femurpatella joints of Aphonopelma and femurpatella
joints of Mastigoproctus).
Contribution by elastic mechanisms to forward locomotion
Combining the data from video recordings and kinetic studies, elastic
recoil within a fourth leg of Eremopus had the potential to perform
7±1 µJ g-1 body mass and Leiobunum
3.3±0.5 µJ g-1 body mass of mechanical work during a step
cycle. A study of energy changes during running in the cockroach Blaberus
discoidalis (average mass 2.6 g, speed 240 mm s-1) measured a
total energy increase of approx. 20 µJ during a step cycle, representing
mechanical work of 7.7 µJ g-1 body mass
(Full and Tu, 1990).
Torque generated by basitelotarsus joints
The basitelotarsus joints of all the arachnids used in this study
moved through a hyperextended range (Table
2) and exhibited elastic recoil after flexion, although torque was
much lower than that measured in more proximal elastic joints or proximal
joints activated by hydraulic pressure. The basitarsustelotarsus joints
of Mastigoproctus generated maximum torque of approx. 0.1 mN mm in
the range used during locomotion. The basitarsustelotarsus joints of
scorpions, which move in a complicated manner, generated maximum torque of
approx. 20 mN mm. The multiply segmented tarsus of Leiobunum was
elastic and flexible, and the tarsus was flexed approx. 50°. Maximum
torque by elastic extension was 0.04 mN mm. The basitarsustelotarsus
joint of Aphonopelma extended elastically
(Fig. 6), with maximum torque
in the walking range of approx. 5 mN mm. This joint also appeared to easily
transduce pressure into torque.
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Discussion |
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Differences in joint morphology also correlate with differences in
magnitude of the torque generated by pressure. Unlike the bellows-like folding
of the femurpatella and tibiabasitarsus joints of
Aphonopelma, the arthrodial membrane of the femurpatella joint
of Mastigoproctus tends to bulge under pressure. Bulging of the
arthrodial membrane can hinder extension because stresses are not resolved
radially (Blickhan and Barth,
1985) and may be an explanation for the lower relative torque
generation in Mastigoproctus. Joints extended by haemolymph pressure
are characterized by internal volume change during joint rotation and a center
of gravity not located at the rotational axis
(Blickhan and Barth, 1985
).
Internal volume changes for some joints were large enough to measure using our
technique (Table 3). The
femurpatella joints of scorpion and Mastigoproctus, while
similar in segmental dimensions, differed both in volume change and in
location of the center of gravity. The volume change of femurpatella
joints of Mastigoproctus is about three times greater than scorpions.
The axis of joint rotation of femurpatella joints of scorpions is
located near the middle of the limb and contrasts with the dorsally located
axis of the femurpatella joints of Mastigoproctus
(Fig. 1). Both the
femurpatella and patellatibia joints of scorpions appear to be
extended by the transpatellar muscle
(Shultz, 1992
), and the role
of pressure in extension of these joints is trivial or absent
(Fig. 7).
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Different extension mechanisms need not be exclusive, and indeed joints of Mastigoproctus display features of both hydraulic and elastic extension. These two mechanisms are probably synergistic in the femurpatella, patellatibia, and tibiabasitarsus joints of Mastigoproctus. The mainly hydraulic femurpatella joint is proximal to the greatly elastic patellatibia joint, and both joints have some sclerotization of the arthrodial membrane. Hydraulic pressure may be present in the patellatibia joint at all times or, if the animal has a method of regulating pressure between joints, only during times of very high torque demand. Mastigoproctus, with its combination of hydraulic and elastic features, demonstrates the functional viability of an intermediate in the transition from dependence on hydraulic pressure to cuticular elasticity.
Eremopus probably represents an extreme example of dependence on
cuticular elasticity for extension. While torque also increases with pressure
in the patellatibia and tibiabasitarsus joints of
Eremopus, it is not known if such pressures are used in these
animals. Walking pressures in Eremopus and Leiobunum have
not been reported but are probably low due to a reduction of prosomal
dorsoventral muscles (Shultz,
1991). Torque at the tibiatarsus joint of
Leiobunum increases very little as pressure is increased, and this is
associated with the small change in joint volume during movement.
Elastic extension in Eremopus and Leiobunum appears to
have replaced the hydraulic system seen in Aphonopelma and
Mastigoproctus (Shultz,
1990,
1991
). The femurpatella
joint of Aphonopelma and Mastigoproctus and the
patellatibia joint of Eremopus are functionally similar `knee'
joints of the fourth leg and are assumed to be the main contributors to
propulsion by this leg. Elastic extension alone produces a midrange scaled
torque of 5.2±0.8 mN mm g-0.67 in the patellatibia
joint of Eremopus, while the femurpatella joints of
Aphonopelma and Mastigoproctus generate no torque except
when pressurized. The femurpatella joint of Aphonopelma
required between 0 and 2.5 kPa of pressure and the femurpatella joint
of Mastigoproctus greater than 4.9 kPa to produce scaled torque
comparable to the elastic extension in Eremopus. These measurements
suggest that torque generated by elastic extension alone may be sufficient for
walking in Eremopus. Scaled midrange torque of the tibiatarsus
joint of Leiobunum is lower than other joints with sclerites, and
this may be partly due to its distal location on the leg. The elastically
generated scaled torque at this joint is similar to the scaled torque produced
by the femurpatella joint of Mastigoproctus at its typical
walking pressures. Both Leiobunum and Mastigoproctus tended
to use lower speeds than Eremopus and Aphonopelma, and this
may associated with the lower torques observed in the joints.
Elastic joint extension may be an evolutionarily simple way of replacing
the ancestral hydraulic mechanism (Shultz,
1989,
1991
) and its potentially
disruptive impact on haemolymph circulation. The pressure used for joint
extension can potentially impede the transport of oxygenated haemolymph from
opisthosomal respiratory organs to the locomotor muscles of the prosoma. Any
cost of the hydraulic mechanism could be reduced by shifting the role of joint
extension to some mechanism intrinsic to the leg, such as an extensor muscle
or transarticular elastic sclerite. The thickening of the pre-existing
arthrodial membrane to form a transarticular sclerite would seem relatively
easy to evolve in comparison to the multiple innovations necessary to generate
a new muscle and a neural mechanism for controlling it. The continuous
resistance of an elastic mechanism to contraction of flexor muscles would be
mechanically similar to that caused by constant elevated haemolymph pressure
during locomotion, as illustrated by a comparison of the loading curves of
elastic joints of Eremopus and Leiobunum
(Fig. 4) to those of the
hydraulic joints of Aphonopelma
(Fig. 6). Further, the energy
exerted by flexor muscles to maintain a posture at hydraulic joints during
inactivity is reduced in Aphonopelma and Mastigoproctus by
lowering internal pressure below levels observed during walking
(Stewart and Martin, 1974
;
Shultz, 1991
), and a
comparable effect is achieved at elastic joints of Eremopus and
Leiobunum via gradual viscoelastic decay in torques exerted by
transarticular sclerites, although this decay still leaves significant torque
remaining in the joint (Fig.
8).
The stiffness of a joint in live animals is determined by membrane
structure, fluid pressure and muscle properties. The dorsalventral
stiffness of the tibiabasitarsus joint of live Aphonopelma was
measured by Blickhan (1986).
To determine the stiffness of the membrane apart from the effects of muscles
and hydraulic fluid, excursion was limited to several degrees and low
frequency (<0.1 Hz). Stiffness measured in that study was essentially the
same as that measured at midrange (slope of the torque versus angle
curve at midrange) during hydraulic extension in the present study, approx.
0.01 mN degree-1. However, flexion of several degrees at a
frequency of 0.1 Hz in the live spider in Blickhan's
(1986
) study resulted in a
stiffness increase of several hundredfold. This high stiffness was probably
the result of muscle tension. Intrinsic stiffness of the membrane is probably
insignificant in operation over most of the excursion range of hydraulically
extended joints, and stiffness in live animals is primarily determined by
hydraulic pressure and muscle tension. At high flexion, however, joint
stiffness increases as a result of compression of the membrane, transarticular
sclerite or limb cuticle. All of the `knee joints' and the
tibiabasitarsus joint of Leiobunum operate close to or at the
flexion limit during normal walking, as indicated by the increase in stiffness
near the end of flexion during the simulated walking cycles (Figs
4,
6,
7). The tibiabasitarsus
joints of Eremopus and Aphonopelma do not appear to operate
near the flexion limit during normal walking (Figs
4,
6).
The resilience of the transarticular sclerite during leg rotation in
arachnids is in the range of that measured for elastic proteins such as
elastin (76%), abductin (91%) and resilin (97%)
(Wainwright et al., 1976;
Vincent, 1982
). Resilin has
been identified at several structures in insects, including the jumping
mechanism of the flea (Bennet-Clark and
Lucey, 1967
) and click beetle
(Sannasi, 1969
), the tibia and
tarsus of the cockroach (Frazier et al.,
1999
; Neff et al.,
2000
) and the wing base of dragonflies (Weis-Fogh,
1960
,
1965
). While elastic
structures in insects are usually loaded by compression and bending forces
operating through a small distance in contrast to the extensive folding
mechanism of the transarticular sclerites of arachnids, it is possible that
the sclerites of arachnids do achieve relatively high resilience through
incorporation of resilin. Alexander
(1967
) has proposed the
existence of resilin in the femurpatella joint of the scorpion
pedipalp, and this protein has been identified in the cuticle of the chelal
hinge of scorpions (Govindarajan and
Rajulu, 1974
). Resilin or similar elastic proteins may be widely
distributed among arachnids, and incorporated into both the transarticular
sclerites and the basitarsustelotarsus joint.
Arachnid joint springs compared to the spring-loaded inverted
pendulum model
Elastic energy storage is well known as a mechanism for increasing
energetic efficiency in running vertebrates, and the simplest model is known
as the spring-loaded inverted pendulum (SLIP)
(Cavagna et al., 1977;
Heglund et al., 1982
; McMahon,
1985
,
1990
; Alexander,
1984
,
1988
,
1992
;
Blickhan, 1989
;
Thompson and Raibert, 1989
;
McMahon and Cheng, 1990
;
Full 1989
;
Farley et al., 1993
). During
the first cycle in a running sequence, the body is accelerated upward and
forward by muscles. As the legs interrupt the body's fall back toward the
substratum, the legs absorb mechanical energy from the impact and store some
of it as elastic deformation in tensed tendons and muscles. The ground
reaction forces may be several times the body weight during running
(Farley et al., 1993
).
Subsequent recoil of elastic elements then assists muscles in accelerating the
body upward and forward at the start of the next locomotor cycle. Thus some of
the muscular energy generated during one cycle is stored in elastic elements
and used in the next cycle.
The SLIP model requires leg springs to be located so that the falling
center of mass can compress the spring. However, most arthropods maintain a
`bent-leg' hanging posture with legs projecting radially around the center of
mass, rather than a typical vertebrate `straight-leg' posture with legs
positioned below the center of mass
(Manton, 1977;
Alexander, 1982
). Though the
motion of the center of mass of certain cockroaches, crabs and centipedes
suggests that they are using a leg spring in the manner predicted by the SLIP
model (Full, 1989
;
Blickhan and Full, 1993
;
Full and Koditschek, 1999
),
the transarticular springs in arachnid joints do not appear to be oriented so
as to be readily compressed by the center of mass. Instead, the elastic
mechanisms of Eremopus and Leiobunum are apparently loaded
by flexor muscles during protraction, the phase of the step cycle when the leg
is not in contact with the substratum. The energy stored during this period is
then recovered when the leg is in contact with the substratum and has the
potential to make a substantial contribution to propulsion. The mechanical
energy inputs calculated for Eremopus (7±1 µJ
g-1 body mass) and Leiobunum (3.3±0.5 µJ
g-1 body mass) are comparable to those of arthropods that rely on
muscle-based joint extension. For example, the cockroach Blaberus
discoidalis performs mechanical work of approx. 8 µJ g-1
body mass during one step cycle (based on
Full and Tu, 1990
). Thus,
elastic storage mechanisms exist in small arthropods and can potentially
generate substantial thrust during walking and running.
Potential advantages of elastic mechanisms in running arthropods
The use of elastic extension by some arachnids requires explanation in
light of its deviation from the SLIP model and its apparent evolutionary
derivation from an ancestral hydraulic mechanism (Shultz,
1989,
1990
,
1991
). We propose three
possible advantages of elastic energy storage during walking and running in
arthropods.
First, the use of elastic structures at leg joints instead of hydraulic
fluid may reduce leg mass and inertia and increase energetic efficiency. While
energetics did not differ between large vertebrates with very different limb
inertias (Taylor et al.,
1974), minimization of leg inertia is likely to be an important
determinant of leg structure and mechanics in arthropods, which tend to use
even higher stride frequencies (>25 Hz in Periplaneta americana;
Full and Tu, 1991
). For
example, the cockroach mass-specific kinetic energy required to swing its legs
is about half that predicted from data on larger two- and four-legged animals
(Kram et al., 1997
). Elastic
mechanisms of the most distal joints are found in scorpions, whipscorpions,
sun-spiders, tarantulas (A.T.S. and J.W.S., unpublished observation),
cockroaches (Frazier et al.,
1999
), stick insects (Radnikov
and Bassler, 1991
), and probably other arthropods. The
tibiatarsus joint of scorpions appears to absorb energy during
propulsion, since any loading of the membrane occurs during this phase. This
is opposite to that seen in the main elastic joints of Eremopus,
Leiobunum, and Mastigoproctus.
Second, elastic structures may reduce energetic costs associated with fluid displacement and pressure maintenance in hydraulic extension. Those arachnids using hydraulic extension show volume displacements of several µl per leg during each step cycle. Viscous drag of hydraulic fluid flow would be much greater in small limbs, assuming drag proportional to r-4 (Poiseuille's Law) and bulk proximal fluid flow during flexion and distal flow during extension. Extrapolating from volume displacements, a unit of fluid probably moves several mm during leg cycling, so that an assumption of bulk fluid flow is reasonable. Assuming that viscosity and velocity are similar in different arachnids, the relative importance of viscous drag can be estimated. Using the leg diameters of our experimental animals, Eremopus would have about 50 times the viscous drag of Aphonopelma and Leiobunum would have about 500 times the drag of Aphonopelma. Legs extended by hydraulic pressure would tend to have large diameters in order to reduce drag. The scorpion pedipalp Aphonopelma walking legs and Mastigoproctus walking legs, are relatively large in diameter and include at least one joint primarily activated by pressure. The patellatibia joint of Eremopus, while extending by cuticular elasticity, has a relatively large diameter, and pressure in amputated preparations can contribute to extension torque. Not only is there potential for energy loss in fluid movement through limbs, but a hydraulic reservoir itself may contribute to inefficiency. A hydraulic system with an ideal reservoir could be perfectly elastic. The reservoir consisting of tubing and a column of solution used in the simulated walking of Aphonopelma and Mastigoproctus resulted in a hydraulic resilience that was very similar to the resilience produced by transarticular sclerites. The hydraulic reservoir (prosoma) of Mastigoproctus and Aphonopelma probably also loses a similar amount of energy to stretching of the haemocoel.
Third, elastic structures may act as passive mechanisms of energy
absorption and dissipation. In the typical hanging stance of
Leiobunum, destabilizing forces such as wind may be absorbed by
elastic loading on the side opposite the disturbing force. With a roughly
radial distribution of legs, the animal is thus equipped with a passive shock
absorbing system that may respond quickly to destabilizing forces. The forces
associated with loading and recoil of elastic mechanisms of the fourth leg are
5-20% of body weight in Eremopus and 5-10% of body weight in
Leiobunum, and thus the ground reaction forces produced by a tipping
animal are sufficient to load the elastic structures of a single leg beyond
that observed in locomotion. While the hanging stance is especially
exaggerated in the long-legged Leiobunum, it is a general
characteristic of arthropods (Manton,
1977), and this mechanism may contribute to stability in other
arthropods as well. The elastic torque generated by extreme flexion in the
tibia-basitarsus of Mastigoproctus and scorpions and in the tarsus of
Leiobunum probably functions as a shock absorber during climbing or
other deviations from walking on smooth horizontal surfaces. High resilience
of an elastic mechanism may not be desirable when it is functioning as an
energy damper. Muscles can also act as dampers. During running, net energy is
absorbed by the primary extensor muscles (trochanterfemur muscle) of
the rear leg of the cockroach Blaberus discoidalis
(Full et al., 1998
), probably
for control purposes. However, these cockroach muscle extensors are located
close to the leg base and their movement and function are probably not
comparable to the more distal elastic extensors of the arachnids studied
here.
In conclusion, transarticular sclerites in arachnids are mechanisms of energy storage, and play a prominent role in leg extension in animals in which they occur. Hydraulic pressure is also an important component of locomotion in many arachnids, and may function in synergy with transarticular sclerites. The evolution of alternative extension mechanisms like elasticity and musculature from the hydraulically operated condition suggest adaptive benefits associated with these alternative mechanisms.
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References |
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