Download Comparison of Isometric Contractile Properties in Hindlimb Extensor

JOURNAL OF MORPHOLOGY 251:309 –322 (2002)
Comparison of Isometric Contractile Properties in
Hindlimb Extensor Muscles of the Frogs Rana pipiens
and Bufo marinus: Functional Correlations With
Differences in Hopping Performance
Brad A. Chadwell, Hadley J. Hartwell, and Susan E. Peters*
Department of Biology, The University of North Carolina at Charlotte, North Carolina 28223
Published online xx Month 2001
ABSTRACT The leopard frog (Rana pipiens) is an excellent jumper that can reach high take-off velocities and
accelerations. It is diurnal, using long, explosive jumps to
capture prey and escape predators. The marine toad (Bufo
marinus) is a cryptic, nocturnal toad, typically using
short, slow hops, or sometimes walking, to patrol its feeding area. Typical of frogs with these different locomotor
styles, Rana has relatively long hindlimbs and large (by
mass) hindlimb extensor muscles compared to Bufo. We
studied the isometric contractile properties of their extensor muscles and found differences that correlate with their
different hopping performances. At the hip (semimembranosus, SM), knee (peroneus, Per) and ankle (plantaris
longus, PL), we found that Rana’s muscles tended to produce greater maximum isometric force relative to body
mass, although the difference was significant only for PL.
This suggests that differences in force capability at the
ankle may be more important than at other joints to
produce divergent hopping performances. Maximum isometric force scaled with body mass so that the smaller
Rana has relatively larger muscles and force differences
This study compares the isometric contractile
properties of three hindlimb muscles between the
frog Rana pipiens and the toad Bufo marinus. Because of their distinctive abilities for hopping and
swimming, anurans have been widely used in biomechanical and locomotor studies (e.g., Zug, 1972,
1978; Calow and Alexander, 1973; Emerson, 1978;
Emerson and De Jongh, 1980; Marsh, 1994; Kamel
et al., 1996; Peters et al., 1996). All anurans share a
similar body plan of elongated pelvis and hindlimbs,
relatively large hindlimb muscles, and a shortened
presacral vertebral column to reduce mass anterior
to the propulsive hindlimbs. However, there is quite
a diversity of locomotor behaviors and range of hopping performance among frogs (Zug, 1978; Marsh,
1994). This diversity appears to derive from variation among species in a number of musculoskeletal
features. Limb lengths and leverage systems, as well
as size of extensor muscles, are well correlated with
hopping performance (reviewed in Emerson, 1985):
species that can leap rapidly over large distances
© 2002 WILEY-LISS, INC.
DOI 10.1002/jmor.1091
between species may reflect size differences only. In addition, Rana’s muscles exhibited greater passive resistance
to elongation, implying more elastic tissue is present,
which may amplify force at take-off due to elastic recoil.
Rana’s muscles also achieved a higher percentage of maximum force at lower stimulus inputs (frequencies and
durations) than in Bufo, perhaps amplifying the differences in force available for limb extension during natural
stimulation. Twitch contraction and relaxation times
tended to be faster in Rana, although variation was great,
so that differences were significant only for Per. Fatigability also tended to be greater in Rana muscles, although,
again, values reached significance in only one muscle (PL).
Thus, in addition to biomechanical effects, differences in
hopping performance may also be determined by diverse
physiological properties of the muscles. J. Morphol. 251:
309 –322, 2002. © 2002 Wiley-Liss, Inc.
KEY WORDS: muscle; contractile properties; hopping;
Rana pipiens; Bufo marinus
and heights have longer hindlimbs and larger extensor muscle masses than species that walk or hop
only short distances.
In addition to mechanical factors such as muscle
size, leverage, and passive properties, behavioral
diversity in frogs may be correlated with physiological differences in their muscles. A number of histochemical studies (Lannergren and Smith, 1966;
Smith and Ovalle, 1973; Lannergren and Hoh, 1984;
Rowlerson and Spurway, 1988; reviewed by Gans
and De Gueldre, 1992) have identified a diversity of
muscle fiber types that parallels the diversity found
in mammals. But few comparative studies have attempted to link differences in muscle fiber diversity
with differences in behavior (Putnam and Bennett,
1983; Rubenstein et al., 1983; Rowlerson and Spur-
*Correspondence to: Susan E. Peters, Department of Biology, 9201
University City Blvd., University of North Carolina at Charlotte,
Charlotte, NC 28223. E-mail: [email protected]
310
B.A. CHADWELL ET AL.
way, 1988; Spurway and Rowlerson, 1989). Likewise, studies of contractile properties have identified
a range of responses among motor units within frogs
(Smith and Lannergren, 1968; Luff and Proske,
1976, 1979; Ridge and Thomason, 1980; Peters,
1994), but few have compared contractile properties
among frogs with different behaviors (Lutz and
Rome, 1996; Peters and Nishikawa, 1999; Peters
and Aulner, 2000).
The goal of our study was to examine the isometric
contractile properties of three hindlimb extensor
muscles from two species of anurans with different
hopping abilities. The leopard frog, Rana pipiens,
jumps very rapidly to many times its body length,
but typically does not sustain continuous hopping
for more than a few strides. Rana has the basic
morphology of a good jumper: very long hindlimbs
and large extensor muscles. Bufo marinus, like most
toads, has relatively short legs and small extensor
muscles. They use short hops, but take multiple
strides in sequence. A comparison of contractile
properties can help to determine whether, in addition to obvious disparities in muscle size which may
account for differences in relative force, intrinsic
properties of their muscles, such as differences in
speed of contraction, force differences in response to
stimuli, and variable fatigability may contribute to
their behavioral differences.
MATERIALS AND METHODS
Wild-captured Rana (n ⫽ 19), ranging in size from
47–110 g (x៮ ⫽ 70.7 ⫾ 4.3 g), were acquired from
Charles Sullivan, Co. (Nashville, TN), and Bufo (n ⫽
21), ranging in size from 65–296 g (x៮ ⫽ 155.6 ⫾
16.9 g), were acquired from Glades Herpetology (Ft.
Myers, FL). The animals were kept in a light- and
temperature-controlled room (12 h light, 12 h dark;
T ⫽ 22 ⫾ 2°C) in large polyethylene tanks (75 ⫻
75 ⫻ 95 cm) with free access to fresh water and fed
a diet of crickets. Three times per week the animals
were exercised on an 8-foot runway (8“ wide, with a
wooden back and Plexiglas front, 18” tall) covered
with low-pile carpet to facilitate traction for hopping. Animals were urged to hop repeatedly until
they refused. No individual was housed for more
than 3 weeks before it was used in an experiment.
Myology
Three hindlimb muscles were chosen for testing in
both species (Fig. 1). The semimembranosus (SM) is
the largest caudal thigh muscle. From its origin on
the ischium, it runs along the posterior femur and
inserts on the proximal, medial side of the tibiofibula (Fig. 1). It is a major hip extensor (Dunlap,
1960). The plantaris longus (PL) is the largest muscle of the lower hindlimb, originating at the back of
the lateral femoral condyle and inserting on the
plantar aponeurosis (Fig. 1). It is thought to be par-
Fig. 1. Dorsolateral view of the right hindleg of a frog illustrates the three experimental muscles. The hip extensor, semimembranosus (SM), originates on the posterior ischium. It inserts partially on the ventromedial surface of the distal femur,
but also crosses the knee to attach to the deep, medial surface of
the tibiofibula, just distal to the knee joint. The other two extensors are also biarticular. At the knee, plantaris longus (PL) originates from two sites: by a slender dorsolateral tendon from the
aponeurosis covering the knee and from the posterior side of the
knee joint by a thick tendon attaching to the heavy joint capsule.
It inserts by a thick, strap-like tendon that wraps posteriorly
around the ankle to form the plantar aponeurosis. The peroneus
(Per) originates from the lateral surface of the distal femur. Its
tendon emerges dorsolaterally from beneath the knee aponeurosis. Distally, Per inserts partially on the tibiofibula via a broad,
flat tendon and via two short tendons onto the proximal tarsus.
tially homologous to the mammalian gastrocnemius
and is the primary ankle extensor of frogs (Dunlap,
1960; Kamel et al., 1996). The peroneus (Per) is a
relatively small muscle on the lateral side of the
lower leg (Fig. 1). During hopping in tree frogs, Per
has a substantial moment arm at the knee until it
reaches full extension (Marsh, pers. comm.), so that
it may contribute to knee extension. Due to its small
size, however, its role in knee extension may be
minor (Marsh, 1994). At the insertion, Per partially
attaches to the distal, lateral tibiofibula, but two
HINDLIMB CONTRACTILE PROPERTIES IN TWO FROGS
tendons continue into the foot, inserting onto the
fibulare (Fig. 1). Thus, Per may also function to
pronate the foot, possibly stabilizing the ankle during stance and/or during ankle extension. The primary role of Per is presently the least certain of the
three muscles and requires EMG studies to better
elucidate its function(s). Its relative size and position suggest that it may have both phasic (knee
extension) and postural (at the ankle) roles.
Kinematics
We examined hopping performance in both species by videotaping (Panasonic Wideview 3260, 30
fps) sample hops within the 8-foot runway. Simultaneous dorsal and lateral views were obtained by
placing a mirror at a 45° angle above the runway.
Good jumps showing clear take-off and landing for
each species were analyzed on a VCR (JVC HRS7500U) using Image-Pro Plus software (Media Cybernetics, Silver Spring, MD). Using the center of
the eye as a landmark, the maximum take-off velocities and accelerations were determined by measuring the linear translation of the center of the eye in
the two frames prior to take-off and two frames
following take-off. Maximum velocity invariably was
reached in the frame in which the toes last touched
the ground. In addition, average jump distance and
height were calculated for each species in both raw
cm and in distance/body length.
In order to generate contractile data over a range
of muscle lengths that are functionally relevant, we
measured the joint angle changes during hopping
from these videotapes. Data for Rana were already
available (Peters et al., 1996), so we concentrated on
describing the joint angles used by Bufo during normal hopping. The anterior iliofemoral (hip), posterior femorotibial (knee), and anterior tibiotarsal
(ankle) joints were measured at positions that corresponded to quiet standing (As), maximum hindlimb extension at take-off (Ae), and maximum hindlimb flexion at the end of the hop (Af). Since the
bones do not lie within the same vertical or horizontal planes, these angles were measured on the video
screen in both the lateral (L) and dorsal (D) views
with a protractor, and the actual joint angles between the bones (⌰) were calculated using the formula:
cos ␪ ⫽
1
冑1 ⫹ tan L ⫹ tan 2D
2
Where L and D exceeded 90°, the resultant angle
was subtracted from 180° to give the correct angle, ⌰
(Peters et al., 1996).
During experiments to measure the contractile
properties, marker ties were placed on the origin
and insertion tendons of each muscle and the limbs
were set to mimic the joint angles found at standing
311
(As), maximum limb extension (Ae), and flexion (Af).
The joint angles were set using a tool which consists
of three 3⬙ lengths of Plexiglas (81⬙ thick and 85⬙ wide),
joined by small machine screws and wing nuts to
produce a central strip with movable joints at each
end. Open grooves of approximately 2 cm length
were cut at each end of the center Plexiglas strip to
allow the screws attaching the two end pieces to
slide. Thus, the distance between the two joints
could be adjusted to match the positions of actual
limb joints. The frog’s leg was placed over this device
and the wing nuts were loosened so the end pieces
could be spaced to match the length of the central
limb element (e.g., femur or tibia). The appropriate
joint angles were set using a protractor and the frog
limb was held against the Plexiglas strips so that
the joint angles matched the set angles. One researcher held the limb in place while a second researcher measured the muscle length between
marker ties. For SM, muscle length is influenced by
hip and knee angles, so these joints were set at As,
Ae, and Af, and each of the resulting muscle lengths
were measured between the marker ties. For both
PL and Per, muscle length is determined by the
positions of knee and ankle joints, so these joints
were set at the three reference angles and muscle
lengths were measured. The metatarsophalangeal
and interphalangeal joints were held at 180°, i.e.,
the foot was kept flat during these measurements.
Marker ties at the origins were set in tough fascia or
joint capsule as close to the middle of the origin as
possible; the insertion ties were placed near the
junction of the muscle fibers with the tendons. Muscle lengths occurring at each of the reference angles
are referred to as Ls (length at quiet standing), Le
(length when the hindlimb is fully extended), and Lf
(length when the hindlimb is fully flexed).
Contractile Properties
The contractile properties we measured reflect the
properties of the muscles maximally stimulated under isometric conditions. Differential recruitment of
motor units cannot be replicated in our tests. In
addition, although isometric or near-isometric conditions often occur in normal muscle behavior (e.g.,
Lutz and Rome, 1996; Biewener, 1998; Peters et al.,
1996), shortening and lengthening contractions are
also typical (e.g., Gillis and Biewener, 2000), certainly for muscles like these, which must generate
power. Our data, therefore, cannot be seen to fully
mimic natural conditions. We report the maximum
possible isometric forces and, in the absence of data
on in vivo forces or shortening velocities, we can only
discuss the comparison of results between species in
relative terms. These data at least provide a common set of parameters within which to compare
muscles and species. We assume that differences in
isometric properties are relevant to the differences
that would obtain in normal behavior.
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B.A. CHADWELL ET AL.
Specimens were anesthetized using tricaine methane sulfonate (MS222; 200 mg/kg body mass; subcutaneous), and then rendered brain-dead by pithing.
Before surgery, snout–vent length and limb segment
lengths (femur, tibiofibula, and foot [from ankle to
tip of longest toe]) were measured for each specimen
to within 0.1 mm using dial calipers and body mass
was determined (⫾0.1 g). Only one of the three muscles under study was tested in an individual. Surgery was performed to expose the muscle and its
nerve and to clear its fascia from surrounding muscles. As appropriate, marker ties were placed at the
origin and insertion of the experimental muscle so
that Ls, Le, and Lf could be measured (see above).
Once these measurements were made, the insertion
tendon was severed close to the bone and the primary muscle nerve branch was cut from its upstream connections.
With the experimental muscle and its nerve isolated, the specimen was clamped to a heavy metal
frame at the pelvis, knee, and ankle. Care was taken
to maintain blood flow to the muscle and nerve and
the preparation was kept moist by constant irrigation with amphibian Ringer’s. All tests were conducted at room temperature (22 ⫾ 2°C). A lowcompliance tie (#2 suture silk) was sutured into the
tendon as close to the muscle fibers as possible and
the tie was attached along a natural line of pull to
the isometric force transducer (Grass FT03 or FT10,
as appropriate). The force transducer was mounted
on a rack and pinion so that muscle lengths could be
varied over the natural range previously determined. A bipolar EMG electrode was implanted in
the muscle belly (0.1 mm coated stainless steel wire;
California Fine Wire, Grover City, CA) parallel to
the predominant muscle fiber direction. The EMG
signals were monitored throughout the experiment,
since a decline in EMG signal might indicate fatigue
at the neuromuscular junction, deterioration of the
muscle, or other stimulation problems. Only tests in
which EMG signals remained ⬎90% of the initial
EMG amplitude were included in this study. Signals
from the force transducer and the EMG electrode
were amplified (respectively, by Grass TM501-1 and
Grass P511 AC preamplifiers) and displayed on a
Tektronix (TDS310) digital oscilloscope. Simultaneous hardcopies were made on an HP LaserIII
printer.
Supramaximal stimuli (2.5⫻ threshold voltage) of
0.1 msec duration were delivered to the severed
nerve via bipolar platinum hook electrodes using a
Grass S88 square wave stimulator. Single stimuli of
0.1 msec duration were delivered to elicit wholemuscle isometric twitch tension (Tw). Tetanic tensions (TT) were stimulated using a train of 0.1 msec
pulses at 80 pps for a duration of 670 msec. These
forces were measured at 1-mm length intervals for
Per and at 2-mm length intervals for PL and SM
over their natural length excursions to produce active length–tension curves. In addition, passive ten-
sions were measured at each length by slackening
the muscle, zeroing the oscilloscope trace, and then
stretching the muscle out to each appropriate
length. Any rise in the oscilloscope baseline due to
passive resistance to elongation was then recorded.
During active stimulation tests, muscles were rested
for 2 min following each tetanic stimulation to minimize the possibility of fatigue.
From the length–tension tests, we determined the
length at which maximum tension is produced
(physiological length, Lo) for each muscle. All further tests were performed at this length. Using the
maximal twitch, contraction time (CT) was measured from the stimulus artifact to peak force, and
half-relaxation time (Tw 1/2 RT) from the peak of
force to the point where force has fallen to one-half of
peak. Tetanic half-relaxation time (TT 1/2 RT) was
measured from the maximal tetanus as the time
from cessation of the EMG signal (offset of stimulation) to the point where the force fell to half of peak
tension. From the values of maximum Tw and maximum TT, a twitch/tetanus ratio (Tw/TT) was calculated to determine the fraction of maximal force
produced by an individual twitch. Two additional
tests were performed to determine the amount of
force that a muscle develops under varying patterns
of stimulation: force–frequency and force– duration
tests. In the force–frequency test, tetanic trains of
constant duration (670 msec) were delivered at varying stimulus frequencies, from 5– 40 pps in 5 pps
increments, and also at 60 pps and 80 pps. A force–
duration test was also done in which stimulation
frequency was kept constant at 30 pps but train
duration was varied from 50 –200 msec in 50 msec
increments, and also delivered at 300 and 670 msec
durations. The frequency of 30 pps was chosen because it is just greater than the fusion frequencies
for all of the experimental muscles (see Table 3).
Throughout these two tests, the muscles were again
rested for 2 min between each stimulus train to
minimize the effects of fatigue. The data in the
force–frequency and force– duration curves are reported as force in percent of maximal force at each
stimulation frequency or duration. This allows easy
comparison of relative amounts of force produced by
different muscles within and between species.
The final test for fatigability was done by stimulating the muscle once every 4 sec using a short
tetanic train of 200 msec duration at 30 pps for a
total of 4 min (Peters, 1994). From these results a
fatigue index (FI) was calculated as the sum of forces
over the first 2 min of the test divided by the sum of
forces over all 4 min (⫻100) (Burke et al., 1973;
Peters, 1994). An FI of 50 indicates that there is no
fatigue; an FI ⬎50 indicates increasing fatigue as
the FI approaches 100. In addition, to visualize the
decay of force over the 4 min for each muscle, we
calculated the average force at 20-sec intervals and
plotted these in percent of the initial force.
HINDLIMB CONTRACTILE PROPERTIES IN TWO FROGS
313
Upon completion of all isometric tests, the muscles from the nonexperimental leg were removed
and their masses measured. Whole-muscle crosssectional areas were estimated by dividing muscle
mass (which is proportional to volume) by Lo for
each muscle in each specimen. From these measurement we could then calculate force per gram of muscle mass and force per cm2 of muscle cross-section in
an effort to see whether these vary between muscles
or species. Our estimate of muscle cross-section assumes that at Lo angles of pinnation are negligible
and are the same between species. What is most
likely is that at Lo for any muscle the angle of pinnation is minimal to allow for the most effective
sarcomere length. Our estimates of force/cm2 assumes that, between these species, the angles of
pinnation for a given muscle are so similar at Lo that
this rough estimate of muscle cross-section can be
used for comparative purposes.
species over the intervals being tested, or whether
there was an overall difference in the curves between species. Thus, within these curves we analyzed each interval between species separately. For
the length–tension curves, the forces in percent of
body mass at each length interval were compared
between Rana and Bufo in a one-way ANOVA. In
the force–frequency, force– duration and fatigue
curves, the forces were converted to percent of maximum force in each animal and one-way ANOVAs
were run to compare the relative forces at each
interval. Fisher’s post-hoc test was then used for
pair-wise comparisons. In all cases of multiple comparisons, to preserve an experiment-wise error rate
of P ⬍ 0.05, alpha levels were adjusted using the
sequential Bonferroni technique (Rice, 1989).
Data Analysis
Our data show that in a direct comparison of body
mass (BM) and snout–vent length (SVL), Bufo was
significantly heavier (⬇2.5 times) and longer (⬇1.5
times) than Rana (Table 1). The ratio of SVL to BM,
however, was higher in Rana, making it relatively
long for its mass; Bufo is comparatively short and
stout (Table 1). The raw hindlimb muscle masses,
muscle cross-sectional areas, and limb segment
lengths are similar between the two species. However, when the differences in body size are taken
into consideration, most hindlimb values were significantly greater in Rana than in Bufo (Table 1). All
segments of the hindlimb (femur, tibiofibula, foot
length, and total hindlimb length) were significantly
longer in Rana and all three muscles were significantly larger relative to body mass in Rana. The PL,
however, was the only muscle whose relative crosssectional area differed significantly between species,
being larger in Rana. Within species, in both Rana
and Bufo the foot was the longest segment of the leg
and the femur did not differ from the tibiofibula.
Thus, in spite of overall size differences, Rana and
Bufo hindlimbs have similar proportions. In both
species, relative muscle masses differed such that
PL was significantly the largest, SM was intermediate in size, and Per was the smallest of the three
muscles (Table 1). Within Rana, the whole muscle
cross-sectional area in PL and SM were equally
large and both were significantly larger than Per.
The cross-sectional areas of PL and SM were also
equally great within Bufo and PL was significantly
larger than Per, but the difference between SM and
Per did not reach significance (Table 1).
A number of the characters we compared between
species (muscle forces, muscle masses and crosssections, height and distance of hops, and limb
lengths) might be expected to differ simply because
of the significant difference in overall body size between Rana and Bufo (see below). Often such body
size differences are accounted for in an ANCOVA in
which the raw data are adjusted by using a body size
factor (such as body mass or snout–vent length) as a
covariate. When we attempted the ANCOVAs, we
found that in most cases there were heterogeneous
slopes in our data, making the results from an
ANCOVA difficult to interpret. Therefore, in order to
adjust for body size effects we converted the data
into percentage ratios (e.g., %TT/BM, %femur
length/SVL, etc.). Tests for normality showed that
the simple percentage data were normally distributed for each species and muscle, so ANOVAs were
done on these percentages to compare between and
within species. Fisher’s post-hoc test was used to
examine all the pair-wise comparisons between species and muscles.
A number of other characters did not require scaling for body size differences. One-way ANOVAs
were performed on CT, Tw 1/2 RT, TT 1/2 RT,
fusion–frequency, and the FI. Three other ratios
were also analyzed using one-way ANOVA, the
Tw/TT ratio, tetanic force/g muscle mass, and tetanic force/cm2 of muscle cross-section. These tests
were also followed by Fisher’s post-hoc test to examine the pair-wise comparisons.
In the length–tension curves, the force–frequency
and force– duration curves and the profile of force
decline during fatigue, we were interested only in
comparing the forces between species at each interval (e.g., length, stimulus, or time). A repeated measures ANOVA, therefore, was not done, since this
only tells us whether the force changed within a
RESULTS
Morphology
Hopping Performance
Comparisons of hopping performance between
anuran species (Zug, 1972, 1978; Emerson, 1985)
have shown that those with relatively the longest
hindlimbs are typically faster and jump further than
314
B.A. CHADWELL ET AL.
TABLE 1. Morphological comparison of Rana and Bufo (x៮ ⫾ SE)
Rana (n ⫽ 19)
70.7 ⫾ 4.3
86.4 ⫾ 1.5
118.0 ⫾ 6.0
Body mass (g)
Snout–vent length (mm)
(%BM)
Muscle mass
Semimembranosus (g)
(%BM)
Plantaris longus (g)
(%BM)
Peroneus (g)
(%BM)
Muscle cross-section
Semimembranosus (cm2)
(%BM)
Plantaris longus (cm2)
(%BM)
Peroneus (cm2)
(%BM)
Femur length (mm)
(%SVL)
Tibiofibula length (mm)
(%SVL)
Foot length (mm)
(%SVL)
Total limb length (mm)
(%SVL)
0.57 ⫾ 0.02
1.03 ⫾ 0.8
1.61 ⫾ 0.2
1.77 ⫾ 0.2
0.30 ⫾ 0.004
0.45 ⫾ 0.02
0.17 ⫾ 0.02
0.30 ⫾ 0.04
0.38 ⫾ 0.03
0.42 ⫾ 0.01
0.08 ⫾ 0.004
0.12 ⫾ 0.007
39.5 ⫾ 0.7
45.8 ⫾ 0.3
43.2 ⫾ 0.9
50.0 ⫾ 0.3
65.6 ⫾ 1.2
76.0 ⫾ 0.4
148.4 ⫾ 2.7
171.8 ⫾ 0.7
Bufo (n ⫽ 21)
夡
155.6 ⫾ 16.9
124.0 ⫾ 3.4
69.8 ⫾ 5.4
*
0.51 ⫾ 0.03
0.65 ⫾ 0.02
1.52 ⫾ 0.3
0.86 ⫾ 0.03
0.37 ⫾ 0.03
0.17 ⫾ 0.005
*
*
*
Within species*
PL ⬎ SM ⬎ Per
0.15 ⫾ 0.02
0.20 ⫾ 0.02
0.38 ⫾ 0.06
0.22 ⫾ 0.009
0.09 ⫾ 0.006
0.11 ⫾ 0.07
45.0 ⫾ 1.3
36.4 ⫾ 0.4
43.9 ⫾ 1.1
35.4 ⫾ 0.5
74.1 ⫾ 1.8
59.9 ⫾ 0.4
163.0 ⫾ 4.0
131.7 ⫾ 1.0
*
*
*
*
*
Within Rana*
PL ⫽ SM ⬎ Per
Within Bufo*
PL ⬎ Per; PL ⫽ SM; SM ⫽ Per
Within species*
foot ⬎ femur ⫽ tibiofib
夡 ⫽ Significant differences between species based on one-way ANOVA on raw data.
* ⫽ Significant differences between species based on one-way ANOVAs on percentage data.
To maintain an experiment-wise error rate of 0.05, all results were subjected to the sequential Bonferroni adjustment; k ⫽ 8.
shorter-legged species. Our morphological data (Table 1), led us to predict that Rana would be the
longer and faster jumper. As Table 2 shows, this is
indeed the case. Rana achieved significantly greater
take-off velocities and accelerations than did Bufo
and produced jumps that were much higher and
longer relative to body length. Thus, the behavioral
differences between species are consistent with past
findings and correlate well with the differences in
limb morphology that we found.
Maximum Isometric Force
As noted above, PL was the largest muscle by
mass and cross-section, SM tended to be intermediate, and Per was smallest (Table 1). A similar relationship is reflected in muscle force (Table 3). In
both Rana and Bufo, the maximum twitch and te-
tanic forces produced by PL were much larger than
those produced by SM and Per (⬇3–7 times more).
The twitch and tetanic forces produced by SM, however, were equal to Per forces within both species.
Between species, PL was relatively larger by mass
in Rana than in Bufo (Table 1) and it produced
significantly relatively larger twitch and tetanic tensions in Rana. The twitch force of SM was larger in
Rana than in Bufo, but the difference between species did not reach significance for the twitch of Per.
Both SM and Per produced equivalent tetanic forces
in both species (Table 3).
If we examine the forces produced relative to muscle size, in Rana PL produced greater tetanic force
per gram of muscle mass and per cm2 of crosssectional area than the other two muscles (Table 3).
Within Rana, SM and Per did not differ from each
other in the amounts of force relative to muscle size.
TABLE 2. Jumping performance of Rana and Bufo (x៮ ⫾ SE)
Rana (n ⫽ 4)
Maximum take-off velocity (m/sec)
Maximum acceleration (m/sec2)
Distance hopped (cm)
(%SVL)
Height hopped (cm)
(%SVL)
2.89 ⫾ 0.2
61.0 ⫾ 8.8
25.2 ⫾ 3.8
2.98 ⫾ 0.45
10.0 ⫾ 1.8
1.2 ⫾ 0.2
Bufo (n ⫽ 4)
夡
夡
*
*
1.88 ⫾ 0.2
31.8 ⫾ 4.2
18.7 ⫾ 1.2
1.61 ⫾ 0.1
7.7 ⫾ 1.2
0.66 ⫾ 0.1
夡 ⫽ Significant difference between species in a one-way ANOVA on raw data.
* ⫽ Significant difference between species in a one-way ANOVA on percentage data.
Alpha levels were adjusted for multiple comparisons to maintain an experiment-wise error rate of 0.05
using the sequential Bonferroni method; k ⫽ 4.
HINDLIMB CONTRACTILE PROPERTIES IN TWO FROGS
315
TABLE 3. Comparison of muscle sizes and contractile properties (x៮ ⫾ SE)
Semimembranosus
Rana
Tw (g)
(N)
(%BM)
TT (g)
(N)
(%BM)
Tw/TT
Fusion frequency (pps)
Force/muscle mass (g/g)
Force/cm2 (kg/cm2)
CT (msec)
Tw 1⁄2 RT (msec)
TT 1⁄2 RT (msec)
Fatigue index
Bufo
Plantaris longus
Rana
Bufo
55.6 ⫾ 6.0
19.5 ⫾ 1.8
448.6 ⫾ 48.5
237.7 ⫾ 48.9
0.54
0.33
3.75
2.33
100.9 ⫾ 16.4PL * 25.2 ⫾ 2.8PL
498.9 ⫾ 45.7 * 132.8 ⫾ 17.0
296.0 ⫾ 18.9
311.4 ⫾ 26.6
1564.0 ⫾ 80.8
1619.4 ⫾ 258.4
2.9
3.0
15.3
15.9
PL
PL
531.5 ⫾ 55.9
388.8 ⫾ 21.0
1756.2 ⫾ 112.3 * 931.8 ⫾ 93.4
0.19 ⫾ 0.01PL * 0.07 ⫾ 0.008PL
0.29 ⫾ 0.03 *
0.14 ⫾ 0.01
22.0 ⫾ 1.2
25.0 ⫾ 1.9
22.0 ⫾ 1.1
24.3 ⫾ 1.7
PL
517.2 ⫾ 33.0
604.2 ⫾ 46.8
991.8 ⫾ 67.0
1088.1 ⫾ 113SM
1.88 ⫾ 0.2PL
2.11 ⫾ 0.2
4.17 ⫾ 0.2
4.24 ⫾ 0.5SM
PL
PL
51.2 ⫾ 2.0
56.5 ⫾ 2.4
64.0 ⫾ 2.2
72.0 ⫾ 3.8
36.8 ⫾ 4.6
52.3 ⫾ 4.5Per
55.4 ⫾ 8.6
65.8 ⫾ 6.3Per
PL
153.1 ⫾ 9.2
150.8 ⫾ 13.5
190.7 ⫾ 15.1 * 134.8 ⫾ 8.8
58.4 ⫾ 0.8Per
54.8 ⫾ 0.8
58.2 ⫾ 1.0Per *
54.4 ⫾ 1.0
Peroneus
Rana
Bufo
34.0 ⫾ 3.3
0.33
53.3 ⫾ 7.0PL
189.8 ⫾ 14.9
1.9
298.2 ⫾ 34.8PL
0.18 ⫾ 0.02PL
23.9 ⫾ 1.1
657.2 ⫾ 72.7PL
2.4 ⫾ 0.2PL
45.6 ⫾ 1.8PL
40.8 ⫾ 6.7
127.5 ⫾ 8.8PL
53.7 ⫾ 1.0
22.1 ⫾ 5.1
0.22
11.0 ⫾ 3.0PL
421.4 ⫾ 34.3
4.1
207.4 ⫾ 20.8PL
0.05 ⫾ 0.009PL
23.6 ⫾ 1.8
1193.1 ⫾ 127SM
4.69 ⫾ 0.4SM
55.2 ⫾ 2.0PL
89.1 ⫾ 7.2
161.8 ⫾ 4.8
56.4 ⫾ 0.4
*
*
*
*
*
*
*Significant difference between species for a given muscle.
Superscript muscle abbreviations indicate which other muscle this muscle differs from within the species.
In order to preserve an experiment-wise error rate of 0.05, alpha levels were adjusted with sequential Bonferroni method; k ⫽ 10.
So the differences in force relative to muscle size
within Rana are the same as the differences we saw
in overall muscle force (PL ⬎ SM ⫽ Per). In Bufo,
however, a different relationship holds for the sizespecific force differences (Table 3): as in Rana, PL
produces greater force per gram and per crosssection of muscle than does SM. However, Per produces force per gram and per cm2 that is equivalent
to PL and significantly larger than in SM. Compared
between species, there was no difference in the force
per gram of muscle mass or per cm2 of cross-section
between SMs and PLs. Because of the relatively
more forceful Per in Bufo, however, there was a
significant difference between force per gram and
per cross-section with the Per of Rana.
Length–Tension
In addition to comparing the maximum isometric
twitch and tetanic forces, we constructed isometric
length–tension curves. Whereas these static forces
do not reflect the actual amounts of force during
normal behaviors (i.e., they cannot account for differences in motor unit recruitment, or dynamic force
changes as with shortening or lengthening), they at
least give us an equivalent set of physiological conditions within which to compare species.
To test the muscles within a meaningful behavioral context, we measured the joint angle and muscle length changes over the natural range of movement in both species. Table 4 shows the pertinent
joint angles and muscle length changes found in
both Rana and Bufo. Most joint angles used by Rana
are more flexed at landing and more extended at
take-off than in Bufo. This is particularly marked in
Rana’s more extended limb joints at take-off (Table
4). In spite of this greater range of joint angles in
Rana, the changes in muscle lengths did not differ
significantly from those in Bufo (Table 4). Since all
three muscles under study cross more than one
joint, there is a reciprocal change in length at each
end of the muscles which results in relatively little
overall length change (e.g., Bock, 1968; Peters et al.,
1996; Gillis and Biewener, 2000). For our muscles,
the difference between maximum and minimum
static lengths varied by a maximum of only about
8 –15% of standing length (Ls). In both species, Per
varied the least over its full range of lengths: by only
⬇5% of Ls in Bufo and virtually no change in Rana
(Table 4).
The active and passive length–tension curves are
shown in Figure 2. The significantly larger active
forces relative to body mass produced by PL over
most of its length change are evident within both
species (Fig. 2a). Within species, SM tended to produce intermediate amounts of force, although the
values in both species did not differ significantly
from the forces produced by Per. Between species,
SM and Per did not differ significantly in force produced at any of the lengths. However, PL values
were significantly greater in Rana than in Bufo at
all lengths ⬎95% Ls. The active length–tension
curves for Rana muscles do not appear to be as flat
as the Bufo muscles, although over the range from
90 –100% Ls the difference in rate of change was only
significant for PL (Fig. 2a).
The passive tension produced over the normal
range of lengths was relatively small in all three
muscles of both species. All three muscles in Bufo
produced maximum passive tension of ⬍5% of maximum active tension, and none differed from each
other in amounts of passive tension over their entire
range of lengths. At maximum lengths in Rana, SM
produced maximum passive tension of about 4% of
active tension, which did not differ from the passive
tension of Bufo’s SM. However, both PL and Per in
Rana produced significantly greater maximum passive tension (PL ⫽ 8.8% of active tension; Per ⫽
316
B.A. CHADWELL ET AL.
TABLE 4. Joint angle and muscle length changes in Rana and Bufo (x៮ ⫾ SE)
Joint angles
Hip
Knee
Ankle
As
Af
Ae
As
Af
Ae
As
Af
Ae
Rana
72 ⫾ 1.9
67 ⫾ 4.3
134 ⫾ 1.6
*
113 ⫾ 3.4
26 ⫾ 1.6
*
41 ⫾ 3.3
26 ⫾ 1.1
*
45 ⫾ 2.2
130 ⫾ 6.6
*
101 ⫾ 3.1
68 ⫾ 1.8
*
56 ⫾ 3.3
52 ⫾ 2.5
Bufo
52 ⫾ 1.0
*
62 ⫾ 2.4
144 ⫾ 4.3
*
121 ⫾ 5.6
1
55 ⫾ 2.5
2
Muscle lengths
PL
Rana (mm)
(%Ls)
Bufo (mm)
(%Ls)
SM
Per
Ls
Lf
Le
Ls
Lf
Le
Ls
Lf
Le
41.2 ⫾ 0.8
100
37.4 ⫾ 1.6
100
41.9 ⫾ 0.9
101.7
37.9 ⫾ 1.6
101.5
38.7 ⫾ 0.9
94.0
34.7 ⫾ 1.3
92.8
35.7 ⫾ 0.6
100
37.7 ⫾ 1.1
100
36 ⫾ 0.3
100.8
38.7 ⫾ 0.8
102.7
30.5 ⫾ 0.9
85.5
31.9 ⫾ 1.0
84.6
35.5 ⫾ 1.1
100
37.7 ⫾ 0.9
100
35.4 ⫾ 0.9
99.7
37.8 ⫾ 0.9
100.4
35.4 ⫾ 1.2
99.7
36.1 ⫾ 1.1
95.8
1
Mean joint angles for Rana pipiens taken from Peters et al., 1996.
No significant differences in muscle lengths were found between species for any muscle at any position.
As ⫽ joint angle during quiet standing.
Af ⫽ joint angle when hindlimb is maximally flexed, at the end of the hop.
Ae ⫽ joint angle when hindlimb is maximally extended, just after foot-off in the hop.
Ls ⫽ muscle length during quiet standing.
Lf ⫽ muscle length when hindlimb is maximally flexed.
Le ⫽ muscle length when hindlimb is maximally extended.
*Significant difference between species. To maintain an experiment-wise error rate of 0.05, alpha levels were adjusted using the
sequential Bonferroni method; k ⫽ 9.
2
13.4% of active tension) than their homologs in Bufo
(PL ⫽ 2.9% of active tension; Per ⫽ 4.4% of active
tension). In fact, Rana’s PL produced greater passive tension than Bufo’s PL at all lengths tested
(Fig. 2b) and Rana’s Per was greater than Bufo’s at
the two longest lengths tested.
Contraction and Relaxation Times
Table 3 summarizes the contraction and relaxation times. Within both species, PL had the slowest
twitch CTs and SM did not differ significantly from
Per in CT. Between species, neither SM nor PL
differed in CT; however, Per in Rana was significantly faster-contracting than Bufo’s Per. Both
twitch and tetanic half-relaxation times were measured. Within Rana, all three muscles had equivalent twitch half-relaxation times (Tw 1/2 RTs). In
Bufo, however, the Tw 1/2 RT of Per was significantly slower than those of PL and SM. This very
slow Tw 1/2 RT in Bufo’s Per also differed significantly from Rana’s Per. Neither PL nor SM differed
significantly in Tw 1/2 RT between species. The tetanic half-relaxation times (TT 1/2 RTs) within Bufo
were equivalent between all three muscles; however,
in Rana, the TT 1/2 RT of PL was significantly
slower than in SM or Per. Across species, both PL
and Per differed in TT 1/2 RT; PL was significantly
slower in Rana than Bufo, but Per of Rana was
significantly faster than Bufo’s Per.
Force Variation With Varying Stimulation
A number of tests help us to examine the variation
in force produced with varying stimuli. A commonly
reported value is the twitch/tetanus ratio (Tw/TT).
This ratio had the same pattern within both species:
SM and Per produced equivalent Tw/TTs which
were significantly smaller than PL’s ratio (Table 3).
Thus, PL produced the largest amount of force in a
single twitch relative to its maximum tetanic force
within both species. Across species, the activation of
twitch force was significantly greater in Rana than
in Bufo. In all three muscles, Rana’s Tw/TT ratios
averaged more than twice those of Bufo (Table 3).
To further test variation in force with different
stimulus regimes, we performed the force–frequency
and force– duration tests (see Methods). In general,
the results showed that, when differences occurred,
Rana’s muscles produced relatively greater force at
lower rates and durations of stimulation. The difference was least marked in the force–frequency results (Fig. 3a). All three muscles in Rana produced a
greater percent of maximum force than their homologs in Bufo at the lowest stimulus frequency (5
pps). At 10 pps, only Rana’s SM still produced more
force than SM in Bufo. At stimulus frequencies
above 10 pps there were no significant differences in
the relative amounts of force produced by the muscles between Rana and Bufo.
In the force– duration test (Fig. 3b), all three Rana
muscles again produced greater relative force at the
lowest stimulus input (50 msec train duration). At
HINDLIMB CONTRACTILE PROPERTIES IN TWO FROGS
Fig. 2. Isometric length–tension curves are shown for both
active (a) and passive (b) tensions. Forces in percent of body mass
are plotted for plantaris longus (PL), semimembranosus (SM),
and peroneus (Per) in both species over a range of lengths mimicking those where the muscles are likely to be active during
hopping. Lengths are plotted relative to the muscle lengths at
quiet standing (Ls). Note the differences in scale between a and
b on both axes. Asterisks (*) indicate significant differences that
occurred between muscles of Rana and Bufo at selected lengths.
all other stimulus durations (from 100 –300 msec),
both SM and Per in Rana also produced significantly
greater relative forces than these muscles in Bufo,
but the difference between PL forces did not reach
significance.
Fatigue
We report two indicators of fatigue, the fatigue
index (FI) and the graphic profile of fatigability over
the entire 4-min fatigue test (Fig. 4). Both of these
results show that, within the parameters of our fatigue test, only moderate fatigue occurred. All muscles maintained 60% or more of their initial force at
the end of 4 min (Fig. 4). The FIs indicate that the
only significant difference between species was in
PL, with Rana’s PL somewhat more fatigable than
Bufo’s (Table 3). Within species, Bufo’s muscles
were all equivalent in fatigability based on their
FIs. Within Rana, SM and PL had equivalent FIs,
but Per was significantly less fatigable than both
(Table 3).
The average force (in percent of initial force) at
each 20-sec time interval over the 4-min test was
compared between the muscles of both species (Fig.
317
4). By 40 sec, both PL and Per of Rana produced
relatively more force than these muscles in Bufo.
This appears to result from a potentiation of force
seen in both muscles. All three muscles in Rana and
SM in Bufo produced ⬎100% of initial force up to
100 sec into the 4-min test. In the case of PL and
Per, this resulted in significantly greater relative
force production in Rana than in the same muscles
of Bufo up to 100 sec. From 120 –160 sec, only Per
differed between species, with Rana Per maintaining relatively more force than Per in Bufo. From 180
sec to the end of the test, both Per and SM differed
significantly between species. As expected from the
FI results, Per of Rana was less fatigable than its
counterpart in Bufo. However, Rana’s SM and PL
were significantly lower on the fatigue graph than
these muscles in Bufo (Fig. 4). This mirrors the
significantly greater FI found in Rana PL and, although the mean FIs did not differ significantly between species for SM, this graphic pattern supports
the trend in the FI of SM to be larger in Rana. Thus,
Rana’s SM and PL, although they potentiated in
force initially, tended to decline more rapidly over
the last 2 min of the test than did Bufo’s SM and PL.
Rana’s Per, however, maintained very high force
levels throughout the fatigue test and declined the
least of any of the muscles.
DISCUSSION
As reviewed by Emerson (1985), characteristics
such as small body mass, relatively long hindlimbs,
and relatively large hindlimb extensor muscles maximize the quickness, height and distance, and the
unpredictability of a frog’s jump. These biomechanical factors have been examined in a wide variety of
anurans and our data contrasting these between
Rana pipiens and Bufo marinus (Tables 1, 2) are
consistent with these earlier results. Clearly, differences in these body proportions have a major effect
on jumping ability. The purpose of our study, however, was to determine whether physiological differences in their whole muscles as measured by isometric contractile properties may also influence the
diversity of hopping behaviors between Rana and
Bufo.
Leopard frogs (Rana pipiens), as well as most
ranids, are diurnal and use their leaping ability both
to capture prey (Gans, 1961) and to elude predators.
In both behaviors, quickness is important (Emerson,
1985) but, since speed is usually achieved at the
sacrifice of stamina (Marsh, 1994; Lutz and Rome,
1994), Rana typically jumps only once or twice in
succession to escape a predator or capture prey. In
our lab, Rana rarely took more than 2–3 strides in
succession, and we could not induce them to take
more than 3– 4 turns through the runway before
they refused. Bufonids, including Bufo marinus, are
typically nocturnal. They patrol their feeding range
by using multiple short hops and many also walk.
318
B.A. CHADWELL ET AL.
Fig. 3. Force–frequency (a) and force– duration (b) curves of three hindlimb muscles are compared between species. In the
force–frequency test, stimulus duration was constant at 670 msec. Muscles were stimulated at frequencies from 5– 40 pps in 5 pps
increments, and at 60 and 80 pps. In the force– duration test, a stimulus train of constant frequency (30 pps) was delivered at 50 msec
intervals from 50 –200 msec and at 300 and 670 msec. Asterisks (*) indicate where all three muscles differed significantly between
species. Abbreviations indicate which muscles differed significantly between species at a given frequency or duration.
They rely on cryptic coloration and toxic secretions
to elude and discourage predators. In our lab, Bufo
commonly hopped 5– 6 strides in sequence and was
able to continue hopping for multiple turns through
the runway.
It should be noted that Rana frequently uses its
hindlimbs in swimming, whereas Bufo is primarily
terrestrial. However, since the movements used in
hopping and swimming are quite similar (Peters et
al., 1996), this behavioral difference would not likely
confound our interpretation of muscular properties.
Also, hopping is apparently the more demanding
behavior in terms of force and muscle activity
(Calow and Alexander, 1973; Kamel et al., 1996;
Gillis and Biewener, 2000), so that hopping may
exert the greatest influence on muscular adaptations.
These differences in behavior lead one to expect
that Rana will have muscles which produce more
force, contract and relax more quickly, but are less
resistant to fatigue than the muscles of Bufo. In
general, our results are consistent with these expectations. Where differences occurred between species,
Rana’s muscles produced more force, contracted
faster, and were more fatigable than in Bufo. A
detailed examination of the isometric contractile
properties gives us further insights, however, into
the design of muscles in these little hoppers.
Force Production
Our data show that, within species, PL consistently produced the largest maximum isometric
forces (both raw force and force relative to body
mass) of the three muscles (Table 3). Small size is
not unexpected for Per, which may function in a
more postural role than the other muscles. However,
the difference in maximum tetanic force between
SM and PL may relate to the fact that PL has no
synergists that produce appreciable power for the
hop. The only other muscle capable of ankle extension in frogs is the tibialis posticus (TP), a relatively
small muscle thought to be postural in function,
Fig. 4. The pattern of fatigue of each experimental muscle is
shown as a change in force relative to initial force. The average
force in each 20-sec interval is plotted from 40 –240 sec of the
fatigue test. Abbreviations indicate which muscles differed significantly between species at each interval.
HINDLIMB CONTRACTILE PROPERTIES IN TWO FROGS
perhaps positioning the ankle (Peters, 1994). SM is
one of several hip extensor muscles that also include
adductor magnus and gracilis. Knee extension is
also powered by several muscles (gluteus magnus,
cruralis, and tensor fasciae latae), including perhaps
Per. Thus, division of labor among synergists likely
occurs at the hip and knee, while PL may act alone
at the ankle.
Between species, there was a tendency for Rana to
produce relatively greater Tw and TT forces than
Bufo. The difference in the means did not reach
significance for the relative tetanic forces of SM and
Per, as the magnitude of the difference was not
great. However, Rana’s PL was nearly twice as
forceful as Bufo’s PL for tetanic force in percent of
body mass (Table 3). EMG studies in both Rana and
Bufo have shown that PL begins contracting at
about the same time as do the other joint extensors
(Kamel et al., 1996; Olson and Marsh, 1998; Gillis
and Biewener, 2000), but remains active after the
other muscles have cut off and well into the suspended phase of the hop (Kamel et al., 1996; Gillis
and Biewener, 2000). Its prolonged activity, as well
as the fact that the PL continues shortening after
foot-off (Gillis and Biewener, 2000), lends support to
the notion that extension of the long hindfeet of
frogs provides a follow-through needed to maximize
take-off velocity and perhaps stabilize the trajectory
by holding the foot in an extended, aerodynamically
stable position (Peters et al., 1996). The relatively
larger PL in Rana may, therefore, contribute to differences in jumping performance and, among the
muscles we examined, may be most important in
producing the power needed to generate relatively
greater take-off velocities and distances seen in
Rana.
Functional Diversity: Relative Forces,
Contraction and Relaxation Times, Fatigue
Within both species, PL produced the largest force
per gram of muscle mass and per cm2 of muscle
cross-sectional area. Its size-specific force production was about twice that of SM. In Rana, Per also
produced about half as much force/g and force/cm2
as PL. The most striking contrast in these data was
the fact that Per in Bufo produced just as much
force/g and force/cm2 as did PL (about twice that of
both SMs and of Rana’s Per). These differences
could result if the muscles with smaller specific tensions are comprised of different amounts of noncontractile tissue; for instance, if one muscle had a
larger proportion of fat and connective tissues that
were counted in our whole-muscle mass and crosssection data. Whereas we cannot rule out this possibility, it is unlikely that different amounts of connective tissue account for these differences. Our
passive tension results (Fig. 2b) showed that Rana’s
PL, which had the greatest force/cm2, likely has the
largest amount of connective tissue since its maxi-
319
mum passive resistance was greatest. In addition,
Bufo’s Per had the same low level of passive resistance as did both SMs, in spite of Bufo Per’s much
greater force/g and force/cm2.
Differences in angles of pinnation might also account for some of the difference in size-specific tension. Our estimates of whole-muscle cross-section
would tend to underestimate the area of a muscle
with greater angles of pinnation and, thus, overestimate its force/cm2. Further studies of muscle architecture are necessary to determine to what extent
this kind of mechanical difference may contribute to
differences in specific tensions.
Our data, however, present evidence that differences between Rana and Bufo result from more than
size and mechanics alone. Such differences between
muscles, as in contraction and relaxation times, fatigability, and differing response to stimulus input,
strongly suggest that there are also likely differences in the muscle fiber types present in these
muscles. In studies of bullfrogs, Peters (1994) found
that PL had a large population of very large motor
units. These motor units were more fatigable than
the smaller units found in the postural muscle, TP.
However, in contrast to motor unit properties in
mammals (Burke, 1981), the large, fatigable units
had slower CTs and Tw 1/2 RTs than the small,
fatigue-resistant units. If we apply this information
to the present whole-muscle results, it is evident
that the large PLs in both species have slower CTs
than either SM or Per. Rana’s Per has the fastest CT
and Tw 1/2 RT of any muscle and is also the most
resistant to fatigue. Thus, Rana’s Per has a profile
similar to another postural muscle, TP (Peters,
1994). These data, however, should be treated with
caution. Rana’s SM was equally as fast as Rana’s
Per and, although Bufo’s Per Tw 1/2 RT was exceptionally slow, its CT was faster than in its PL. These
results, however, suggest that these muscle are composed of different populations of muscle fibers with
varying physiological properties which could account for the differences in size-related forces. Further studies identifying the muscle fiber types and
motor unit properties of these different muscles are
needed to better understand the basis for these differences.
As noted above, a striking result that may relate
to differences in muscle fiber properties is the contrast between Per in the two species. We saw that,
although the differences in force/body mass did not
reach significance, the force/g of muscle mass and
per cm2 of cross-section were twice as large in Bufo’s
Per as in Rana’s Per. Also, the CTs and Tw 1/2 RTs
were significantly faster in Rana’s Per. In addition,
the TT 1/2 RT was faster in Rana’s Per. Marsh
(1994) proposed that TT 1/2 RT is the best indicator
of deactivation rates in muscle contraction (i.e., cessation of cross-bridge activity). Faster TT 1/2 RTs
indicate faster deactivation, which would allow more
rapid reactivation of muscle contraction. Therefore,
320
B.A. CHADWELL ET AL.
faster TT 1/2 RT in Rana’s Per would allow more
rapid reactivation following a train of stimuli. This
along with its relatively low fatigability would allow
Rana’s Per to be active in repetitive stimulation. It
is not obvious how this difference would relate to
differences in hindlimb function, especially if we
focus just on the Per muscles. The important difference may not be between Rana and Bufo Per, but
that Per in Rana is faster and less fatigable than its
own PL. In Bufo, Per has a faster CT than PL, but
the TT 1/2 RT and fatigability are the same. In
Rana, both CT and TT 1/2 RT are faster in Per than
PL, and Per is significantly less fatigable. This may
indicate a greater divergence of function between PL
and Per in Rana than in Bufo, and perhaps a greater
postural rather than phasic role for Per in Rana.
This would be especially significant if future studies
find that slower CTs, Tw 1/2 Rs, and TT 1/2 Rs are
typical of muscles with a high proportion of the
large, fast muscle fibers with low oxidative capacity
(F1 fibers, Rowlerson and Spurway, 1988). The presence of a high percentage of these fibers could explain the size-specific force differences seen in PL in
both species and in Bufo’s Per.
The patterns of fatigue over a 4-min test (Fig. 4)
clearly show that Rana muscles have a tendency to
potentiate over the first minute of repetitive stimulation; a pattern that was found only in SM of Bufo.
This result further suggests that muscle fiber types
differ between these two species and that Rana’s
muscles may be better capable of producing relatively larger forces with short-term stimulation. The
rapid decline in Rana’s force in both SM and PL
after about 2 min of repetitive stimulation also
shows that Rana’s muscles are probably less capable
of contracting repeatedly over a longer time-frame.
The exception is Rana’s Per, which was least fatigable in both FI and force decline. Again, this divergence in fatigability suggests that Per may have a
more postural function in Rana than in Bufo. Further studies that include EMG are necessary to test
this hypothesis.
Length–Tension and Passive Properties
Our results from static measurements show that
all three muscles change lengths relatively little
during a hop (Per ⬍5% of Ls; PL ⬇10% of Ls; SM
15–20% of Ls). Recently, SM and PL were studied
using sonomicrometry to record in vivo fascicle
length changes (Olson and Marsh, 1998; Gillis and
Biewener, 2000). These data show that our static
measurements of whole-muscle lengths underestimate the length changes in a hop. These averaged
about 20% of resting length in PL in Bufo marinus
(Gillis and Biewener, 2000), and 25–30% of resting
length in SM of both Rana catesbeiana (Olson and
Marsh, 1998) and Bufo marinus (Gillis and Biewener, 2000). In vivo measurements are unavailable
for Per, but if it is relatively similar to the other
muscles we can still assume that it changes length
the least (by about 10% of Ls).
With these more accurate estimates of length
change, we can better interpret the effects of length
on the muscle forces available during hopping. In all
three muscles the maximum isometric force is
reached on the length–tension curve at lengths close
to standing length (⬇100 –105% of Ls) (Fig. 2a).
These lengths are close to those at which the muscles begin to contract (Kamel et al., 1996; Olson and
Marsh, 1998; Gillis and Biewener, 2000). Shortening
contraction of PL from 103% Ls (length at maximum
tension) to 95% Ls produces a drop in isometric force
to about 75% of maximum; at 90% Ls only about 35%
of maximum force is still available. In Bufo, the
same percentage length changes would cause forces
to fall to 80% of maximum and to 60% of maximum.
In SM, a 10% shortening causes force to fall by about
9% of maximum in Rana, but by only about 1% in
Bufo. Likewise in Per, the more sharply peaked
length–tension curve of Rana produces greater falloff in available force. In Rana a 10% shortening
causes a fall in force to about 50% of maximum; in
Bufo the force only falls to 75% of maximum. Thus,
over a range of lengths where the muscles in both
species are most likely to be active, Rana’s muscles
have relatively less potential force available, although actual force is still relatively greater than in
Bufo, particularly for PL. Since maximum tetanic
force/cm2 of muscle cross-section is the same between Rana and Bufo PLs, they are not likely to
differ much in the angles of pinnation at Lo. However, shorter muscle fibers in Rana, and/or a complex internal tendon arrangement that might cause
angles of pinnation to increase more sharply in
Rana as length shortens, could account for the differences in shape of the length–tension curves. Architectural studies are needed in order to clarify the
sources of this difference.
In actual hopping, how might these differences in
force at different lengths be functionally significant?
In explosive jumping, where muscles may be maximally activated at once from resting length, the fact
that forces fall off as the muscles shorten may have
little behavioral significance. The greatest challenge
is to mobilize as much power as possible at the
beginning of the jump in a quick movement that
rapidly overcomes inertia and establishes acceleration of the mass in the proper direction (Lutz and
Rome, 1994). Therefore, initial, maximal force may
be the key to producing explosive jumps. Both Bufo
and Rana may use these explosive jumps, and with
relatively smaller maximal forces, Bufo does not
reach the speeds and distances that Rana does. Behavioral observations suggest that Bufo also commonly uses continuous hopping and even walking.
For these behaviors the potential to develop force in
a slow movement over a greater range of lengths
may be important for sustaining momentum and
maintaining stability.
HINDLIMB CONTRACTILE PROPERTIES IN TWO FROGS
Our data also suggest that Bufo cannot rely as
much on elastic recoil to amplify the power produced
by its muscles. Long tendons, such as in PL, may act
to store elastic energy during hopping that may be
recovered rapidly during take-off (Roberts and
Marsh, 1997; Olson and Marsh, 1998). Rana muscles, particularly PL, have much greater passive
tension than do Bufo’s (Fig. 2b). This passive tension
presumably results from more tendinous tissues in
Rana, which are likely able to store and recover
more elastic energy.
Force Properties With Varying Stimulation
Among the functionally significant differences in
contractile properties between species that our data
reveal are those in Tw/TT ratio, force–frequency and
force– duration curves. Each of these measures show
that all three muscles in Rana are activated to produce a higher percentage of their maximum force at
a lower stimulus input. Within both species, the
Tw/TT of PL was greatest and SM was equal to Per.
Between species, Rana muscles produced maximum
twitch force relative to tetanic force that was twice
or more of that produced by Bufo muscles (Table 3).
A high Tw/TT ratio may result from 1) greater activation of the contractile mechanism with a single
twitch stimulus, or 2) less damping due to series
elastic tissue of the twitch force relative to maximum tetanus. In our muscles, the high Tw/TT ratios
of Rana are most likely due to greater activation
since, as we have seen, the amount of elastic tissue
in Rana muscles (inferred from passive tensions) is
actually greater than in Bufo.
This tendency toward relatively greater activation
in Rana muscles is also seen with low frequency and
short duration stimulation, as evidenced by our
force–frequency (Fig. 3a) and force– duration (Fig.
3b) data. Rana muscles were significantly higher on
these curves than Bufo muscles at the lowest stimulus frequency (5 pps) and over durations up to 300
msec. It is hard to assess the functional significance
of the response to differing frequencies, since we
have little information from which to infer natural
stimulus frequencies. We assume that in ectotherms
stimulus frequencies average less than in mammals,
but are likely affected by temperature. We do know
from EMG studies that the duration of the EMG
burst in PL averages around 85 msec in Rana (Kamel et al., 1996) and 95 msec in Bufo (Gillis and
Biewener, 2000). The SM has a mean EMG burst
duration of 135 msec in Rana (Kamel et al., 1996)
and 130 msec in Bufo (Gillis and Biewener, 2000).
Thus, our force– duration data suggest that over the
natural durations of muscle activation Rana’s muscles would be able to produce relatively greater force
than would Bufo’s. This may amplify the actual difference in force production between these two species that our isometric data have revealed.
321
The differences in force response with varying
stimulation provide additional evidence of possible
differences in the physiology and distribution of
muscle fiber types between Rana and Bufo. It is also
consistent with differences found in two of our previous studies. Force–frequency tests on hindlimb
motor units (Peters, 1994) revealed that large, slow,
fatigable units in PL tended to produce a greater
percent of maximum force at low frequency than in
TP which had smaller, faster, but less fatigable motor units. Similar results were found in the major
protractor and retractor muscles of the tongue (Peters and Nishikawa, 1999), although the results
were not as clear-cut in these whole-muscle measurements as in the motor units.
Our current data do not strongly support a correlation between high force activation and speed and
fatigability. In both PL and SM, CTs were about
equal between species (Rana’s actually tended to be
faster; Table 3), and Rana’s muscles were more fatigable (the difference reached significance only in
PL). In Per, the mean CT was faster in Rana and
Rana’s Per was least fatigable. It may not be possible to establish correlations that may exist from
studies of these properties in whole muscles. Further motor unit studies are necessary along with
histochemical analyses of muscle fiber types before
we can better understand the diversity of functional
properties within anuran muscles.
In summary, our data show that in addition to the
biomechanical differences among frogs that produce
different hopping abilities, intrinsic properties of
their muscles may also affect hopping performance.
Muscle mass and cross-section can be used as rough
indicators of force differences between species, but
because of possible differences in the fiber types
present, and in their architectural and physiological
properties, mass and cross-section cannot be used
definitively. Besides gross force differences, there
are differences in contraction times and fatigabilities that correlate with hopping diversity. Differences in muscle properties at one joint (ankle) may
have more influence on behavior than differences at
other joints, so that the organization of muscle recruitment may differ between species. Active and
passive tension properties may vary over the normal
range of muscle length excursion and affect differences in behavior. In particular, the properties of
muscles that influence how much force they can
produce under normal stimulus frequencies and durations can differ strongly. These differences, along
with possible differences in the contribution of elastic recoil, can ultimately produce strong divergence
in locomotor function among anurans. Thus, as we
have seen, good hoppers are not just scaled-up versions of poor hoppers. In addition to proportional
differences, there are clear physiological differences
in contractile properties that produce the diversity
of locomotor behaviors seen in anurans.
322
B.A. CHADWELL ET AL.
LITERATURE CITED
Biewener AA. 1998. Muscle function in vivo: a comparison of
muscles used for elastic energy savings versus muscles used to
generate mechanical power. Am Zool 38:703–717.
Bock WJ. 1968. Mechanics of one- and two-joint muscles. Am Mus
Novitates 2319:1– 45.
Burke RE. 1981. Motor units: anatomy, physiology and functional
organization. In: Brooks VB, editor. Handbook of physiology,
sect 1, vol. 2. The nervous system: motor control. Bethesda, MD:
Am Physiol Soc. p 345– 422.
Burke RE, Levine DN, Tsairis P, Zajac FE. 1973. Physiological
types and histochemical profiles in motor units of the cat gastrocnemius. J Physiol Lond 234:723–748.
Calow LJ, Alexander R McN. 1973. A mechanical analysis of a
hindleg of a frog (Rana temporaria). J Zool Lond 171:293–321.
Dunlap D. 1960. The comparative myology of the pelvic appendage in Salientia. J Morphol 106:1–76.
Emerson SB. 1978. Allometry and jumping in frogs: helping the
twain to meet. Evolution 32:551–564.
Emerson SB. 1985. Jumping and leaping. In: Hildebrand M,
Bramble DM, Liem KF, Wake DB, editors. Functional vertebrate anatomy. Cambridge, MA: Belknap Press. p 58 –72.
Emerson SB, De Jongh HJ. 1980. Muscle activity at the ilio-sacral
articulation of frogs. J Morphol 166:129 –144.
Gans C. 1961. A bullfrog and its prey. Nat Hist 70:26 –36.
Gans C, De Gueldre. 1992. In: Feder ME, Burggren WW, editors.
Environmental physiology of the amphibians. Chicago: Univ
Chicago Press. p 277–313.
Gillis GB, Biewener AA. 2000. Musculoskeletal mechanisms for
accommodating locomotion in different environments: hindlimb
extensor muscle function during hopping and swimming in the
toad (Bufo marinus). J Exp Biol 203:3547–3563.
Kamel LT, Peters SE, Bashor DP. 1996. Hopping and swimming
in the leopard frog, Rana pipiens. II. A comparison of muscle
activities. J Morphol 230:17–31.
Lannergren J, Hoh JFY. 1984. Myosin isoenzymes in single muscle fibers of Xenopus laevis: analysis of five different functional
types. Proc R Soc Lond B222:407– 408.
Lannergren J, Smith RS. 1966. Types of muscle fibres in toad
skeletal muscle. Acta Physiol Scand 68:263–274.
Luff AR, Proske U. 1976. Properties of motor units of the frog
sartorius muscle. J Physiol 258:673– 685.
Luff AR, Proske U. 1979. Properties of motor units of the frog
iliofibularis muscle. Am J Physiol 236:C35–C40.
Lutz GJ, Rome LC. 1994. Built for jumping: the design of the frog
muscular system. Science 263:370 –372.
Lutz GJ, Rome LC. 1996. Muscle function during jumping in
frogs. II. Mechanical properties of muscle: implications for system design. Am J Physiol 271:C571–C578.
Marsh RL. 1994. Jumping ability of anuran amphibians. Adv Vet
Sci Comp Med 38B:51–111.
Olson JM, Marsh RL. 1998. Activation patterns and length
changes in hindlimb muscles of the bullfrog Rana catesbeiana
during jumping. J Exp Biol 201:2763–2777.
Peters SE. 1994. Properties of twitch motor units of the ankle
extensor muscles in the bullfrog Rana catesbeiana. J Morphol
221:121–131.
Peters SE, Aulner DA. 2000. Sexual dimorphism in forelimb
muscles of the bullfrog, Rana catesbeiana: a functional analysis
of isometric contractile properties. J Exp Biol 203:3439 –3654.
Peters SE, Nishikawa KC. 1999. Comparison of isometric contractile properties of the tongue muscles in three species of
frogs, Litoria caerulea, Dyscophus guinetti, and Bufo marinus. J
Morphol 242:107–124.
Peters SE, Kamel LT, Bashor DP. 1996. Hopping and swimming
in the leopard frog, Rana pipiens. I. Step cycles and kinematics.
J Morphol 230:1–16.
Putnam RW, Bennett AF. 1983. Histochemical, enzymatic and
contractile properties of skeletal muscles of three anuran amphibians. Am J Physiol 244:R558 –R567.
Rice WR. 1989. Analyzing tables of statistical tests. Evolution
43:223–225.
Ridge RMAP, Thomason AM. 1980. Properties of motor units in a
small foot muscle of Xenopus laevis. J Physiol 306:17–27.
Roberts TJ, Marsh RL. 1997. Elastic energy storage in jumping
frogs. Am Zool 37:174A.
Rowlerson AM, Spurway NC. 1988. Histochemical and immunohistochemical properties of skeletal muscle fibres from Rana
and Xenopus. Histochem J 20:657– 673.
Rubenstein NS, Erulkar SD, Schneider GT. 1983. Sexual dimorphism in the fibres of a ’clasp’ muscle of Xenopus laevis. Exp
Neurol 82:424 – 431.
Smith RS, Lannergren J. 1968. Types of motor units in the
skeletal muscles of Xenopus laevis. Nature 217:281–283.
Smith RS, Ovalle WK. 1973. Varieties of fast and slow extrafusal
muscle fibres in amphibian hind-limb muscles. J Anat 116:1–
24.
Spurway NC, Rowlerson AM. 1989. Quantitative analysis of histochemical and immunohistochemical reactions in skeletal
muscle fibres of Rana and Xenopus. Histochem J 21:461– 476.
Zug GR. 1972. Anuran locomotion: structure and function. 1.
Preliminary observations on relation between jumping and osteometrics of appendicular and postaxial skeleton. Copeia
4:613– 624.
Zug GR. 1978. Anuran locomotion: structure and function. 2.
Jumping performance of semiaquatic, terrestrial and arboreal
frogs. Smithsonian Contrib Zool 276:1–31.