Minimal shortening in a high-frequency muscle
1 Department of Biology, PO Box 42451, University of Louisiana at Lafayette,
Lafayette, LA 70504-2451, USA
2 Department of Radiology, Box 357115, University of Washington Medical
Center, Seattle, WA 98195, USA
3 Department of Biological Sciences, Northern Arizona University, Flagstaff,
AZ 86011, USA
* Author for correspondence (e-mail: BradMoon{at}louisiana.edu)
Accepted 21 January 2003
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Key words: tailshaker muscle, rattlesnake, Crotalus atrox, muscle contraction, elastic recoil, cross-bridge, biomechanics
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Minimal cross-bridge cycling has been determined in insect muscles using
energetic measurements, work loop experiments and strain recordings
(Casey and Ellington, 1989;
Chan and Dickinson, 1996
;
Gilmour and Ellington, 1993
;
Josephson, 1973
,
1985
). Although muscle strain
has not yet been measured in vivo in vertebrate muscles contracting
at very high frequencies, several lines of evidence suggest that these
contractions involve minimal strains produced by only one or two cross-bridge
cycles per contraction. For example, muscle fibres can generate work in
vitro at very low strains of 0.5% and very high contraction frequencies
(90 Hz in rattlesnake tailshaker muscle and 200 Hz in toadfish swimbladder
muscle; Rome et al., 1996
).
Tailshaker muscle and swimbladder muscle use very little energy and generate
very low forces, work and power (Conley
and Lindstedt, 1996
; Moon et
al., 2002
; Rome et al.,
1999
). Modelling of the key sources and sinks for ATP in active
muscle indicates that the major factor keeping the cost of contraction low is
a small number of cross-bridge cycles per contraction
(Conley and Lindstedt, 2002
).
These results argue strongly for minimal cross-bridge cycling during
high-frequency contractions. However, direct measurements of muscle shortening
are needed to determine whether high-frequency contractions in vertebrate
muscle involve truly minimal strains produced by only 1-2 cross-bridge cycles
per contraction.
One major consequence of minimal strains and cross-bridge cycling may be
that the resulting low forces and low work output limit power output. However,
because power is proportional to contraction frequency, very high frequencies
may compensate for the limited work per contraction and still generate high
power. At moderate to high contraction frequencies, muscle power is typically
optimized whenever the relative shortening velocity
(V/Vmax, the ratio of actual to maximal shortening
velocity) is between 0.2 and 0.3 (Askew and
Marsh, 1998; Hill,
1938
; Rome and Lindstedt,
1997
). Therefore, one indicator of contractile minimization would
be low power output, but despite high contraction frequencies and optimal
V/Vmax. We have previously reported high frequencies of
contraction and low power output in rattlesnake tailshaker muscle
(Conley and Lindstedt, 1996
;
Moon et al., 2002
), although
we were unable to relate the low power to suboptimal
V/Vmax or to contractile minimization because in
vivo muscle strains and shortening velocities were not yet known. Direct
measurements of muscle shortening can be used to test whether low power output
derives mainly from suboptimal V/Vmax or from truly
minimal strains.
Another major consequence of minimal strains and minimal cross-bridge
cycling in high-frequency muscle contractions may be limited potential for
elastic energy storage and recoil. For example, the low work and mechanical
efficiency of rattlesnake tailshaker muscle contractions suggest limited
energy savings by elastic recoil (Moon et
al., 2002). A simple model of contractile energetics also
indicates that energy recycling is not necessary to account for the low cost
of contraction (Conley and Lindstedt,
2002
). Elastic strain energy can only be stored in muscle or
connective tissue during periods of isometric or eccentric contraction
(Biewener, 1998
;
Cavagna et al., 1994
;
Lindstedt et al., 2001
).
Therefore, the duration of isometric or eccentric contraction is an indicator
of the potential for energy savings by elastic energy storage and recoil.
Limited isometric or eccentric contraction would indicate little potential for
elastic energy storage and recoil.
In the present work, we used sonomicrometry and electromyography to record tailshaker muscle strains and activation patterns in vivo during rattling in western diamondback rattlesnakes Crotalus atrox. Our specific goals were to test the hypotheses that (1) the high-frequency contractions of tailshaker muscle involve minimal strains, (2) suboptimal V/Vmax does not explain the low power output, and (3) the high-frequency contractions involve little isometric or eccentric contraction and therefore have little potential for strain energy storage and recoil.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Rattling frequency is temperature-dependent
(Chadwick and Rahn, 1954;
Martin and Bagby, 1972
). We
used a thermocouple placed in the cloaca to measure each animal's body
temperature as it was controlled over a range of 10-30°C by circulating
temperature-controlled water through tightly coiled copper tubing in the
bottom of the container. We varied the starting temperature and direction of
temperature change (heating or cooling by approximately 5°C per hour) for
each animal, and collected data at 10, 20 and 30°C.
Muscle mass and anatomy
Three major tailshaker muscles insert directly onto the bony shaker element
in the base of the rattle without any measurable tendons
(Clark and Schultz, 1980;
Czermak, 1857
;
Martin and Bagby, 1973
;
Zimmerman and Pope, 1948
). We
used external measurements to determine the volume of the tail around the
tailshaker muscles, and then subtracted 15% to account for non-muscle
components such as vertebrae, blood vessels and scent glands; this adjustment
for non-muscle components was based on measurement from magnetic resonance
images of in vivo tail anatomy
(Moon et al., 2002
). This
method gives a more accurate measure of tailshaker muscle mass than by
estimating it as a function of body mass, as in Schaeffer et al.
(1996
), because tailshaker
muscle mass appears to be conserved even when body mass changes. We then
converted the volume into mass by assuming a muscle density of 1.06 g
ml-1.
Muscle strain and shortening velocity
We measured muscle strain using sonomicrometry, in which a pair of small
piezoelectric crystals is implanted in each muscle. The crystals use the time
delay between the transmission and reception of ultrasound pulses to measure
muscle length as it changed during contraction. We implanted pairs of 0.75 mm
sonomicrometer crystals in alignment with the muscle fibres by first making a
1-2 mm incision in the skin, then puncturing the epimysium with the tip of a
16-gauge needle, and then inserting the crystals into the muscles where they
cross the joint between the last caudal vertebrae and the shaker element in
the base of the rattle. After crystal implantation, the incisions were sealed
with surgical glue. Crystals were implanted in the lateral muscle in every
snake, and also in the dorsolateral muscle and the inferior part of the
ventrolateral muscle in some snakes.
For data collection, the sound velocity in muscle was set to 1540 m
s-1, which is most accurate at 20°C (based on data from Goss et
al., 1978,
1980
;
Sonometrics Corporation,
2001
). The velocity of sound in muscle changes with temperature,
however, with a Q10 of 1.025 (based on Goss et al.,
1978
,
1980
). Therefore, to correct
for differences in sound velocity in muscle at different temperatures, lengths
measured at 10°C were reduced by 2.5%, and lengths measured at 30°C
were increased by 2.5%. We were unable to measure resting muscle lengths and
temperature-induced changes in the velocity of sound in tailshaker muscle
directly because the snakes typically rattled whenever we moved to start
recording data.
For analysis, the signals were digitized at 1050 Hz with a Sonometrics TRX Series 4 sonomicrometer (Sonometrics Corp., London, ON, Canada) with a distance resolution of 0.024 mm. The muscle length signals were digitally smoothed using a 3-point moving average. A ninth order polynomial curve-fitting algorithm was used on some signals from which sequences of a few data points had been dropped during signal acquisition.
From the digitized signals we measured the times and muscle lengths at the
points of activation, maximum length and minimum length. We then calculated
contraction frequency, muscle strain (shortening distance divided by the
resting length; presented here as a percentage), average shortening velocity
from peak to trough (in muscle lengths per second, L s-1)
and activation phase (as a percentage of contraction cycle). At each
temperature, we used our shortening velocity data along with
Vmax and Q10 values from Rome et al.
(1996) to compute the relative
shortening velocity, V/Vmax, which is the ratio of actual
shortening velocity (V) to maximum shortening velocity
(Vmax).
Muscle activation
We recorded electromyograms (EMGs) simultaneously with the muscle length
changes. For the EMG recordings, we used bipolar hook electrodes made from
0.08 mm diameter insulated stainless steel wire (California Fine Wire; Grover
Beach, CA, USA). The electrodes had 1-2 mm bipole spacings and 1-2 mm bare
tips, and were inserted into the muscle with 23-gauge hypodermic needles. The
EMG signals were amplified with an A-M Systems differential AC amplifier Model
1700 (A-M Systems, Carlsborg, WA, USA). The amplifier gain was 1000 with a
bandwidth of 10-500 Hz and a 60 Hz notch filter. Although some of the EMG
spikes occurred in the range of 60 Hz, the waveform of each spike was much
higher than 60 Hz and was not severely attenuated by the notch filter.
Statistical analyses
For every individual snake and tailshaker muscle, we selected three
consecutive contractions from each of three different rattling bouts at each
temperature, and then computed mean values for strain, shortening velocity and
V/Vmax. Therefore, each data point analyzed here
represents a mean value for nine contractions by a single muscle at a single
temperature. Prior to the statistical analyses, we inspected plots of the
strain data to be sure that the slopes of strain against contraction frequency
for each individual had the same polarity and similar magnitude as the overall
slope for the entire sample. To determine whether the three tailshaker muscles
could be analyzed together, we first used analysis of variance (ANOVA) to test
for differences in strain among the three muscles. In these analyses, the
dependent variables were strain, shortening velocity, and
V/Vmax; the independent variable was muscle identity
(dorsolateral, lateral, ventrolateral), and the covariates were contraction
frequency and muscle mass. We chose to use frequency rather than temperature
as an independent variable because it varies as a direct function of
temperature and it better accounts for variation in muscle function.
The ANOVA results showed that the dorsolateral muscle shortened less and more slowly than the other two muscles, which did not differ from each other in these variables. Consequently, we pooled lateral and ventrolateral muscle data and then used multiple regressions to test for the effects of twitch frequency on muscle strain. We did not compute regressions for the small number of data points from the dorsolateral muscle. Because the ANOVA results also showed that shortening variables were size-dependent, we included muscle mass as an independent variable along with contraction frequency. The dependent variables in the regression analyses were muscle strain, shortening velocity and V/Vmax. Values are given as means ± S.D.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Muscle strain
Tailshaker muscle strain was approximately sinusoidal, with contralateral
muscles shortening out of phase with each other
(Fig. 1). Strains were very
small and averaged 3.1±0.95% (mean ± S.D.) for the lateral and
ventrolateral muscles over all temperatures. The average strain of 1.5% in the
dorsolateral muscle was significantly lower than that of the other two muscles
(F=8.2, d.f.=2, P=0.001). Muscle shortening increased
slightly with temperature and twitch frequency
(Fig. 2; Tables
1,
2).
|
|
|
|
Shortening velocity
Shortening velocity averaged 2.8±1.5 L s-1 for
the lateral and ventrolateral muscles over all temperatures, and increased
substantially with temperature and twitch frequency (Tables
1,
2,
Fig. 3). In the dorsolateral
muscle, the mean shortening velocity of 1.4 L s-1 was
significantly lower than for the other two muscles (F=8.3, d.f.=2,
P=0.001).
|
In the lateral and ventrolateral muscles, mean relative shortening velocity (V/Vmax) was 0.26±0.07 over all temperatures, increasing to 0.31±0.06 at 30°C. In the dorsolateral muscle, the average V/Vmax of 0.19 was significantly lower than for the other two muscles (F=3.8, d.f.=2, P=0.03).
Muscle activation
Tailshaker muscles were activated by a single, or occasionally a double,
EMG spike (Fig. 1). Muscles
were activated 4.6 ms (at 10°C) to 2.4 ms (at 30°C) before reaching
maximal stretch. Therefore, the contraction on one side of the tail appeared
to involve a maximum of 0.5% (at 10°C) and 1.2% (at 30°C) active
stretching by the contralateral muscles. This active lengthening, called
eccentric contraction, is necessary for the storage of elastic strain energy,
and it may dramatically increase muscle force exertion per unit energy
consumed. However, because there is a delay between electrical excitation (as
indicated by the EMG spike) and actual contraction (cross-bridge formation),
some of the time between excitation and the onset of shortening does not
involve actual contraction. Assuming excitationcontraction delays of
4.4 ms at 10°C and 1.9 ms at 30°C (based on data for an analogous
high-frequency muscle; Josephson,
1973), tailshaker muscle contractions actually involved only 0.2
ms and 0.002% active lengthening at 10°C, and only 0.5 ms and 0.035%
active lengthening at 30°C.
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Tailshaker muscle strain increases slightly with contraction frequency, but
rattle displacement decreases (Moon et
al., 2002). Rattle motion must therefore be ballistic: muscle
contraction accelerates the rattle but does not limit how far it moves.
Instead of being limited by muscle strain, rattle displacement is limited by
the timing of contralateral muscle contraction and perhaps by tissue
stiffness. Ballistic motion is also indicated by the relationship between
contraction frequency and shortening velocity. If rattle motion were limited
by muscle strain, then an increase in shortening velocity should produce a
corresponding one to one decrease in contraction period, and hence a one to
one increase in rattling frequency. However, shortening velocity increases
more (3.5 times) from 10° to 30°C than does twitch frequency (2.4
times), which accelerates the rattle faster but does not appear to limit its
maximal displacement.
Are muscle strains minimal?
The 2-4% strains of tailshaker muscle contractions are among the lowest
ever recorded in vertebrate muscle during movement (Conley and Lindstedt,
1996,
2002
;
Rome and Lindstedt, 1998
;
Rome et al., 1996
). These low
strains explain the low work and power of rattling reported by Moon et al.
(2002
). Although tailshaker
muscle contractions are nearly isometric, they are quite different from
isometric contractions in typical skeletal muscles, in which substantial
cross-bridge cycling produces large forces. In contrast to these typical
isometric contractions, tailshaker muscle contractions generate very low
forces (Moon et al., 2002
),
which suggests that cross-bridge cycling is very limited.
The extremely low costs of contraction in sound-producing muscles,
including tailshaker muscles, indicate that approximately 10% of available
cross-bridges form and undergo only one cycle per contraction
(Conley and Lindstedt, 2002).
One cross-bridge cycle comprises a truly minimal contraction. Do the small
strains in tailshaker muscle contractions reflect minimal cross-bridge
cycling? It is possible to estimate the number of cross-bridge cycles required
to produce the observed muscle strains if the sarcomere length and compliance
are known. For example, if the sarcomere length in tailshaker muscle is
approximately 2.4 µm (Clark and Schultz,
1980
), then muscle strains of 0.025-0.037 correspond to
half-sarcomere strains of 30-44 nm. If a cross-bridge stroke is 20 nm
(Ishijima et al., 1996
) and
stiffness is moderately high (which appears to be the case;
Martin and Bagby, 1973
), then
the observed muscle strains would be truly minimal, with only 1-2 cross-bridge
cycles per contraction. The minimal cross-bridge cycling explains the low
force and cost of tailshaker muscle contractions.
Is low muscle power best explained by contractile minimization or by
suboptimal V/Vmax?
Power is the rate at which work is done by muscle, and it is proportional
to the frequency of contraction. Muscle power is optimized when the relative
shortening velocity (V/Vmax) is between 0.2 and 0.3
(Askew and Marsh, 1998;
Hill, 1938
;
Rome and Lindstedt, 1997
).
Therefore, a major indicator of contractile minimization would be low power
output, but despite high contraction frequencies and optimal
V/Vmax.
Although the contraction frequencies of tailshaker are very high, power
output is very low (mean of 3.0 W kg-1 muscle at 30°C; based on
data from Moon et al., 2002).
Is the low power due to contractile minimization or to suboptimal
V/Vmax? In our previous study
(Moon et al., 2002
), we were
unable to relate the low power to suboptimal V/Vmax or to
contractile minimization because in vivo muscle strains and
shortening velocities were not yet known. In this study, we measured
V and used Vmax and Q10 values from
Rome et al. (1996
) to
determine that V/Vmax varies between 0.2 (at 10°C) and
0.3 (at 30°C) in tailshaker muscle. These values conform to the optimal
range for maximum power generation (Askew
and Marsh, 1998
; Hill,
1938
; Rome and Lindstedt,
1997
), which indicates that suboptimal V/Vmax
is not the primary cause of low power output by tailshaker muscle. Instead,
the minimal strains involving only one or two cross-bridge cycles per
contraction limit muscle force, work and power, despite high contraction
frequencies and optimal V/Vmax. These results support the
hypothesis of contractile minimization in tailshaker muscles.
Do high-frequency contractions involve elastic recoil?
The lack of measurable tendons in the tailshaker muscle segments that we
measured indicates limited structural potential for elastic strain energy
storage outside the muscle compared to muscles that have long tendons.
However, elasticity may occur in other connective tissues or in cytoskeletal
elements such as titin molecules and the cross-bridges themselves
(Huxley and Simmons, 1971;
Lindstedt et al., 2002
;
Reich et al., 2000
).
There are three lines of evidence that there is little potential for
storing and recycling elastic strain energy in tailshaker muscle. First, if
energy recycling were important in tailshaker muscle contractions, then it
should produce high apparent efficiencies. However, the mechanical efficiency
of tailshaker muscle is very low, 0.3-11%, which indicates that energy
recycling is limited (Moon et al.,
2002).
Second, eccentric contraction (active stretching), or isometric contraction
together with stretching in a tendon, is required for storing elastic strain
energy in muscle (Biewener,
1998; Cavagna et al.,
1994
; Lindstedt et al.,
2001
). However, there are no measurable tendons and eccentric
contraction is limited in the tailshaker muscles that we measured. At low
contraction frequencies, nearly all of the apparent eccentric contraction can
be accounted for by the excitationcontraction coupling (ECC) delay. In
contrast to tailshaker muscle activation 0.7-3% of the cycle before the onset
of shortening, some mammal and bird muscles that recycle substantial amounts
of strain energy are activated 14-29% of the cycle in advance of shortening
(Biewener, 1998
). Although the
moderate passive stiffness (see fig. 6 of
Martin and Bagby, 1973
) and
the limited eccentric contraction (0.002-0.035%) may enhance force output and
allow some strain energy to be stored and recycled, the low mechanical
efficiency (
11%; Moon et al.,
2002
) suggests that energy recycling is considerably less than
11%. Limited strain energy recycling (approximately 10%) also occurs in the
high-frequency contractions of Drosophila flight muscles
(Dickinson and Lighton, 1995
),
and in the limb muscles that produce rapid accelerations in small mammals such
as kangaroo rats (Biewener et al.,
1981
).
It is possible to estimate the potential range of energy storage if
tailshaker muscle is assumed to act as a simple spring that obeys Hooke's Law
(Alexander, 1988): strain
energy=Fx/2, where strain energy is in Joules, F is muscle
force in N (derived from Moon et al.,
2002
), and x is the magnitude of active lengthening in m
from this study. The strain energy can then be divided by the energy used to
shake the rattle (from Moon et al.,
2002
) to estimate energy recycling. The muscles on one side of the
tail are stretched by the force from the contralateral muscles. We estimated
strain energy storage and recoil using the amount of active lengthening after
accounting for the ECC delay, and assuming that the muscles are stretched by
maximal force. Under these conditions, tailshaker muscle could store and
recycle 9.0x10-9 J or 0.04% of the energy required to rattle
at 10°C and up to 5.5x10-7 J or 0.78% at 30°C. Thus,
although this model greatly simplifies the muscle mechanics, it supports the
inference that energy storage is very limited in tailshaker muscle.
Third, this very limited energy storage and recoil is quantitatively
consistent with a simple model of contractile energetics
(Conley and Lindstedt, 2002).
The energetic analysis showed that the major factor keeping the cost of
contraction low is a small number of cross-bridge cycles per contraction;
energy recycling is not necessary to account for the low cost of
contraction.
Energy recycling versus energy reducing strategies
Muscles that recycle elastic strain energy typically exert high forces that
produce large joint displacements, do considerable work, and appear to have
high efficiency (Biewener,
1998; Ettema,
1996
; Heglund and Cavagna,
1987
; Minetti et al.,
1999
; Roberts et al.,
1997
; Woledge et al.,
1985
). In contrast, synchronous muscles that contract at very high
frequencies appear to be `energy reducers' rather than `energy recyclers'
(Conley and Lindstedt, 2002
).
Rattlesnake tailshaker muscles sustain high-frequency contractions with low
metabolic energy use by contracting with minimal strains and by generating
very low forces, work and power (Conley and Lindstedt,
1996
,
2002
;
Moon et al., 2002
). These
features indicate that tailshaker muscles, and perhaps other high-frequency
muscles, primarily minimize cross-bridge cycling and reduce metabolic energy
input rather than recycle mechanical energy output.
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Alexander, R. M. (1988). Elastic Mechanisms in Animal Movement. Cambridge: Cambridge University Press.
Askew, G. N. and Marsh, R. L. (1998). Optimal
shortening velocity (V/Vmax) of skeletal muscle during
cyclical contractions: length-force effects and velocity-dependent activation
and deactivation. J. Exp. Biol.
201,1527
-1540.
Biewener, A. A. (1998). Muscle function in vivo: A comparison of muscles used for elastic energy savings versus muscles used to generate mechanical power. Amer. Zool. 38,703 -717.
Biewener, A. A., Alexander, R. M. and Heglund, N. C. (1981). Elastic energy storage in the hopping of kangaroo rats (Dipodomys spectabilis). J. Zool. Lond. 195,369 -383.
Casey, T. and Ellington, C. (1989). Energetics of insect flight. In Transformations in Cells and Organisms: Proceedings of the 10th Conference of the European Society for Comparative Physiology and Biochemistry (ed. W. Wieser and E. Gnaiger). Stuttgart: Georg Thieme.
Cavagna, G. A., Heglund, N. C., Harry, J. D. and Mantovani, M. (1994). Storage and release of mechanical energy by contracting frog muscle. J. Physiol. Lond. 481,689 -708.[Abstract]
Chadwick, L. E. and Rahn, H. E. (1954). Temperature dependence of rattling frequèncy in the rattlesnake, Crotalus v. viridis. Science 119,442 -443.[Medline]
Chan, W. P. and Dickinson, M. H. (1996). In
vivo length oscillations in indirect flight muscles in the fruit fly
Drosophila virilis. J. Exp. Biol.
199,2767
-2774.
Clark, A. W. and Schultz, E. (1980). Rattlesnake shaker muscle: II. Fine structure. Tissue and Cell 12,335 -351.[Medline]
Conley, K. E. and Lindstedt, S. L. (1996). Minimal cost per twitch in rattlesnake tail muscle. Nature 383,71 -72.[Medline]
Conley, K. E. and Lindstedt, S. L. (2002).
Energy-saving mechanisms in muscle: the minimization strategy. J.
Exp. Biol. 205,2175
-2181.
Czermak, J. (1857). Ueber den schallerzeugenden Apparat von Crotalus. Zeitschr. wiss. Zool. 8, 294-302.
Dickinson, M. H. and Lighton, J. R. B. (1995). Muscle efficiency and elastic storage in the flight motor of Drosophila.Science 268,87 -90.[Medline]
Ettema, G. J. C. (1996). Mechanical efficiency
and efficiency of storage and release of series elastic energy in skeletal
muscle during stretchshorten cycles. J. Exp.
Biol. 199,1983
-1997.
Gilmour, K. M. and Ellington, C. P. (1993).
In vivo muscle length changes in bumblebees and the in vitro
effects on work and power. J. Exp. Biol.
183,101
-113.
Goss, S. A., Johnson, R. L. and Dunn, F. (1978). Comprehensive compilation of empirical ultrasonic properties of mammalian tissues. J. Acoust. Soc. Am. 64,423 -457.[Medline]
Goss, S. A., Johnson, R. L. and Dunn, F. (1980). Compilation of empirical ultrasonic properties of mammalian tissues. II. J. Acoust. Soc. Am. 68, 93-108.[Medline]
Heglund, N. C. and Cavagna, G. A. (1987).
Mechanical work, oxygen consumption, and efficiency in isolated frog and rat
muscle. Am. J. Physiol.
253,C22
-C29.
Hill, A. V. (1938). The heat of shortening and the dynamic constants of muscle. Proc. Roy. Soc. B 126,136 -195.
Huxley, A. F. and Simmons, R. M. (1971). Mechanical properties of the cross bridges of frog striated muscle. J. Physiol. Lond. 218,59P -60P.[Medline]
Ishijima, A., Kojima, H., Higuchi, H., Harada, Y., Funatsu, T. and Yanagida, T. (1996). Multiple- and single-molecule analysis of the actomyosin motor by nanometer-piconewton manipulation with a microneedle: unitary steps and forces. Biophys. J. 70,383 -400.[Abstract]
Josephson, R. K. (1973). Contraction kinetics of fast muscles used in singing by a katydid. J. Exp. Biol. 59,781 -801.
Josephson, R. K. (1985). The mechanical power output of a tettigoniid wing muscle during singing and flight. J. Exp. Biol. 117,357 -368.
Lindstedt, S. L., LaStayo, P. C. and Reich, T. E.
(2001). When active muscles lengthen: Properties and consequences
of eccentric contractions. News Physiol. Sci.
16,256
-261.
Lindstedt, S. L., Reich, T. E., Keim, P. and LaStayo, P. C.
(2002). Do muscles function as adaptable locomotor springs?
J. Exp. Biol. 205,2211
-2216.
Marsh, R. L. (1990). Deactivation rate and
shortening velocity as determinants of contractile frequency. Am.
J. Physiol. 259,R223
-R230.
Martin, J. M. and Bagby, R. M. (1972). Temperaturefrequency relationship of the rattlesnake rattle. Copeia 1972,482 -485.
Martin, J. M. and Bagby, R. M. (1973). Properties of rattlesnake shaker muscle. J. Exp. Zool. 185,293 -300.[Medline]
Minetti, A. E., Ardigo, L. P., Reinach, E. and Saibene, F.
(1999). The relationship between mechanical work and energy
expenditure of locomotion in horses. J. Exp. Biol.
202,2329
-2338.
Moon, B. R., Hopp, J. J. and Conley, K. E. (2002). Mechanical tradeoffs explain how performance increases without increasing cost in rattlesnake tailshaker muscle. J. Exp. Biol. 204,667 -675.
Reich, T. E., Lindstedt, S. L., LaStayo, P. C. and Pierotti, D.
J. (2000). Is the spring quality of muscle plastic?
Am. J. Physiol. Regul. Integr. Comp. Physiol.
278,R1661
-R1666.
Roberts, T. J., Marsh, R. L., Weyand, P. G. and Taylor, C.
R. (1997). Muscular force in running turkeys: the economy of
minimizing work. Science
275,1113
-1115.
Rome, L. C., Cook, C., Syme, D. A., Connaughton, M. A.,
Ashley-Ross, M., Klimov, A., Tikunov, B. and Goldman, Y. E.
(1999). Trading force for speed: why superfast crossbridge
kinetics leads to superlow forces. Proc. Natl. Acad. Sci.
USA 96,5826
-5831.
Rome, L. C. and Lindstedt, S. L. (1997). Mechanical and metabolic design of the muscular system in vertebrates. In Handbook of Physiology: Comparative Physiology. Sect. 13, vol. 1 (ed. W. H. Dantzler), pp.1587 -1651. Oxford, England: Oxford University Press.
Rome, L. C. and Lindstedt, S. L. (1998). The
quest for speed: Muscles built for high-frequency contractions.
News Physiol. Sci. 13,261
-268.
Rome, L. C., Syme, D. A., Hollingworth, S. H., Lindstedt, S. L.
and Baylor, S. M. (1996). The whistle and the rattle: The
design of sound producing muscles. Proc. Natl. Acad. Sci.
USA 93,8095
-8100.
Schaeffer, P. J., Conley, K. E. and Lindstedt, S. L.
(1996). Structural correlates of speed and endurance in skeletal
muscle: The rattlesnake tailshaker muscle. J. Exp.
Biol. 199,351
-358.
Sonometrics Corporation (2001). SonoSOFT manual for software version 3.1.x. London, Ontario: Sonometrics Corporation.
Woledge, R. C., Curtin, N. A. and Homsher, E. (1985). Energetic Aspects of Muscle Contraction. London: Academic Press.
Zimmerman, A. A. and Pope, C. H. (1948). Development and growth of the rattle of rattlesnakes. Fieldiana Zool. 32,357 -413.