Submaximal power output from the dorsolongitudinal flight muscles of the hawkmoth Manduca sexta
Department of Biology, University of Washington, Seattle WA 98195-1800, USA
* Author for correspondence (e-mail: mstu{at}u.washington.edu)
Accepted 1 October 2004
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Summary |
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Key words: flight, muscle, work, power, Manduca sexta
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Introduction |
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During terrestrial locomotion, muscles function in weight support and
braking (Full et al., 1998;
Ahn and Full, 2002
), mechanical
energy transfer (Olson and Marsh,
1998
), and elastic strain energy storage and recovery
(Roberts et al., 1997
;
Biewener et al., 1998
). These
demands may place constraints on muscle design that conflict with maximal
power generation. During swimming and flying, relaxation of these constraints
may permit muscles to operate closer to the conditions of strain and
activation that maximize power output. Support for this view comes from the
recent demonstration of maximal power generation by the deep red trunk muscle
of swimming skipjack tuna (Syme and
Shadwick, 2002
). The unique anatomical arrangement of the red
muscle of skipjack tuna and other thunniform swimmers may be critical in
allowing these muscles to function solely as a motor. This high level of
performance, however, may be the exception rather than the rule during steady
swimming in fish. For example, in carangiform swimmers, the trunk muscles do
not achieve their maximum potential power output during sustained swimming
(Rome et al., 1999
;
Swank and Rome, 2001
;
Josephson, 1997
;
Coughlin, 2000
;
Hammond et al., 1998
).
We currently lack the direct comparisons between realized and optimized
power output necessary to assess the extent to which power output is maximized
during flight. During take-off, the power generated by the pectoralis muscle
of quail (Askew et al., 2001)
is substantially higher than that reported for cockatiels during steady flight
(Hedrick et al., 2003
). While
such extraordinary high levels of power generation may be an adaptation of
ground-dwelling birds, this difference in performance suggests that birds may
generate sub-maximum power during steady flight, with substantial reserve
capacity for escape behaviors. For flying insects, a comparison between
optimized and realized power output is available for the asynchronous
(fibrillar) wing elevator muscles of bumble bees
(Josephson and Ellington,
1997
; Josephson,
1997
). These muscles undergo length oscillations near the
frequency that maximizes power output, but the in vivo strain
amplitude is suboptimal for maximal power generation. These particular
characteristics could be related to specializations for stretch activation
(Machin and Pringle, 1960
;
Josephson et al., 2000
). Among
insects with synchronous flight muscles, the conditions that maximize power
output have been well documented in hawkmoths
(Stevenson and Josephson,
1990
), locusts (Mizisin and
Josephson, 1987
) and katydids (Josephson,
1985a
,b
).
These studies, however, do not address the extent to which optimized
experimental conditions match the full set of in vivo operating
conditions.
The mesothoracic dorsolongitudinal muscles (dl1 muscles;
nomenclature of Nüesch,
1953) of the hawkmoth Manduca sexta provide an
advantageous system in which to compare potential vs realized
performance. The dl1 muscles are the largest muscles in the moth,
comprising 58% of the total body mass. Because these synchronous
muscles are typically activated only once in each wing stroke
(Kammer, 1967
), the timing of
activation can be unambiguously determined from extracellular muscle
recordings. During flight, the dl1 muscles function exclusively to
generate most if not all of the mechanical power used to depress the wings.
Optimization of the dl1 muscles for maximum power output would
therefore be consistent with their role as the major source of aerodynamic
power. In a previous study (Tu and Daniel,
2004
), we determined the in vivo operating conditions of
the dl1 muscles of Manduca during steady state tethered
flight. Here, we determine the extent to which power generation is maximized
in a synchronous insect flight muscle by comparing the maximum potential power
output of the dl1 muscles to their power output realized under
in vivo operating conditions.
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Materials and methods |
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The dl1 muscles span the length of the mesothorax and attach to
the 1st and 2nd phragmata (Fig.
1B). The phragmata are deep invaginations of the dorsal
exoskeleton that form broad areas for muscle attachment. Each of the
bilaterally paired dl1 muscle consists of five subunits,
designated, from ventral to dorsal, dl1a to dl1e
(Nüesch, 1953;
Eaton, 1988
).
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Force transducer
The force transducer consisted of a cantilevered 6.25 mm x1.5 mm
brass beam with a free length of 35.25 mm. We used an optical sensor (Spot 2D,
UDT Sensors Inc., Hawthorne, CA, USA) to track the position of a short length
of stainless steel hypodermic tubing soldered to the end of the beam. The
force beam had a compliance of 3.6x10-4 mm
mN1 and an unloaded resonant frequency of 640 Hz. The force
transducer was mounted on a 3-axis micromanipulator, which in turn was mounted
on a linear translation stage. Using the calibrated micrometer on the
translation stage, we could adjust the force transducer position with a
precision of 0.01 mm. A custom-built PID controller used the outputs of the
optical length sensor and the voltage-controlled oscillator as comparator
signals. This feedback circuit minimized variation in length changes as we
varied either amplitude or stimulus phase.
Muscle length oscillation
Sinusoidal length changes were imposed on the muscle using a magnetic coil
oscillator (V200 series, Ling Dynamic Systems, Yalesville, CT, USA), modified
with a leaf spring to increase its unloaded stiffness. To measure muscle
length changes, we used an optical sensor (LSC 30D, UDT Sensors Inc.,
Hawthorne, CA, USA) to track the position of a red LED attached to the shaft
of the oscillator.
Temperature
We measured thoracic temperature to the nearest 0.1°C using a 0.15 mm
diameter copper-constantan thermocouple inserted into the dl1
muscle through a small hole in the exoskeleton. The entire experimental
apparatus was enclosed within an insulated plywood box. Heated water
circulating through copper pipe within the box maintained the muscle
temperature at 36±0.5°C.
Muscle stimulation
We elicited twitches using bipolar, supramaximal stimuli, 0.2 ms in
duration, delivered through a pair of electrodes formed from stainless steel
minuten pins. The electrodes were inserted through the anterior notum and into
the dl1 muscle, one on either side of the midline.
Muscle preparation
The dl1 muscles receive their primary respiratory air supply
from large tracheal trunks originating at the mesothoracic spiracles. On each
side of the moth, these tracheal trunks run anteriorly between the
dl1 muscles and the dorsoventral muscles, supplying both muscle
groups. This arrangement of tracheae made it impossible to remove the
dl1 muscles from the thorax without compromising their oxygen
supply. In addition, respiratory pumping by the abdomen appears critical for
prolonged viability of the dl1 muscles; muscle performance
deteriorated rapidly if we removed the abdomen in order to expose the
posterior muscle attachments on the 2nd phragma. We therefore developed a
semi-intact preparation that minimized the dissection necessary to
mechanically isolate the dl1 muscles between two specially
constructed grips.
The anterior grip consisted of a small aluminum block shaped to match the contours of the anterior mesoscutum and the 1st phragma (Fig. 1A). After being weighed, each moth was decapitated, its legs and wings removed, and the scales rubbed off the dorsal surfaces of the thorax. The 1st phragma was exposed by severing the pronotum near its articulation to the mesothoracic prescutum and by clearing away the prothoracic dorsolongitudinal muscles. After scraping away the waxy epicuticle, we used cyanoacrylate adhesive to attach the grip to the cuticle overlying the anterior origins of the dl1 muscles. Any gaps between the grip and the exoskeleton were filled with a composite formed from cyanoacrylate and sodium bicarbonate powder.
The posterior grip consisted of a pair of 0.68 mm diameter stainless steel hypodermic needles soldered to a small brass block (Fig. 1A). The needles were parallel to each other and were separated by a distance slightly less than the lateral width of the 2nd phragma. A drop of cyanoacrylate adhesive was placed in the deep groove overlying the phragma. We then pushed the needles down into the groove so that they punctured the metathoracic scutellum and passed down along the posterior face of the phragma (Fig. 1A). Cyanoacrylate flowing between the needles and the cuticle solidly bonded the phragma and scutellum to the needles and brass block (Fig. 1B). We discarded trials if dissection following the measurements showed that the needles had pierced the phragma, or if the needles and phragma were not solidly bonded.
To preserve the orientation of the dl1 muscles as the thorax was transferred to the experimental apparatus, we glued two strips of acetate transparency film, one strip on each side, across the gap separating the two grips. The acetate strips restricted length changes and minimized bending and torsion of the muscles. We then mechanically isolated the dl1 muscles from the thoracic exoskeleton by excising a thin strip of cuticle from around the anterior grip (Fig. 1B).
The anterior grip was attached to the force beam via a short, threaded steel rod projecting from the front of the grip (Fig. 1B). The threaded end of the rod was inserted through a hole near the end of the force beam and secured with a nut. The posterior grip was attached to the shaft of the magnetic coil oscillator via a short length of stainless steel tubing projecting from the back of the grip. The tubing terminated in a ball bearing, which fitted into a depression in the end of the oscillator shaft, and formed a ball joint when secured with a slotted retaining nut.
Once the two grips were secured, we cut the acetate strips connecting the two grips. The dl1 muscles then formed the only direct mechanical linkage between the oscillator and the force beam. We used the ball joint and the micromanipulator mount of the force beam to restore the initial muscle length and orientation. The position of the muscle was adjusted until the cut edges of the acetate strips were just touching and exactly aligned. The force beam manipulator was then locked in position and the retaining nut on the oscillator shaft was tightened to prevent movement of the posterior grip relative to the oscillator shaft. Finally, the acetate strips were trimmed away to prevent mechanical interference with imposed muscle length changes.
Muscle length, mass and cross-sectional area
The length Lmax at which the dl1 muscles
generate their maximum isometric twitch force provides a reliable
physiological reference length that is independent of the experimental method
and of any offsets introduced in the initial preparation. We therefore
referenced previous measurements of in vivo operating length and
strain amplitude to Lmax
(Tu and Daniel, 2004), and we
continue the procedure here. However, because of the internalized skeletal
attachments of the dl1 muscles, we could not measure the absolute
value of Lmax until after completing all of our work loop
measurements. To solve this difficulty, we first performed a series of
lengthtension measurements to determine the position of
Lmax relative to the initial muscle length. We then
calculated values for experimental length offsets and strain amplitudes based
on an average value of Lmax determined from a series of
preliminary length tension measurements.
To measure the position of Lmax relative to the initial muscle length, we performed a series of isometric twitch lengthtension measurements on each muscle prior to measuring power output. At each length, the muscle received five supramaximal stimuli at 1 Hz. We changed the muscle length during a 5 s interval separating each burst of stimuli. Starting at a length 0.4 mm shorter than the initial length, we increased length in steps of 0.1 mm up to 0.20.3 mm beyond our estimate of Lmax. We then repeated the length series in reverse order. From the average twitch amplitude at each length step, we identified Lmax for the ascending and descending length series. If the two series gave different values of Lmax, we used the average of the two values.
At the conclusion of each experiment, we dissected the thorax to expose the
dl1 muscles. We first used the calibrated micrometer on the
translation stage to return the dl1 muscles to their initial
length. Two strips of stainless steel shim, one on each side, were glued
across the gap separating the grips, securing the muscle at its initial
length. We then removed the preparation from the experimental apparatus. The
dl1 muscles of one side were dissected free of the thorax and
placed in Manduca saline (Tublitz
and Truman, 1985). We then recorded a video image of the medial
aspect of the intact, contralateral dl1 muscles. The remaining
dl1 muscles were then dissected free of the thorax and placed in
saline. Immediately afterwards, we blotted the muscles and weighed them
together to the nearest 1 mg.
The absolute value of Lmax was calculated from the
recorded offset between the initial length and Lmax, and
the distance between the ventral margins of the 1st and 2nd phragma, measured
on the video image. We previously defined the in vivo operating
length, Lop, to be the median length of dl1a
during flight (Tu and Daniel,
2004). By mapping length changes of the dl1 muscles
onto their isometric twitch length-tension curve, we found that on average,
Lop was equal to 0.89Lmax±0.04
(mean ± S.D.; Tu and
Daniel, 2004
). Using the specific value of
Lmax for each muscle, and this average value of
Lop relative to Lmax, we calculated an
estimate of Lop for each muscle.
Muscle volume was calculated from the measured muscle mass, assuming a muscle density of 1 g cm3. Muscle fiber length measurements were taken on the video image of the medial surface of the dl1 muscles on one side. We calculated an average fiber length from six measurements taken at locations that were evenly distributed between the dorsal and ventral margins of the muscle.
Timing and phase of muscle activation
In our recordings of in vivo muscle activation and length changes
during tethered flight (Tu and Daniel,
2004), we calculated the phase of activation of the dl1
muscle as the time from the start of muscle lengthening to the peak of the
spike in the subsequent extracellular spike, divided by the cycle period. Here
we applied these measurements of in vivo activation phase to power
measurements on isolated muscles. To do so, we first had to account for a
possible difference in the timing between spikes in extracellular muscle
recordings, and stimuli delivered to the muscle through extracellular
electrodes. We therefore performed a series of measurements using muscle
preparations identical to those used for power measurements, with the addition
of bipolar extracellular recording electrodes implanted in the right
dl1c, as described in Tu and Daniel
(2004
). For each preparation,
we recorded evoked extracellular potentials during trains of supramaximal
stimuli delivered at 1 Hz. We performed signal averaging of successive
responses using the stimulus as a time reference, and measured the delay
between the onset of the stimulus and the peak of the evoked muscle potential
(Fig. 2). We define the phase
of activation in our work loop measurements as the projected time of the
evoked potential following an applied stimulus, normalized to the cycle
period:
phase=(
ts+
tep)/P,
where
ts is the delay from the onset of muscle
lengthening to the onset of the applied stimulus,
tep is the average delay between the onset of the
stimulus and the peak of the evoked muscle potential, and P is the
cycle period.
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Experimental protocols
During flight, Manduca regulate their internal thoracic
temperature in the range of 3242°C
(Heinrich, 1971;
Heinrich and Bartholomew,
1971
; McCrea and Heath,
1971
), and have a wing stroke frequency of approximately 25 Hz
(Willmott and Ellington,
1997
). In all trials, therefore we held muscle temperature and
cycle frequency constant at 36±0.5°C and 25 Hz, respectively, and
systematically varied the phase of activation, mean length and strain
amplitude. The range of experimental variation in each of these parameters was
sufficient to include both the in vivo value, and the value that gave
the maximum mechanical power output. Each combination of parameters was tested
at three strain amplitudes, with peak-to-peak values normalized to the
estimated value of Lop, approximately 0.10, 0.075 and
0.05. Together with any experimental length offsets, all amplitudes were
determined precisely for each individual after all power measurements were
complete. For each measurement of power output, the muscle was subjected to a
burst of 25 cycles of stimulation combined with sinusoidal length changes
imposed symmetrically around an experimental length. Experimental parameters
were adjusted to new values during the 5 s that separated each burst. We
performed two sets of measurements of mechanical power output, one to examine
the effects of stimulus phase, and the second to focus on the effects of mean
muscle length.
Our first set of measurements focused on the effects of stimulus phase on power output. For each of the three amplitudes tested, we performed measurements at four experimental lengths: Lmax, the initial muscle length L0, and two intermediate lengths. At each experimental length, a complete phase series consisted of power measurements at 19 values of stimulus phase, evenly spaced throughout the length cycle in fractional increments of 0.05. The three amplitudes were tested in increasing order. Within each amplitude set, the order in which the four experimental lengths was randomized, as was the order of phase values within each length series. Randomization was performed separately for each animal prior to the start of the measurements (rand.m, Matlab v.4, The Math Works Inc., Natick MA USA), and the randomized length and phase sequences were programmed into the software controlling the work loop measurements. The 228 measurements of the 12 experimental series (three amplitudes, each at four experimental lengths) required approximately 50 min to complete.
We performed a second set of measurements to examine power output in greater detail over a restricted range of phase and a greater range of experimental lengths. We employed five values of stimulus phase, evenly spaced at fractional increments of 0.05. These values encompassed both the phase measured in vivo and the optimum stimulus phase for power output determined from the first set of work loop measurements. We performed three series of measurements on each muscle, one at each strain amplitude. Each series started with the muscle length set to 0.10.2 mm shorter than the estimated value of Lop. At each length, the muscle was given five bursts of stimulation and sinusoidal length change. Randomization of the phase presentation at each length was performed as described for the first set of measurements. We then increased the experimental length by 0.1 mm, and repeated the measurements at the five phase values. Each of the three length series consisted of 100 measurements at 20 length steps and five phase values, for a total of 300 measurements on each preparation.
Force and length data were both digitized at a rate of 5 kHz, and digitally low-pass filtered with zero phase delay and a cutoff frequency of 400 Hz. We calculated the net work performed per cycle by integrating force with respect to muscle length over the last five complete cycles of each burst. Power was calculated as the product of the net work per cycle and the cycle frequency. Values are given as means ± 1 S.D.
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Results |
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Muscle length at Lmax
The mean value of Lmax determined from a series of
length tension measurements on six muscles was 12.3±1.13 mm.
Muscle power output
We measured power output from a total of six muscle preparations, three to
examine the effects of the phase of activation and three to examine the
effects of experimental length. The six moths used for work loop measurements
were all females with a mean body mass of 2.75±0.029 g. The left and
right dl1 muscles from these moths had a mean combined mass of
0.164±0.017 g, a mean combined cross sectional area of
21.58±2.51 mm2, and a mean mean fiber length of
7.63±0.40 mm. The three strain amplitudes used in all six preparations
had mean values of 5.0±0.4Lop,
7.7±0.4Lop, and
10.3±0.6Lop. We calculated distortion of the
imposed sinusoidal length changes as the amplitude of the 2nd harmonic of the
Fourier power spectrum, expressed as a percentage of the 1st harmonic. The
mean distortion averaged across all measurements was 7.0±1.7%
(Fig. 3). The magnitude of
isometric twitch forces, measured at the beginning and at the end of each
preparation, declined by 13.7 to 19.2% during the hour required to complete
the series of measurements on each muscle. Because we randomized the order of
the length, phase and strain amplitude, this decline in performance should not
have introduced a systematic bias in our results. Within all of the power
measurements, the largest discrepancies between initial and final values of
muscle stress and length over a segment of five cycles were 3.8% and 1.4%,
respectively.
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In the first three preparations, at each experimental length and strain amplitude, power output varied through a single maximum and a single minimum value as we changed the phase of activation from 0 to 1 (Fig. 4). All three muscles generated positive power output between fractional phase values of 0.2 and 0.6, and maximal power between 0.3 and 0.4. Both the magnitude of the peak positive power output and the peak rate of energy dissipation (negative power) increased with increasing strain amplitude. Average values of the four experimental lengths, normalized to Lop, were 0.97±0.01, 1.01±0.01, 1.05±0 and 1.12±0. Positive power output was consistently lower at the shorter two lengths, which were also the lengths closest to the in vivo operating length. In all cases, differences in power output due to changes in strain amplitude and experimental length were small compared to differences due to changes in the phase of activation.
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The dl1 muscles of all six preparations generated a mean maximum power output of 83.3±13.2 W kg1 (Table 1). On average, the dl1 muscles generated maximum power output at a phase of 0.36±0.03, an experimental length of 1.11±0.05Lop, and a strain amplitude of 0.092±0.011Lop.
We based our estimate of in vivo power output on a subset of
measurements taken using experimental parameters that most closely matched the
in vivo operating conditions measured by Tu and Daniel
(2004). For each of the six
muscle preparations, we first identified measurements taken at phase values
within one standard deviation of the mean phase measured in vivo
(0.49±0.04). We further reduced this data set by selecting measurements
taken at lengths (0.961.05Lop) within one
standard deviation of the mean in vivo operating length. Finally, we
selected the subset of measurements taken at strain amplitudes between
0.08Lop and 0.10Lop. This range of
amplitudes was well within the range of strain amplitudes measured in
vivo (0.055L0.013Lop; mean
0.09±0.02Lop;
Tu and Daniel, 2004
). The mean
power output from all six preparations measured under in vivo
conditions was 47.4±11.3 W kg1
(Table 2). This power output
was measured at a mean phase of 0.48±0.01, a mean experimental length
of 1.01±0.01 and a mean strain amplitude of
0.086±0.005Lop. Under in vivo conditions
the dl1 muscles generated only 57% (range: 4067%) of their
maximum potential power output (Table
2, Fig. 5). Using
the same search procedure, the mean power output at the maximum and minimum
values of phase measured in vivo
(Tu and Daniel, 2004
) was
29.9±11.5 W kg1 at phase values of 0.56±0.03,
and 65.3±12.8 W kg1 at phase values of
0.45±0.02. This range corresponds 35.777.9% of the maximum power
output measured in this study. The strain amplitude that maximized power
output in our measurements was similar to the measured in vivo strain
amplitude. However, relative to the mean in vivo phase of activation,
the phase that maximized power output was advanced by 12% of the cycle period,
and the length that maximized power output was 10% longer than the in
vivo operating length. With changes in the phase of activation, power
output varied as a result of changes in the size of the work loops, without
any lemniscate behavior in the forcelength trajectories
(Fig. 6).
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Discussion |
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Assessment of in vivo power output
Assessment of in vivo power output requires accurate replication
of the in vivo operating parameters of a muscle
(Marsh and Olson, 1994). Our
experimental protocol reproduced the in vivo values of temperature,
cycle frequency, phase of activation, mean muscle length and strain amplitude
previously reported for Manduca
(Heinrich, 1971
;
Heinrich and Bartholomew,
1971
; McCrea and Heath,
1971
; Willmott and Ellington,
1997
; Tu and Daniel,
2004
). Two other variables, the strain distribution within the
dl1 muscles, and the shape of the strain trajectory, were the most
potentially troublesome to replicate in the isolated muscle.
Although our experimental methods minimized any initial distortion of the
dl1 muscles, localized strains within the muscle during imposed
length changes may have differed from the strain distribution in
vivo. Josephson and Ellington
(1997) suggested that strain
amplitudes within bumblebee flight muscle might be uniform, but the actual
spatial distribution of muscle fiber strain has yet to be mapped in
Manduca or in any other insect. Lacking such data, we applied uniform
length changes to the whole muscle. Differences in fiber length among the five
subunits of the dl1 muscles necessarily produced local variation in
strain. Our data show that the magnitude of power output at a given phase
varies with strain amplitude, suggesting that inhomogeneous strains within the
muscle could in fact affect our measurements of total power output. We based
the imposed length changes, however, on those measured directly from subunit
dl1a, the largest subunit of the dl1 muscles, and the
subunit with the largest lever arms on the 1st and 2nd phragmata. This
protocol should have minimized errors in strain amplitude within
dl1a, and the power output of this subunit should dominate the
performance of the muscle as a whole. More importantly, we have no evidence to
suggest that strain inhomogeneities could have altered the relationship
between power output and the phase of activation. Because all subunits of the
dl1 muscles are mechanically coupled, local gradients in strain
could not have produced local differences in the phase of activation. In
addition, the phase of activation that maximized power output did not change
with strain amplitude (Fig. 4).
It is therefore unlikely that we would measure peak power output at the in
vivo phase of activation, even if we were to precisely replicate the fine
scale distribution of strain amplitudes within the muscle.
Our use of sinusoidal motions to approximate in vivo length
changes represents an additional potential complication. Asymmetrical triangle
strain trajectories with prolonged shortening can augment power output
relative to that generated during sinusoidal length oscillations
(Askew and Marsh, 1997;
Girgenrath and Marsh, 1999
).
Length changes of the dl1 muscles, however, did not show
appreciable asymmetries between the duration of lengthening and shortening
(Tu and Daniel, 2004
). For
symmetrical strain trajectories, the available evidence suggests that even
fairly substantial variation in trajectory shape does not greatly alter the
net power output. Josephson
(1989
) used a mathematical
model to predict that muscles would perform similar amounts of work during
both sinusoidal and triangle wave length changes. This result has been
confirmed experimentally for muscles undergoing sinusoidal and triangle length
oscillations with equal shortening and lengthening duration
(Askew and Marsh, 1997
). During
swimming, the natural strain trajectory of the scallop adductor muscle departs
strongly from either a simple sinusoidal or triangle waveform. The net power
output of the adductor muscle, however, is similar during both sinusoidal and
natural strain cycles (Marsh et al.,
1992
; Marsh and Olson,
1994
). These results suggest that the comparatively small
discrepancies between the applied and in vivo length changes in our
measurements did not greatly affect the magnitude of our measured power
output.
Our assessment of in vivo power output would be most seriously in
error if the discrepancies between the applied and in vivo strain
trajectories were sufficient to shift the phase of activation that maximized
power output. Variation within and among individuals complicates exact
replication of the in vivo strain trajectories. Neither an exact
replica of the strain measured from one individual, nor an average strain
trajectory compiled from multiple individuals would have been entirely
appropriate for any one muscle. Sinusoidal length changes, however, did in
fact replicate the dominant features of the strain trajectory common to all of
our in vivo measurements (Fig.
3). Our applied sinusoidal length changes lacked the higher
frequency components contained in the in vivo strain waveform at
roughly twice wingstroke frequency (Fig.
3; Tu and Daniel,
2004). It is unlikely, however, that the inclusion of this missing
component would be sufficient to augment the power output at the in
vivo length and phase of activation by the 40 W kg1
necessary to match the maximum measured power output. Gilmour and Ellington
(1993
) examined the effect of
including the second harmonic from the in vivo strain waveform in the
driving signal for in vitro work loop measurements. In glycerinated
fibers from the asynchronous flight muscles of bumblebees, inclusion of the
second harmonic generally reduced the net power output. Although these results
suggest that purely sinusoidal strain trajectories might overestimate in
vivo power output, there are currently no published studies bearing on
the consequences of the sequential addition or subtraction of the Fourier
components of a complex strain trajectory of synchronous muscle. Without such
data, it is difficult to assess the importance of subtle complexities in the
in vivo strain trajectory for our data, or to draw generalized
conclusions from specific measurements of power output made under more complex
strain regimes.
In vivo power output and muscle function
From recent studies, it is now clear that in addition to power generation,
muscles used in terrestrial locomotion serve a variety of functions, such as
braking (Full et al., 1998;
Ahn and Full, 2002
), energy
storage (Roberts et al. 1997
;
Biewener et al., 1998
) and
energy transmission (Olson and Marsh,
1998
). It is further evident that these additional functions can
conflict with maximum power generation. During swimming and flying, however,
the absence or relaxation of these additional demands could permit greater
optimization of muscle function for maximum power. Surprisingly, maximal power
output by the red muscle of skipjack tuna currently stands as the lone example
of such optimization for swimming fish
(Syme and Shadwick, 2002
).
Submaximal power output by the propulsive muscles of other fish suggests that,
as in terrestrial locomotion, multiple functions such as energy transmission
and stabilization of the body may compromise power output in swimming
(Altringham et al., 1993
;
Hammond et al., 1998
;
Rome et al., 1999
;
Coughlin, 2000
;
Swank and Rome, 2001
).
Among flying insects, submaximal power output by both the asynchronous
flight muscles of bumblebees (Josephson,
1997) and the synchronous dl1 muscles of
Manduca suggest that insect flight muscles may also operate under
constraints that compromise their ability to generate maximal power under
in vivo conditions. For Manduca, the indirect mechanical
linkages between the dl1 muscles and the wing hinge clearly do not
indicate a major role in the stabilization and control of flight. These
functions almost certainly reside primarily in the small, laterally placed,
flight muscles, which insert directly onto elements of the wing articulation
(Kammer, 1971
;
Rheuben and Kammer, 1987
;
Wendler et al., 1993
;
Ando and Kanzaki, 2004
). It is
therefore unlikely that the in vivo performance of the dl1
muscles reflects a compromise between power generation and direct control of
wing kinematics. There remains, however, the possibility that submaximal power
output by these muscles represents a design compromise related to some degree
of intrinsic regulation of the wing stroke, maintenance of elevated thoracic
temperature, efficiency, or coupling among different elements of the flight
system.
The in vivo operating range of the dl1 muscles lies
entirely on the ascending limb of their isometric twitch lengthtension
curve (Tu and Daniel, 2004).
Due to the steepness of this lengthtension curve, transient increases
in the wingstroke amplitude that increase in the strain of the dl1
muscles will automatically enhance the capacity of these muscles to generate
force. The combination of the lengthtension characteristics of the
dl1 muscles, their pattern of activation, and their operating
length range may therefore provide some degree of non-neuronal regulation of
wingstroke frequency and amplitude. Such intrinsic regulation at the level of
the muscle appears to come at the cost of power generation, since the in
vivo operating length is substantially shorter than the operating length
that maximizes power output.
As the largest muscles in the thorax of Manduca, the
dl1 muscles are likely to be the primary source of heat during
pre-flight warm-up and during flight, in addition to their function as the
primary wing depressors (Dotterweich,
1928). We do not know if submaximal power output by the
dl1 muscles is related to this dual role, or if the dl1
muscles of non-endothermic moths generate power at levels approaching their
maximum capacity. Interestingly, the red muscles of skipjack tuna also
function to maintain regionally elevated muscle temperatures
(Barrett and Hester, 1964
)
while attaining maximal power output, suggesting that these two functions are
not mutually exclusive.
We do not yet know the extent to which the efficiency of the dl1
muscles may be optimized during flight. Maximum efficiency and maximum power
output may not occur under the same conditions; Curtin and Woledge
(1996) showed that the
stimulus duty cycle that maximizes efficiency in dogfish swimming muscle
differs from the duty cycle that maximizes power output. Although Josephson
and Stevenson (1991
) measured
the efficiency of the dorsoventral muscles under conditions that optimize
power output, the relationships between power, efficiency and operating
parameters of the dl1 muscles are unknown. A decrease in efficiency
with increasing power output would suggest that submaximal power output during
steady flight represents a compromise between optimization for power and
muscle efficiency. Increased efficiency at higher levels of power output would
be particularly puzzling since steady flight conditions would then be
associated with both low power output and low efficiency.
In addition to potential compromises related to control, heat generation or
efficiency, coupling between different elements of the flight system could
constrain the temporal patterns of strain and activation in the dl1
muscles to values that do not maximize power output. Controlled, stable
locomotion arises from complex coupling between musculoskeletal mechanics,
propulsors and the external medium, and neural control
(Daniel, 1985;
Daniel and Tu, 1999
). The
variables that determine muscle power output, especially length changes and
the temporal pattern of activation, arise from interactions between these
systems at multiple levels. The design of complex muscle systems could involve
compromises that maximize the net power output at the level of the entire
system rather than at the level of individual muscles. In addition, mechanical
coupling between internal musculoskeletal mechanics and external fluid
dynamics could impose constraints on the possible trajectories, amplitudes and
frequencies of muscle length oscillations, and these constraints could
conflict with maximum power output.
Finally, operation at submaximal levels of power output could leave
reserves for use in extreme behaviors such as escape locomotion, instances
where efficiency may be less critical. Our results suggest that flying
Manduca could obtain most of this reserve power by advancing the
phase at which they activate the dl1 muscles. We do not yet know,
however, if Manduca modulates the phase of activation of the
dl1 muscles during maneuvers. It is important to note that
variation in aerodynamic power generation by the wings may not be directly
coupled to variation in mechanical power generation by the dl1
muscles. Transmission of mechanical power from the dl1 muscles to
the wings is potentially regulated by the actions of 12 pairs of flight
muscles that insert directly onto elements of the wing articulation
(Nüesch, 1953;
Eaton, 1988
). In flies,
changes in the firing patterns of the small direct flight muscles can produce
large changes in wing kinematics (Tu and Dickinson, 1996;
Balint and Dickinson, 2001
).
These changes in wing kinematics are likely to occur independently of
modulation of power output by the large elevator and depressor muscles, since
in flies, these are asynchronous muscles that are not under direct neural
control. Similar modulation in the phase and frequency of activation in direct
flight muscles is seen in Manduca
(Rheuben and Kammer, 1987
;
Kammer, 1971
;
Wendler et al., 1993
;
Ando and Kanzaki, 2004
).
Assesment of the range of possible modulation of power output in the dl1
muscles must await technologies that permit simultaneous measurement of muscle
activation and muscle length changes in freely flying insects.
With the relatively small but growing number of muscles for which we can compare potential and realized power output, generalizations about muscle design may be premature. The available evidence does suggest, however, that maximal power output by muscles during locomotion may be restricted to burst performance and a small number of specialized cases such as thunniform swimmers. Understanding the principles that underlie the design of locomotor muscles will clearly require investigations into additional performance measures such as efficiency, as well as a better understanding of the consequences of coupling between neural control, musculoskeletal mechanics, and the external environment.
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