Submaximal power output from the dorsolongitudinal flight muscles of the hawkmoth Manduca sexta

Over the last two decades, work loop studies have provided new insights into the principles of design that underlie muscle performance. In particular,a growing number of studies have compared maximal power output under experimental conditions to realized power output in vivo. The diversity in performance revealed by such comparisons suggests that maximization of power output (Hill,1950), may not be the dominant principle underlying the design of muscle systems used in locomotion. Muscles may indeed attain their maximal power output during escape responses (Lutz and Rome, 1996; Askew and Marsh, 2001; Askew et al.,2001; Franklin and Johnston,1997; James and Johnston,1998). During sustained locomotion, however, maximal power output may be rare (Syme and Shadwick,2002). Some of the observed diversity in muscle performance may reflect differences in function such as power generation vs stability and control (Full et al.,1998; Ahn and Full,2002; Tu and Dickinson,1994). Variation in muscle performance may also reflect fundamental differences in the demands on muscles in terrestrial locomotion vs. swimming and flight.

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 5–8% 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.

Adult Manduca sexta L. were obtained from a colony maintained in the Department of Biology at the University of Washington. Larvae were raised on artificial diet at 26°C. Both larvae and adults were maintained under a 17 h:7 h L:Dphotoperiod. We shifted the photoperiod of the moths so that the onset of their dark period occurred in mid-morning. Adults were used within 1–3 days of eclosion.

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, dl_1a to dl_1e(Nüesch, 1953; Eaton, 1988).

The force transducer consisted of a cantilevered 6.25 mm ×1.5 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 3.6×10^-4 mm mN^–1 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.

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.

We measured thoracic temperature to the nearest 0.1°C using a 0.15 mm diameter copper-constantan thermocouple inserted into the dl₁muscle 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.

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.

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 dl₁muscles 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.

The length L_max 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 L_max(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 L_max until after completing all of our work loop measurements. To solve this difficulty, we first performed a series of length–tension measurements to determine the position of L_max relative to the initial muscle length. We then calculated values for experimental length offsets and strain amplitudes based on an average value of L_max determined from a series of preliminary length tension measurements.

To measure the position of L_max relative to the initial muscle length, we performed a series of isometric twitch length–tension 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 0.2–0.3 mm beyond our estimate of L_max. We then repeated the length series in reverse order. From the average twitch amplitude at each length step, we identified L_max for the ascending and descending length series. If the two series gave different values of L_max, 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 L_max was calculated from the recorded offset between the initial length and L_max, 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, L_op, to be the median length of dl_1aduring 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, L_op was equal to 0.89L_max±0.04(mean ± s.d.; Tu and Daniel, 2004). Using the specific value of L_max for each muscle, and this average value of L_op relative to L_max, we calculated an estimate of L_op for each muscle.

Muscle volume was calculated from the measured muscle mass, assuming a muscle density of 1 g cm^–3. Muscle fiber length measurements were taken on the video image of the medial surface of the dl₁muscles 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.

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 dl₁muscle 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 dl_1c, 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=(Δt_s+Δt_ep)/P,where Δt_s is the delay from the onset of muscle lengthening to the onset of the applied stimulus,Δ t_ep is the average delay between the onset of the stimulus and the peak of the evoked muscle potential, and P is the cycle period.

During flight, Manduca regulate their internal thoracic temperature in the range of 32–42°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 L_op, 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: L_max, 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 0.1–0.2 mm shorter than the estimated value of L_op. 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.

In four moths, the average delay Δt_ep between the stimulus and the peak of the evoked muscle potential was 5.9±1.4 ms(Fig. 2).

The mean value of L_max determined from a series of length tension measurements on six muscles was 12.3±1.13 mm.

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±0.4L_op,7.7±0.4L_op, and 10.3±0.6L_op. 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.

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 L_op, 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.

The experimental lengths tested using the second group of three muscle preparations fell in the range of 0.95±0.01L_op to 1.17±0.01L_op. Based on the results of the first three preparations, we used five values of fractional phase between 0.3 and 0.55. At each of the three amplitudes tested, these values of phase and length were sufficient to resolve a distinct maximum in power output while including the values of phase and length measured in vivo(Fig. 5). The maximum power output increased with strain amplitude, although the difference between the maximum power output at the two higher amplitudes was consistently small.

The dl₁ muscles of all six preparations generated a mean maximum power output of 83.3±13.2 W kg^–1(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±0.05L_op, and a strain amplitude of 0.092±0.011L_op.

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 (0.96–1.05L_op) within one standard deviation of the mean in vivo operating length. Finally, we selected the subset of measurements taken at strain amplitudes between 0.08L_op and 0.10L_op. This range of amplitudes was well within the range of strain amplitudes measured in vivo (0.055L–0.013L_op; mean 0.09±0.02L_op; Tu and Daniel, 2004). The mean power output from all six preparations measured under in vivoconditions was 47.4±11.3 W kg^–1(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±0.005L_op. Under in vivo conditions the dl₁ muscles generated only 57% (range: 40–67%) 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 kg^–1 at phase values of 0.56±0.03,and 65.3±12.8 W kg^–1 at phase values of 0.45±0.02. This range corresponds 35.7–77.9% 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 force–length trajectories(Fig. 6).

Our measurements of mechanical power output from the dl₁ muscles of Manduca are the first direct comparisons of in vivo and optimized performance for a synchronous insect flight muscle. At a cycle frequency of 25 Hz and at 36°C, the average maximum power output from the dl₁ muscles, 83 W kg^–1, falls within the range of maximal power output previously reported for a dorsoventral muscle of Manduca at 28 Hz: 80 W kg^–1 at 35°C and 90 W kg^–1 at 40°C(Stevenson and Josephson,1990). Maximal power output from the dl₁ muscles was also similar to values reported for other synchronous insect muscles: a metathoracic wing elevator muscle from two species of locust (72–73 W kg^–1; Mizisin and Josephson, 1987) and from a katydid (76 W kg^–1; Josephson, 1985a), and the basalar muscle of a dragonfly (91–124 W kg^–1; Marden et al., 2001). However,under conditions that replicated in vivo length, strain trajectory,cycle frequency, activation timing and temperature, the dl₁ muscles achieved only 40–67% of their maximum potential mechanical power output. Both the in vivo phase of activation and the in vivooperating length differed substantially from values that maximized power output. Submaximal power output from the dl₁ muscles is surprising since these muscles generate most if not all of the power for the downstroke,and therefore a large fraction of the mechanical power for flight. In the following discussion, we first address possible sources of error in our measurements. We then discuss possible implications of submaximal power output for our understanding the design of musculoskeletal systems.

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 dl_1a, 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 dl_1a, 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 kg^–1necessary 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.

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 dl₁muscles 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 length–tension curve (Tu and Daniel, 2004). Due to the steepness of this length–tension curve, transient increases in the wingstroke amplitude that increase in the strain of the dl₁muscles will automatically enhance the capacity of these muscles to generate force. The combination of the length–tension 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 dl₁muscles 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 dl₁muscles 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 dl₁muscles 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 dl₁muscles. 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.

This work was supported by NSF Grant 9511681 to T.L.D., a Packard Interscience Grant to T.L.D., and by an ONR MURI Grant.