A motor and a brake: two leg extensor muscles acting at the same joint manage energy differently in a running insect
Department of Integrative Biology, University of California at Berkeley, Berkeley, CA 94720-3140, USA
*Present address: Concord Field Station, Harvard University, Old Causeway Road, Bedford, MA 01730, USA (e-mail: aahn{at}oeb.harvard.edu)
Accepted 16 November 2001
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Summary |
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Key words: muscle, electromyography, work loop, neural control, locomotion, biomechanics, insect, arthropod, Blaberus discoidalis, cockroach.
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Introduction |
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The realization that individual muscles can function as motors, brakes, springs or struts during locomotion presents the possibility that muscles of a single anatomical group may not necessarily share the load or even share a common mechanical function. It is most often assumed that synergistic muscles share the work or load because muscles within a multiple muscle group are capable of executing the same action. In vivo studies show that the multiple ankle extensors in the cat and the wallaby operate together to share the force and power demands during locomotion (Walmsley et al., 1978; Abraham and Loeb, 1985
; Prilutsky et al., 1996
; Biewener et al., 1998
). Numerous studies have modeled the functions of multiple muscles using assumptions of equal load-sharing (Seireg and Arvikar, 1975
; Crowninshield, 1978
; Dul et al., 1984
; Davy and Audu, 1987
; Herzog and Leonard, 1991
). Variation in function among muscles of a common anatomical group to generate coordinated movement is seldom considered a possibility.
For muscles of the same anatomical group to function similarly, one might expect the muscles to have similar intrinsic and extrinsic properties. Although many factors determine muscle force and power output during cyclical contractions (for a review, see Josephson, 1999), in the present study, we focus on three muscle properties: the kinetics of force generation, forcevelocity relationships, and history-dependent effects. The twitch kinetics of a muscle are often tuned to the cycle frequency at which the animal locomotes. A muscle with faster twitch durations will generate maximum power at higher cycle frequencies, whereas a muscle with slower twitch durations will generate maximum power at lower cycle frequencies (Rome et al., 1988
; Johnson et al., 1993
; James et al., 1995
; James et al., 1996
; Swoap et al., 1993
). At higher cycle frequencies, a muscle with faster twitch kinetics can generate force during muscle shortening, then relax before lengthening begins (Marsh, 1990
; Johnson et al., 1993
; Coughlin et al., 1996
; Swank et al., 1997
). A muscle with slower contraction kinetics tends to absorb energy at higher operating frequencies because its twitch duration exceeds the shortening period of the muscles (Caiozzo and Baldwin, 1997
). Moreover, muscles operating on different regions of their forcevelocity curves are more likely to manage energy differently (Biewener and Gillis, 1999
). A muscle operating at approximately one-third of its maximum contraction velocity (Vmax) tends to maximize power, whereas a muscle contracting near its Vmax tends to generate lower forces and reduced power output (Curtin and Woledge, 1988
; Rome et al., 1988
) (for a review, see Josephson, 1993
). History-dependent effects of muscle activity can also influence muscle function: shortening-induced force depression tends to reduce the work and power output of muscles undergoing large strains during cyclic contractions (Edman, 1975
; Josephson, 1997
; Askew and Marsh, 1998
; Josephson and Stokes, 1999
).
In the present study, we ask whether individual muscles within an anatomical muscle group necessarily function similarly during locomotion. We define muscle function as a muscles ability to produce, store and return, or absorb mechanical energy over a cycle. We compare two of the six muscles (muscles 177c and 179, using the notation of Carbonell) (Carbonell, 1947), that can generate extensor moments at the coxafemur joint of the cockroach hindlimb. One of the two muscles (muscle 179) is already known to absorb mechanical energy under in vivo running conditions (Full et al., 1998
). Here, we ask whether both extensors share the load and function to absorb energy during running. To test the hypothesis of common mechanical function, we determined the strain and activation patterns of muscles 177c and 179 during running at the preferred speed. We then imposed cyclic in vivo strain and stimulation patterns on semi-isolated muscle while measuring force to determine work and power (Josephson, 1985a
). Next, we explored the mechanisms responsible for the similarities or differences in function by measuring twitch kinetics and forcevelocity relationships. We replicated the in situ energy measurements for muscle 179 under in vivo conditions to provide a direct and complete comparison of its function with that of muscle 177c. We selected these hindlimb extensor muscles because both muscles are parallel-fibered, are a single motor unit, lack inhibitory innervation, and act at a joint with a single degree of freedom.
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Materials and methods |
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Electromyography and kinematics
Electromyographic (EMG) activity patterns from both muscles (177c and 179) were acquired during free running on a Plexiglas track. Simultaneously, we videotaped, from underneath, the clear track with a high-speed video camera system at 500 frames s1 (Redlake Camera Systems, MotionScope) to determine the two-dimensional joint kinematics as the animals ran at their preferred speed. White spots (Liquid Paper) were painted with a pen onto the head, tail and hindlimb joints. We marked the bodycoxa, coxafemur, femurtibia and tibiatarsus joints and the pre-tarsal claws of both hindlimbs. Joint angles were calculated from the digitized points (Peak Performance Technology, Motus) for each run. The joint angles were then filtered with a third-order, low-pass Butterworth filter with a cut-off frequency of 25 Hz, determined by residual analysis (Biewener and Full, 1992).
For the EMG recordings, bipolar electrodes were made from 50 µm diameter (44 gauge) silver wire insulated with polyurethane (California Fine Wire) (for details, see Full et al., 1998). Each electrode was heated to form a small ball (Full et al., 1998
). The ends of the electrodes were inserted into small holes in the basalar plate for muscle 177c and in the ventral, exoskeletal surface of the coxa for muscle 179. Inserted electrodes were fixed in place using dental wax. All wires were braided together to prevent electrical crosstalk and to form a convenient tether, which was waxed onto the pronotum. Muscle action potentials recorded from the running animals were amplified 100 times at a bandwidth of 3 Hz to 1 kHz (Grass P5 series a.c. pre-amplifiers) (Full et al., 1998
) and were acquired at 3 kHz (Labview DAQ system; NI PCI-1200 boards) on a computer (Macintosh Power PC 9500/132). EMG signals were filtered with a second-order, high-pass Butterworth filter with a cut-off frequency of 100 Hz. We ensured the absence of crosstalk between the muscles and between the wires inserted into the muscles by using behaviors that resulted in muscle action potentials from one muscle, but not the other. During tethered flight trials, the animal activated muscle 177c, but not 179. During slow runs, the animals activated muscle 179, but not 177c. After the recordings, the animals were fixed in 70 % ethanol. Electrode placement was re-checked by careful dissection after fixation of the animals.
The animals ran at their preferred speed along a Plexiglas track (9 cmx66 cm) at room temperature (23°C). Trials during which the animal ran straight at a steady speed and did not bump into the walls were accepted. Ten trials were obtained from six animals. Two consecutive cycles from each trial were analyzed (20 cycles in total). Six animals were used to determine the kinematic and electromyographic variables.
Muscle strain during running
The kinematics of the hindlimb determined during the videotaped EMG trials were played into a three-dimensional musculo-skeletal model of the cockroach hindlimb (Full and Ahn, 1995). Using a computer program (SIMM, Software for Interactive Musculoskeletal Modeling, MusculoGraphics, Inc) (Delp and Loan, 1995
) and the kinematic variables measured during running, muscle strain for 177c and the strain patterns for 177c and 179 were determined (see Delp et al., 1990
; Full and Ahn, 1995
). Muscle strain is directly proportional to joint angle in insect legs because these muscles insert on apodemes (arthropod tendon), which are 40 times stiffer than vertebrate tendon (Ker, 1977
). Given the apodeme stiffness, the apodeme strains less than 0.01 % for the forces experienced by the muscles.
Muscle experiments
Animals were chilled and attached to a Lucite chamber using epoxy resin. Details of the apparatus were as described by Full et al. (1998). The Lucite chamber restrained the animal while the epoxy resin held the hindlimb fixed so that the coxafemur joint angle was set at approximately 90°. This joint angle was chosen to approximate the resting length for muscle 179 (104 %) (Full et al., 1998
). We assumed that the resting length occurred at the same joint angle for muscle 177c. The dissection began with removal of the exoskeleton from the area of the metathoracic ganglion so that the connectives between thoracic ganglia 2 and 3 (i.e. the ventral nerve cord) could be severed. The resting length of the muscle was estimated before and after the experiment using an ocular micrometer and digital calipers. The dissected area was periodically moistened with insect Ringers solution as required (Becht et al., 1960
). Muscle cross-sectional area was determined from muscle mass and muscle length assuming a muscle density of 1 g cm3. Muscle forces were measured with a servo motor system (Cambridge Technology, Inc; model 300B) and recorded with a computer program (Labview, National Instruments) that controlled muscle length while measuring muscle force. A small hook on the lever arm held the muscle apodeme. The muscle was stimulated (Grass S48 stimulator) through the nerve (nerve 4 for muscle 177c and nerve 5 for muscle 179) using a suction electrode. The stimulation consisted of 0.5 ms square-wave pulses at approximately twice the threshold voltage. Trials were separated by 2 min intervals to minimize potentiation and fatigue. Maintenance of muscle performance was periodically checked with contractions generated by the in vivo stimulation pattern for each muscle (two or three muscle action potentials). The experiment was stopped when the amplitude of muscle contraction force declined by more than 10 % of its original force. The in situ muscle force measurements were all performed at 25°C.
Muscle 177c was isolated by dissecting away the ventral exoskeleton of the coxa and removing the other extensor muscles (179, 177a, 177e and 177d). It was particularly important to cut away muscle 177a because it inserts onto the same apodeme as 177c and is innervated by the same motor neuron as 177c. The trochanteral exoskeleton connected to the 177 apodeme was carefully cut, allowing the distal end of the muscle to attach to the lever arm (Fig. 1). To expose the distal end of muscle 179, we cut away a small area of the ventral exoskeleton of the coxa. The dissection to expose 179 was minimal because this muscle is the most superficial/ventral muscle in the group (Fig. 1). Tracheae or other muscles were not exposed. The trochanteral exoskeleton connected to the 179 apodeme was cut carefully, allowing the distal end of the muscle to be attached to the lever arm.
Isometric contractions
The semi-isolated muscle was stimulated through the nerve using a suction electrode, as described above. For isometric contractions, we used trains of 16 stimuli at a stimulation frequency of 100 pulses s1. Tetanic stimulation bursts consisted of 200 ms bursts at 200 pulses s1. Muscles were rested for 510 min after each tetanic stimulation.
Twitch kinetics included the time to peak force (Tmax), time to 50 % relaxation (T50off) and time to 90 % relaxation (T90off). These times began with the onset of stimulation to represent most closely the time between muscle activation and force generation in vivo and, therefore, include the latency period or the time between the onset of stimulation and the onset of force.
Maximum shortening velocity
The maximum velocity of shortening was estimated by determining the forcevelocity relationships of the muscles using the force-clamp method (Edman, 1979). Maximally stimulated muscles were allowed to shorten isotonically at different force levels. The velocity of shortening was determined for each force level. The maximum shortening velocity (Vmax) for each muscle was determined using the least-squares method, which extrapolated the forcevelocity measurements to zero force (Wohlfart and Edman, 1994
). The muscles were rested for 5 min between trials unless the maximum tetanic force declined. If the maximum tetanic force declined by 5 % or more, then the experiment was stopped. The in situ contraction velocities for both muscles were filtered using a third-order, low-pass Butterworth filter with a cut-off frequency of 25 Hz.
Work loop method
Animals were mounted and muscles dissected as described above for isometric contractions. The in vivo conditions used to determine muscle work (muscle strain, phase, frequency and duration of stimulation) were obtained from the EMG/kinematics trials. The area of the third loop formed by plotting muscle force as a function of muscle length gave the work per cycle (Josephson, 1985a). Net in vivo power was calculated by dividing net in vivo work by the cycle period. To test the effects of small changes in phase and strain on muscle power output, we varied these parameters independently. While keeping the other in vivo conditions constant, the phase of stimulation onset was varied independently of strain, and strain was varied independently of the phase of stimulation. The force and stress results for muscle 179 were filtered using a third-order, low-pass Butterworth filter with a cut-off frequency of 50 Hz, because the lowest signal-to-noise ratio was 35:1, on average. Forces for 177c were not filtered because the signal-to-noise ratio was 300:1.
Statistical analyses
All data were calculated as the mean ± S.D. To avoid pseudo-replication, each animal generated a single data point for all data sets, unless a parameter was varied (e.g. strain amplitude, phase of stimulation). If there were duplicate data from any given animal under a single set of conditions, the values were averaged to represent that animal under that set of conditions. Groups of data were compared using the unpaired t-test to give P-values (StatView 5.0). MannWhitney U-tests were used to test for differences in activity patterns between the two muscles (StatView 5.0).
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Results |
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Muscle 177c was activated after the beginning of joint extension (or muscle shortening). The activation began at a phase of 37.6±10.7 % (Fig. 2), where 0 and 100 % represent midway through joint flexion (or muscle lengthening) (Full et al., 1998). The number of muscle action potentials for 177c ranged from one to four per cycle, averaging 1.8±0.6. The interspike interval was 11±2 ms. Muscle 177c was activated for 7.3±6.2 % (or 7.3±6.8 ms; N=6) of each cycle.
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The number of discrete muscle action potentials per burst differed between the two muscles during running (two muscle action potentials for 177c; three muscle action potentials for 179; P=0.01). Although the phase of burst onset differed for the two muscles (P=0.037), the bursts ended at the same phase of the cycle (offset phase 44.9±12.7 % for 177c; offset phase 42.7±6.1 % for 179; P=0.20). These patterns of onset and offset correspond to overlapping periods of activation of the two muscles during running (Fig. 2). Although the number of muscle action potentials differed with similar interspike intervals (P=0.76), the burst durations of the two muscles were not statistically different (P=0.078). The burst duration normalized to stride period (i.e. duty cycle) of the two muscles were also similar (P=0.055). Variation in our sample size resulted in the paradox that the number of action potentials differed between the muscles, yet no difference could be resolved in interstimulus interval or burst duration. To characterize the activation pattern during running, we first selected the variable that showed the strongest statistical difference, the mean number of muscle action potentials per cycle (two for muscle 177c and three for 179). Next, we chose a constant interstimulus interval of 11 ms because we found no statistical difference between the muscles and this was exactly the interval measured previously for muscle 179 (Full et al., 1998). Finally, we selected the onset phase of the burst on the basis of the statistically significant difference between the muscles (38 % for muscle 177c and 26 % for 179).
The muscles shortened and lengthened cyclically with each stride during running. During the stance phase, the joint extended as the extensor muscles shortened. Conversely, during the swing phase, the muscles lengthened as the joint flexed. Total muscle strain over a stride during running was calculated as 7 % for muscle 177c (7.5±1.5 %; N=6) and 16.4±2.8 % (Full et al., 1998) for muscle 179.
Muscle properties
Isometric contraction kinetics
The rates of isometric force development and relaxation of single twitches did not differ between 177c and 179 (Table 1). The times to 90 % relaxation (T90off) were approximately twice as long as the times to peak force (Tmax) for both muscles.
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Forcevelocity relationships
Both absolute and relative forcevelocity relationships differed between the two muscles. Muscle 177c (mean length 8.95±0.47 mm; N=7; measured from the muscles that were used to determine in vivo power) was more than twice as long as muscle 179 (mean length 4.14±0.25 mm; N=6). The absolute, maximal rate of shortening of muscle 177c (49.2±6.7 mm s1; N=4) was much greater than that of muscle 179 (20.6±3.0 mm s1; N=4; Fig. 3A). However, once normalized for muscle length, the forcevelocity relationships of 177c and 179 were more similar. The relative Vmax for 177c (5.7±0.4 L s1; N=4, where L is muscle length), was greater than the relative Vmax of 179 (4.9±0.4 L s1; N=4; P=0.02; Fig. 3B).
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Muscle strain
We used muscle strains of 7 % for muscle 177c and 16.4 % for muscle 179 to determine the work done by the muscles under in vivo conditions. To ensure that our conclusions would not be affected by errors in strain measurement, we tested the sensitivity of muscle power output to strain amplitude. Muscle 177c always generated net positive power over the range of muscle strains (5.78.4 %; N=6; Fig. 5) used during running (stimulation phase 35 %; two muscle action potentials per cycle; Fig. 5). Muscle 179 always absorbed net energy over the range of strains (1418.5 %; N=6) used under in vivo conditions (stimulation phase 28 %; three muscle action potentials per cycle; Fig. 5).
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Discussion |
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Twitch kinetics
Twitch kinetics (times to peak force, 50 % relaxation, and 90 % relaxation) did not explain why one muscle (177c) generated energy and the other (179) absorbed energy during running. The twitch kinetics were similar between muscles 177c and 179 (Table 1). For both muscles, twitch duration (i.e. time to 50 % relaxation) lasted less than half the stride period (62.5 ms at 8 Hz stride frequency). A twitch duration shorter than half the stride period suggests that the muscle has the capacity to produce power during running because it could generate force during the shortening phase and then relax before lengthening begins.
In vivo contraction velocities
Strain rate and amplitude can also influence a muscles ability to generate force and produce power (Josephson, 1985a; Josephson and Stokes, 1989
; Marsh, 1999
). Muscles generate maximum power output at approximately one-third Vmax in fish (Curtin and Woledge, 1988
; Rome et al., 1988
), mammals (Syme and Stevens, 1989
; James et al., 1996
; Swoap et al., 1997
), frogs (Stevens, 1988
) and crabs (Josephson and Stokes, 1989
). However, if the muscle shortens quickly, near its Vmax, then the positive work done by the muscle during shortening may not exceed the work needed to re-lengthen the muscle. Therefore, a muscle shortening near Vmax during cyclic contractions may not generate positive power (Josephson, 1985b
; Josephson and Stokes, 1989
). The strain rate of a muscle depends on the length of its moment arm (r) and the angular velocity of the joint. Because muscles 177c and 179 operate at the same joint and have similar mean moment arms (r=0.76 mm for 177c; r=0.54 mm for 179) (Full and Ahn, 1995
), they shorten at similar absolute velocities (maximum in situ velocity approximately 15 mm s1; Fig. 3A). However, muscle 177c was approximately twice as long as muscle 179, thus shortening relatively half as fast as 179. The greatest relative in situ shortening velocity for muscle 177c was only 1.7 L s1, whereas muscle 179 shortened more than twice as fast (3.7 L s1; Fig. 7B). Although the two muscles contracted at the same peak absolute velocities, they operated on different regions of their relative forcevelocity relationships (Fig. 3B). The longer, relatively slower-contracting muscle (177c) operated near one-third Vmax (1.75 L s1), the relative velocity at which isotonic power is maximized. In contrast, the shorter muscle (179) shortened near its Vmax (Fig. 3B), resulting in very little force production during shortening (Fig. 7B,D). These differences in relative shortening velocities largely account for the observed differences in muscle performance during running.
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History-dependent effects: force depression due to active shortening
Force depression due to active shortening of muscle is another intrinsic property that is influenced by muscle strain and determines force and work output. Shortening-induced force depression reduces the work and power output of muscles undergoing large strains during cyclic contractions (Edman, 1975; Josephson, 1997
; Askew and Marsh, 1998
; Josephson and Stokes, 1999
). Moreover, force depression induced by active shortening increases with increasing strain (Edman, 1975
). This effect may further depress the force generated by muscle 179 during shortening (Fig. 7D). Muscle 179 experiences greater strain amplitudes (16.4 %) than muscle 177c (7 %) and, therefore, would be expected to experience greater force depression than muscle 177c (Edman, 1975
). When stimulated at the beginning of shortening or later, muscle 179 only absorbed energy over the cycle (Fig. 6A; phase >20 %), while this muscle generated power when stimulated before shortening (phase <20 %). When stimulated during shortening (phase >20 %), the force of muscle 179 may be depressed as a result of active shortening. This phenomenon probably depressed force in muscle 177c as well, but to a lesser degree because it experienced smaller strain amplitudes. The difference in force depression due to active shortening between the muscles may contribute to the difference in mechanical performance of the muscles during running.
Integration of neural control and muscle mechanics
A major determinant of muscle power output during cyclical contractions is the phase of stimulation (Josephson, 1985a, 1999
). As expected, the function of muscles 177c and 179 varied with stimulation phase (Fig. 6). When stimulated before shortening (phase <20 %), both muscles functioned as motors. When stimulated between the beginning of shortening and mid-shortening (phase 2040 %), the two muscles functioned differently, even when stimulated at the same phase. When stimulated after mid-shortening (phase >40 %), both muscles absorbed mechanical energy. Under in vivo conditions during running, the animal generally activated muscle 177c when this muscle generated mechanical energy while activating 179 at phases at which this muscle absorbed mechanical energy (Fig. 6).
The similarity in twitch kinetics would not predict differences in mechanical function if the animal activated the muscles by single muscle action potentials. Differences in contraction kinetics due to differences in muscle action potential number did, however, offer a partial explanation of how one muscle functioned as a motor and the other as a brake. With their in vivo stimulation patterns, muscle 177c contracted and relaxed faster than 179 (Table 1). Within a cycle, muscle 177c generated force during shortening and then relaxed before lengthening began. In contrast, on the basis of the duration of activation predicted from isometric contractions, muscle 179 remained active throughout shortening and through part of lengthening (Fig. 7). However, the kinetics of isometric force development provide only a first approximation of how long a muscle can generate force when contracting isometrically and do not provide sufficient information to predict muscle function during locomotion.
Although the simplest assumption concerning the operation of a multiple muscle system is that of synergy or equal load-sharing, we show that muscles within a muscle group do not necessarily manage energy similarly during running. Individual muscles within the same anatomical muscle group can function as power-generating motors (177c) or as energy-absorbing dampers (179) during running. Anatomy, muscle activation patterns, kinematics, twitch kinetics or isotonic forcevelocity measurements alone may be insufficient to predict in vivo muscle function. Muscle function depends on the dynamic interactions between a large number of variables (Josephson, 1999). Without the direct determination of muscle forces under in vivo stimulation and strain conditions, predicting in vivo muscle function during locomotion can be difficult, if not impossible. Depending on activation pattern, contraction velocity and history-dependent effects under the in vivo strain and stimulation conditions, apparent redundancy within a multiple muscle group may instead represent diversity in muscle function.
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Acknowledgments |
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