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First published online December 3, 2004
Journal of Experimental Biology 207, 4651-4662 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01321

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

Michael S. Tu^* and Thomas L. Daniel

Department of Biology, University of Washington, Seattle WA 98195-1800, USA

View larger version (30K): [in a new window]   Fig. 1. Muscle preparation for work loop measurements. (A) Placement of the anterior (a) and posterior (p) muscle grips for force measurements on mechanically isolated muscles. (B) After decapitating the moth, the 1st phragma was exposed and the anterior grip placed over the anterior insertion of the dl1 muscles. The paired needles of the posterior grip were driven through the dorsal cuticle and down along the posterior face of the 2nd phragma. Both grips were secured to the exoskeleton with cyanoacrylate adhesive. After gluing acetate strips (not shown) across the gap between the two grips to fix their relative positions, cuticle strips were excised (arrows, broken line) to mechanically isolate the anterior grip and muscle insertions from the rest of the thorax. The anterior grip was then secured to the force transducer via the treaded rod projecting from the grip. The ball bearing (bb) mounted on the posterior grip fit into a depression in the end of a threaded rod (tr) mounted on a magnetic coil oscillator. When secured by a slotted retaining nut (n), the ball bearing and threaded rod formed a ball joint. The acetate strips spanning the two grips then were cut, and any misalignment of the cut ends was corrected using the ball joint and oscillator. a–e, dl1 muscle subunits.

View larger version (9K): [in a new window]   Fig. 2. To adjust for the difference in timing between a stimulus applied to the muscle and muscle activation recorded during tethered flight, we recorded extracellular potentials (A) and force (B) from the dl1 muscles during isometric twitches. Stimuli were delivered through extracellular electrodes spanning all subunits of the dl1 muscles and were 0.2 ms in duration. Extracellular potentials were recorded from dl1c. (A) Three extracellular muscle potentials in response to stimuli of increasing amplitude. The stimulus artifact (s) varied in amplitude with the amplitude of the applied stimulus. Subthreshold stimuli (a) produced only a stimulus artifact whereas suprathreshold stimuli (b,c) resulted in a clearly identifiable extracellular spike of constant amplitude. We defined the delay between the onset of the stimulus and the evoked potential (tep) as the time between the onset of the stimulus artifact and the peak of the evoked potential. The large voltage deflections of the stimulus artifact in b and c exceeded the range of the data acquisition system and are cut off at ±10 V. (B) Muscle force recorded following the three stimuli shown in A. Note that the time scale differs from that in A. Subunits of the dl1 muscles responded in an all-or-none manner to stimuli. Subthreshold stimuli (a), defined by the absence of an evoked extracellular spike, generally did not result in twitch forces. Supramaximal stimuli (b,c) consistently produced a maximal twitch of nearly constant amplitude. In some preparations, subthreshold stimuli evoked submaximal twitches with discreet amplitudes. In these cases, the submaximal twitches probably resulted from selective recruitment of subunits other than dl1c, the subunit in which we had implanted the recording electrodes. Stimulus amplitude in our measurements of mechanical power output was adjusted to the level that produced the maximal twitch force from the whole muscle. We defined the phase of activation in our work loop measurements as the projected time of the evoked potential normalized to the cycle period (see text for details).

View larger version (20K): [in a new window]   Fig. 3. Sinusoidal length changes replicated the major components of the in vivo strain trajectory. (A) Two cycles of length change from work loop measurements (solid lines) and from tethered flight (dotted lines, from Tu and Daniel, 2004) chosen on the basis of their closely matching frequency and amplitude. Trajectories recorded during tethered flight matched sinusoidal length changes through most of the cycle but were typically more complex at the transitions from lengthening to shortening. (B) Fourier spectra calculated from the two records shown in A. Sinusoidal length changes replicated the dominant characteristics of the length changes recorded in tethered flight.

View larger version (50K): [in a new window]   Fig. 4. Mechanical power output is plotted against the phase of muscle activation at four mean experimental lengths, and three strain amplitudes. The data shown are from one muscle preparation (Moth 1 in Tables 1, 2). (A–C) The muscle was subjected to length oscillations at three experimental strain amplitudes with mean values of 0.105±0.0053Lop (A), 0.078±0.0058Lop (B), and 0.049±0.0143Lop (C) (N=76 for each amplitude). At each amplitude setting, we imposed muscle length changes symmetrically around four experimental lengths: 0.98Lop (red), 1.02Lop(blue), 1.05Lop(green), and 1.12Lop(yellow). We measured mechanical power output at each combination of amplitude and experimental length as we varied the phase of activation through the strain cycle in 19 evenly spaced increments, expressed as a fractions of the cycle period. (D) Combined data from A–C. Limitations of our feedback controller resulted in some variation in strain amplitude within any one sweep of phase values. The effects of changes in strain amplitude and experimental length were small compared to the variation in mechanical power output with changes in the phase of activation. At each combination of strain amplitude and experimental length, power varied through a single maximum and minimum as we changed the phase of activation from 0 to 1. Power was positive between phase values of 0.2 and 0.6, and maximal between 0.3 and 0.4. With increasing amplitude, both the magnitude of the peak positive power output as well as the peak rate of energy dissipation (negative power) increased. Positive power output was consistently lowest at the experimental lengths (0.98Lop (red), and 1.02Lop (blue)) that were closest to the in vivo operating length.

View larger version (31K): [in a new window]   Fig. 5. Power output of the dl1 muscles is plotted over a range of activation phases, experimental lengths and strain amplitudes that encompass both peak power and in vivo operating conditions. (A–C) Variation in mechanical power output as a function of experimental length. Experimental length is normalized to operating length. Each plot shows measurements taken at one peak-to-peak strain amplitude normalized to Lop: (A) 0.048, (B) 0.083, (C) 0.115. Within each plot, each curve shows data from measurements at one of five values of the phase of activation: 0.31, 0.37, 0.42, 0.47, • 0.52. At each amplitude power output was consistently lowest at the phase values (0.47 and 0.52) that were closest to the phase of activation measured in vivo (0.49±0.04; Tu and Daniel 2004). (D–F) Contour plots showing power output, coded by color, as a function of the phase of activation and experimental length. Each plot is based on 90 measurements of power taken at five values of activation phase and 18 values of experimental length. The contour lines were fitted to the data by interpolation using an inverse distance method (griddata.m, Matlab v.4, The Math Works Inc., Natick MA USA). Each plot shows measurements taken at one peak-to-peak strain amplitude, normalized to Lop: (D) 0.048, (E) 0.083, (F) 0.115. At all three amplitudes, power output near the values of operating length and phase of activation measured in vivo (open circle) was substantially lower than the peak power output. The mean strain amplitude measured in vivo (0.090±0.031Lop) lies between the amplitudes tested in B,C, and E,F. Data in A–F are from one muscle preparation (Moth 6 in Tables 1, 2).

View larger version (17K): [in a new window]   Fig. 6. Work loops measured under conditions that maximized power output [blue, phase of activation: 0.34; mean length: 9.81 mm (1.05Lop); peak-to-peak strain amplitude: 0.95Lop; power output: 91.0 W kg–1] and under conditions that replicated conditions measured in vivo during tethered flight [red, phase of activation; 0.52, mean length: 9.81 mm (1.05Lop); peak-to-peak strain amplitude: 0.77Lop, power output: 53.9 W kg–1]. Time progresses in each loop in a counterclockwise direction, as indicated by the arrowhead on each loop. The filled circle on each loop indicates the time of muscle activation. Both work loops are from Moth 1 in Tables 1 and 2. Activation of the muscle prior to the onset of shortening maximized power output. Under in vivo conditions in which muscle activated occurred near the onset of shortening, the muscle generated relatively low force during shortening and did not relax completely prior to lengthening.