R. McNeill Alexander is with the Department of Biology, University of Leeds, Leeds ... Chris 1. Barclay. Most investigations of the energetics of isolated skeletal ...
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below its natural frequency. This is the only situation in which efficiencies close to the 0.45 obtainable in experiments with isolated muscles cannot be obtained by judicious choice of vmaxand tendon compliance. Figure Ib shows that when the mass parameter is zero (the muscles are driving a resonant system at its natural frequency), maximum efficiency is obtained with relatively fast muscles and zero compliance. With a positive mass parameter (Figure lc), tendon compliance is advantageous. And when the mass parameter is large (inertial forces are much larger than hydrodynamic forces, Figure Id), efficiency is maximized with a relatively slow muscle (low vmax) and a precisely tuned tendon compliance. The approach described here is crude and requires refinement, but it promises to improve our understanding of the role of series compliance in muscle action. It indicates that the speeds (vmax) of muscles and the compliances of their tendons both must be optimized to minimize the metabolic cost of a cyclic activity. Data for locomotion of some animals indicate that their muscles and tendons are adapted more or less as the theory requires (Alexander, 1997).
References Alexander, R.M. (1997). Optimum muscle design for oscillatory movements. Journal of Theoretical Biology, 184,253-259. Alexander, R.M., & Bennet-Clark, H.C. (1977). Storage of elastic strain energy in muscle and other tissues. Nature, 265, 114-117. Ingen Schenau, G.J. van, Bobbert, M.F., & Haan, A. de. (1997). Does elastic energy enhance work and efficiency in the stretch-shortening cycle? Journal of Applied Biomechanics, 13, 389415. R. McNeill Alexander is with the Department of Biology, University of Leeds, Leeds LS2 9JT, UK.
Initial Mechanical Efficiency in Cyclic Contractions of Mouse Skeletal Muscle
Chris 1. Barclay Most investigations of the energetics of isolated skeletal muscle have used contraction protocols designed to facilitate understanding of basic aspects of muscle contraction. Such protocols typically use relatively long isometric, isovelocity, or isotonic contractions during which the muscles are fully activated. While these are well suited to their purpose, they bear little relation to most in vivo muscle activity, particularly that occurring during locomotion. This disparity inspired the development of the "cyclic contraction" protocol (Josephson, 1985), which involves sinusoidal alterations in muscle length, at physiological frequencies, with a brief contraction in each cycle. This approach has been used to study locomotor muscles from many animals (for reviews, see Johnston, 1991; Josephson, 1993). In all types of muscle studied so far, mechanical performance assessed in the laboratory using cyclic contractions has compared favorably with in vivo performance (James, Altringham, & Goldspink, 1995; Johnston, 1991; Josephson, 1993), providing empirical support for the idea that cyclic contractions reasonably simulate muscle function during locomotion.
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Two studies (Barclay, 1994; Curtin & Woledge, 1993) compared muscle efficiency during conventional isovelocity protocols (in fully activated muscle) with that during cyclic contractions. In both studies, efficiency was calculated-frommeasurementsof muscle output and initial heat production. It was found that for the fast twitch white myotomal muscle from dogfish and the slow twitch mouse soleus muscle (but not fast twitch mouse EDL muscle), efficiency was considerably higher in cyclic contractions than in isovelocity contractions. For instance, maximum initial mechanical efficiency of mouse soleus muscle was -35% in isovelocity contractions (Barclay, Constable, & Gibbs, 1993) but over 50% in cyclic contractions (Barclay, 1994). It should be noted that initial mechanical efficiency encompasses both the energetic cost of power development by cross-bridges and also the cost of non-cross-bridge processes (predominantly due to ATPuse by the Ca2+pump of the sarcoplasmic reticulum). The cause of the relatively high efficiency in cyclic contractions is not known. However, it is clearly not due to an increase in power output resulting from release of energy stored in elastic elements of the muscles during the stretch phase. Two features of the protocols used in the myothermal studies (Barclay, 1994; Curtin & Woledge, 1993) preclude this possibility. First, efficiency was calculated using the net work produced in each cycle (i.e., work output - work input). Thus, any work input that was absorbed and subsequently released as work during the shortening phase would not affect the magnitude of net work (Curtin & Woledge, 1993). Second, the magnitude of work done on muscles during the stretch phase (the source of any stored elastic energy in these experiments) was only a small fraction of the work done by the muscles during shortening (Curtin & Woledge, 1996). Therefore, the relatively high efficiency of these muscles during cyclic contractions was not a consequence of release of stored elastic energy. An observation that may cast some light on the cause of high efficiency in cyclic contractions is that the force output during shortening in these contractions is considerably higher than would be expected on the basis of steady-state force-velocity properties (Stevens, 1993). For example, Figure 1A compares the steady-state force-velocity relationship for mouse soleus muscle with the non-steady-state force-velocity relationship determined during cyclic contractions. The cyclic contractions were performed at the cycle frequency and using stimulus parameters that maximized initial mechanical efficiency (Barclay, 1994). When the velocity of shortening was most rapid during the cyclic contraction, more force was produced than during an isovelocity contraction at those same velocities. Thus, it appears that starting to develop force during the latter stages of the stretch phase of a cycle, perhaps combined with the slow increase in shortening velocity at the start of shortening, enabled force output to exceed steady-state force corresponding to those shortening velocities. Consequently, peak power output (force x velocity) was also markedly greater than during isovelocity contractions (cf. Josephson, 1993). A further interesting observation is that the force output in mouse EDL (a fast twitch muscle) was not similarly enhanced (Figure 1B); efficiency in this muscle was also no greater in cyclic contractions than in isovelocity contractions. Thus, it may be that the high efficiency of mouse soleus muscle in cyclic contractions was related to its enhanced power output. However, this alone does not account for the increased efficiency; for efficiency to be higher, power output must have been enhanced without a comparable increase in energetic cost. One way this could occur would be if, in this protocol, the total amount of energy to be expended was determined quite early in each contraction, as would be the case if each cross-bridge performed only
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Figure 1 -Comparison of the steady-state force-velocity relationship in isovelocitycontractions (broken limes) and the non-steady-state force-velocity relationship during sinusoidal cyclic contractions (solid lines) for mouse soleus (A) and EDL (B) muscle. The lines for cyclic contractions are the average of data from four successive contraction cycles of one preparation. Stimulus characteristics and cycle frequency were those giving maximum mechanical efficiency (for details, see Barclay, 1994). The isovelocity force-velocity curves were constructed using
where V' = V/Vmm,the velocity of length change relative to the maximum shortening velocity, P/P, is the force output relative to maximum isometric force, and Pda is proportional to the curvature of the force velocity relationship. PJa was determined from reported values (Barclay, 1996) that were adjusted to the appropriate value for 31 O C (the temperature at which the cyclic contractions were performed) using a Q,, of 1.2 (Rall & Woledge, 1990).
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one ATP-splitting cycle per contraction, leaving the energetic cost relatively insensitive to the pattern of contractile activity later in the contraction (Woledge & Curtin, 1993). Using the method described by Woledge and Curtin (1993) and assuming that 65% of the initial energy output arose from cross-bridge cycling (Barclay, 1996), it can be estimated that the average number of ATP molecules split per cross-bridge per cycle in the mouse soleus (contracting at the frequency at which efficiency was maximal) was -0.7. This figure suggests that not all cross-bridges were active (i.e., submaximal activation) and that those which were active probably completed only a single ATPsplitting cycle. This does not necessarily preclude detachment-attachment cycles occurring without ATP hydrolysis (Woledge & Curtin, 1993). In contrast to the soleus, each cross-bridge in mouse EDL muscle would have split -2.5 ATP molecules per cycle. In summary, efficiency of some muscles (i.e., those with slow rates of cross-bridge turnover) may be high in cyclic contractions because (a) the combination of the timing of stimulation, the time course of length changes, and muscle force dynamics enhances power generation (Figure 1A) and (b) energetic cost is relatively insensitive to the muscle's mechanical performance because each cross-bridge only performs -1 ATPsplitting cycle which, in turn, means that the total energy to be expended is determined early in the contraction. Such a mechanism could account for the relatively high efficiency of soleus muscle in cyclic contractions. In contrast, in EDL muscle, with crossbridges that perform multiple cycles in each contraction, neither power nor efficiency was enhanced. As stated earlier, cyclic contraction protocols were developed to study muscle function during animal locomotion; that is, experiments with mouse muscles provide us with information specifically related to locomotion in this animal (e.g., James et al., 1995). However, researchers should use considerable caution when extrapolating from in vitro data obtained from muscles of small animals (from which all in vitro data have been obtained) to much larger animals in vivo. For example, small animals are much less efficient during locomotion than large animals, even when the larger mass-specific basal metabolism of small animals is accounted for (Heglund, Fedak, Taylor, & Cavagna, 1982). Therefore, the relatively low efficiency values for isolated muscles from small animals are probably consistent with the efficiency of those animals during locomotion. It is also relevant that Heglund et al. (1982) suggested that storage of energy in elastic elements of muscle and its subsequent release during shortening may be much more important in energetics of large animals than small ones. This reinforces the notion that attempts to compare efficiency of isolated muscles from small animals to efficiency of large animals (e.g., humans) during locomotion involve considerable uncertainty.
References Barclay, C.J. (1994). Efficiency of fast- and slow-twitch muscles of the mouse performing cyclic contractions. Journal of Experimental Biology, 193,65-78. Barclay, C.J. (1996). Mechanical efficiency and fatigue of fast and slow muscles of the mouse. Journal of Physiology, 497,781-794. Barclay, C.J., Constable, J.K., & Gibbs, C.L. (1993).Energetics of fast- and slow-twitch muscles of the mouse. Journal of Physiology, 472,61-80. Curtin, N.A., & Woledge, R.C. (1993).Efficiency of energy conversion during sinusoidal movement of white muscle fibres from the dogfish scyliorhinus canicula. Journal of Experimental Biology, 183,137-147.
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Curtin, N.A., & Woledge, R.C. (1996). Power at the expense of efficiency in contraction of white muscle fibres from dogfish scyliorhinus canicula. Journal of Experimental Biology, 199,593601. Heglund, N.C., Fedak, M.A., Taylor, C.R., & Cavagna, G.A. (1982). Energetics and mechanics of terrestrial locomotion. Journal of Experimental Biology, 97,57-66. Ingen Schenau, G.J. van, Bobbert, M. F., & Haan, A. de. (1997). Does elastic energy enhance work and efficiency in the stretch-shortening cycle? Journal of Applied Biomechanics, 13, 389415. James, R.S., Altringham, J.D., & Goldspink, D.F. (1995).The mechanical properties of fast and slow skeletal muscles of the mouse in relation to their locomotory function.Journal ofExperimental Biology, 198,491-502. Johnston, I.A. (1991). Muscle action during locomotion: A comparative perspective. Journal of Experimental Biology, 160, 167-1 85. Josephson, R.K. (1985). Mechanical power output from striated muscle during cyclic contraction. Journal of Experimental Biology, 114,493-5 12. Josephson, R.K. (1993). Contraction dynamics and power output of skeletal muscle. Annual Review of Physiology, 55,527-546. Rall, J.A., & Woledge, R.C. (1 990). Influence of temperature on mechanics and energetics of muscle contraction. American Journal of Physiology, 259, R197-R203. Stevens, E.D. (1993). Relation between work and power calculated from force-velocity curves to that done during oscillatory work. Journal o f Muscle Research and Cell Motility, 14,518526. Woledge, R.C., & Curtin, N.A. (1993). The efficiency of energy conversion by swimming muscles of fish. In H. Sugi & G.H. Pollack (Eds.), Mechanism of myofilament sliding in muscle contraction (pp. 735-747). New York: Plenum Press.. C.J. Barclay is with the Department of Physiology, Monash University, Clayton, Victoria 3168, Australia.
Effects of Elastic Energy Storage on Muscle Work and Efficiency
Andrew A. Biewener Ingen Schenau et al. question (a) whether elastic energy recovery contributes to increased muscle work when contractions are preceded by an eccentric (stretch) phase and (b) whether such stretch-shortening contractions (SSCs) enhance muscular efficiency. Three variables are considered in terms of the increased work performed by muscles that undergo SSCs: an increased time for activation, elastic energy storage, and force potentiation. Based on a review of available data, Ingen Schenau et al. conclude that only an increased time for developing muscular force and the cross-bridge dynamics of force potentiation can explain the increased work performed by muscles that undergo active prestretch before shortening, arguing correctly that any energy recovered from series elastic elements during the shortening phase of a contraction cannot exceed the amount of (negative) work done to store strain energy as the muscle is stretched. Consequently, elastic storage and recovery cannot enhance the net work performed by a muscle. Elastic energy savings, however, may reduce the amount of work that muscles must perform to power oscillatory movements of the body, such as in running, trotting, and hopping locomotion. For these locomotor gaits, kinetic and potential energy lost by the body can be recovered usefully by elastic structures (particularly tendons and ligaments)
