The efficiency of contraction in rabbit skeletal muscle fibres ...

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852 than the actual ATPase rate in the first turnover (10·7 s¢) for these same 29 experiments. As reported earlier, some shortening does take place in the period immediately prior to the period of applied shortening, with a mean shortening velocity of 0·05 ML s¢. If the muscle fibres were extended at this velocity during this period, sarcomere shortening would be abolished. Hence, the measured ATPase activity of 5·1 s¢ for nominally isometric fibres corresponds to shortening at 0·05 ML s¢, but extrapolation of the hyperbola in Fig. 8to an extension velocity of 0·05 ML s¢ results in an ATPase activity of 3·1 s¢. This latter value may be the true isometric ATPase. If this were the case, the acceleration of the ATPase activity of isometric muscle fibres produced by shortening would increase from a factor of 3·7 (18·7Ï5·1) to 6·0 (18·7Ï3·1). The period immediately prior to the period of applied shortening, which in most cases was set at 0·4 s after photolysis, is that which most closely resembles the steady, isometric state because Pé release and force levels are relatively constant at this time. We use the term isometric to describe this phase, but the slow shortening which we observe shows that this isometric phase is not truly a steady state. The ATPase rate during the first turnover was typically twice as high as that in this isometric phase (for 41 experiments the ratio was 2·06 ± 0·06). The ATPase rate constant in the first turnover is about half the ATPase rate constant measured at the maximal shortening velocity (10·3 vs. 18·5 s¢ for 41 measurements) and is not fully accounted for by initial sarcomere shortening, suggesting that the mechanism underlying the initial ATPase rate is not equivalent to that responsible for the acceleration of the ATPase during shortening at a constant velocity. The initial ATPase rate accompanies a period of rapid force development. A similar rapid rise in force is seen at the end of the period of rapid shortening, but here the ATPase rate is slower than during the shortening phase or than during the initial phase of contraction. Instead, at the end of the shortening phase the ATPase rate is similar to the slower rate seen immediately prior to the period of applied shortening (Figs 1, 2 and 5). As discussed in He et al. (1997) a change in the distribution of force-generating states during the first seconds of activation probably accounts for the change from the high initial ATPase to that seen 0·4 s after photolytic release of ATP. In the isometric phase immediately prior to the period of applied shortening, the ATPase rate constant measured here (5·0 s¢) is 2—5 times faster than that measured by others, e.g. 1·27 s¢ in the presence of 3 mÒ Pé at 10 °C (Cooke et al. 1988), 1·8 s¢ at 15 °C (Glyn & Sleep, 1985) and 2·1 s¢ at 15 °C (Potma & Stienen, 1996). As discussed by He et al. (1997), this discrepancy may arise from the different time scales in the experiments or from methodological limitations of the linked assay system, and is unlikely to be caused by Z.-H. He and others Downloaded from J Physiol ( jp.physoc.org) by guest on March 5, 2013 J. Physiol. 517.3 the slow shortening which we observed at this time. Such shortening probably also occurred in the work cited. The ATPase rate constant during shortening near Vmax is 3—4 times higher than that immediately prior to the period of applied shortening (5·0 vs. 18·5 s¢), similar to the 2·7fold increase in ATPase caused by shortening seen by Potma & Stienen (1996) in rabbit psoas fibres at 15 °C using the NADH-linked assay, although these authors obtained absolute values for the ATPase rate constants in isometric and shortening muscle fibres which were approximately 3_fold lower than the values found here. Curvature of the force—velocity relationship The curvature of the force—velocity relationship is well described by the value for aÏPï, although combinations of thevaluesfor(f1 + g1)orforgµ also describe it (Simmons & Jewell, 1974). The value for aÏPï of 0·42 is higher (force—velocity relationship is less curved), and Vmax is lower than that found by others under similar conditions. For example Cooke et al. (1988) obtained 0·23 and 1·6 ML s¢ for aÏPï andVmax, respectively, at 10 °C and Sweeney et al. (1988) obtained Vmax of 2·1 ML s¢ at 12 °C for muscle fibres of the same type. Binding of NPE-caged ATP to muscle fibres was found to reduce the maximal shortening velocity of rabbit fibres at 20 °C for ATP concentrations of 1 mÒ or less (Thirlwell et al. 1995). The 3·5 mÒ NPE-caged ATP present in the fibres following the laser flash is likely to cause our measurement of maximal shortening velocity to be lower than if it was carried out in the absence of NPE-caged ATP. It is also the most likely explanation for the high value for aÏPï found herecomparedwiththatintheliterature.Usingthesame preparation at 10 °C and the same technique, He et al. (1998a) obtained a value for aÏPï of 0·12, lower than the value obtained here because in He et al. (1998a) few data points were obtained at high shortening velocities, resulting in a larger value for Vmax obtained by extrapolation (1·45 ML s¢), and because the initial sarcomere length was 3·0 ìm, where resting tension contributes to the restoring force during shortening. Adifferencebetweenourworkandthatofothersisthat here the presence of MDCC-PBP results in a low concentration of Pé during the measurements (< 1 ìÒ). However, Cooke et al. (1988) showed that in the concentration range 3—20 mÒ,PédidnotalteraÏPïorVmax, althoughaneffectofPéonaÏPï andVmax is possible at Pé
J. Physiol. 517.3 Efficiency of muscle contraction 853 in rat fast muscle fibres (9·6 W l¢; Reggiani et al. 1997) or in human type IIB fibres (3·5 W l¢; Bottinelli et al. 1996). Potma & Stienen (1996) measured •20 W l¢ at a shortening velocity of 1 ML s¢ and 15 °C, although these authors did not show that this is maximal because no data were obtained for higher shortening velocities. The high power output obtained here results from the relatively linear force—velocity relationship: at intermediate shortening velocities, force is 2—3 times higher than in other studies. Maximal power output is temperature and species dependent so that the variations in power output measurements found in the literature are not surprising. For example, Ranatunga (1998) found that at 35 °C, power output of fast muscle fibres of the rat was 250 W l¢, dropping to less than 13 W l¢ at 10 °C, with a QÔÑ in the 5—7 range below 20 °C. The efficiency of contraction obtained here reached 0·36 (interpolation in Fig. 9). As power output is more temperature sensitive than the ATPase (Ranatunga, 1998), it is expected that the efficiency will increase with increasing temperature. In this calculation, the energy input includes the ATP hydrolysed to maintain the isometric state. The relationship between efficiency and speed of contraction is very similar to that obtained in intact frog muscle shortening at 0 °C (Fig. 4.38A in Woledge et al. 1985), even though the ATP cleavage in frog muscle includes that required for pumping calcium into the sarcoplasmic reticulum. Potma & Stienen (1996) obtained a value of 0·25, but these authors did not investigate shortening at velocities higher than 1 ML s¢. Reggiani et al. (1997) reported a value of 0·28. The experimental conditions differ mainly in the animal used (rabbit vs. rat) and in the concentration of Pé in the solution. In our work the Pé concentration was very low (< 1 ìÒ) because of its binding to MDCC-PBP, whereas in the work of Reggiani et al. and of Potma & Stienen, it would have been in the millimolar range. Power output and ATPase activity during shortening have been shown to be modulated by free Pé concentration (Potma & Stienen, 1996). These authors found that in rabbit psoas muscle fibres at 15 °C, the power output and ATP turnover rate decreased at low shortening velocities when 30 mÒ Pé was added to the solutions. The high force at shortening velocities where power output is maximal is accompanied by a high ATPase rate so that the ratio of power output to energy consumed remains close to that found elsewhere. The slightly higher efficiency (0·4) reported by He et al. (1998a) is a consequence of the passive, restoring force encountered for muscle fibres shortening from an initial sarcomere length of 3·0 ìm. Step size, duty ratio and myosin head interaction distance with actin The maximum ATPase rate of 18·5 s¢ at 12 °C is comparable to that obtained by Ma & Taylor (1994) in shortening myofibrils of rabbit psoas muscle at 20 °C (22 s¢), but faster than their value at 10 °C (6·5 s¢). The direct measurement of the ATPase in shortening muscle fibres obtained here can Downloaded from J Physiol ( jp.physoc.org) by guest on March 5, 2013 be used to estimate the distance travelled by myosin heads for each ATP hydrolysed. At Vmax, assuming that all myosin heads in the overlap region are active, namely participating equally in the hydrolysis, the distance travelled per ATP for each sarcomere, d, isgivenbyd = VÏk where V is the shortening velocity (in nm s¢) and k is the maximum myosin head cycling rate (18·5 s¢). For Vmax = 1·21 ML s¢ at 12°C and a sarcomere length of 2·7 ìm, each half-sarcomere shortens at 1633 nm s¢, giving a myosin head travel distance of 88·3 nm per ATP (1633Ï18·5). For a step size of 9 nm (mid-range of Goldman & A. F. Huxley, 1994), myosin heads may only remain attached to actin for 10 % of their cycle time (9Ï88·3) (cf. duty cycle ratio of 0·2; Ma & Taylor, 1994). This number is in agreement with stiffness measurements (Ford et al. 1985), X-ray diffraction data (Yagi & Takemori, 1995) and kinetic measurements (Brenner, 1988; Ma & Taylor, 1994), which suggest that, during shortening, the fraction of attached myosin heads at any one time is low. The ATPase rate is seen to increase continuously with shortening velocity (Fig. 8), even though the number of attached myosin heads is decreasing. If shortening reduces the number of participating myosin heads, the ATPase activity of the active fraction is proportionally greater. It is more likely that all myosin heads participate in shortening, and that the rate limiting step in the ATPase during shortening is the hydrolysis step which occurs while the myosin heads are detached from the thin filament. In the isometric state, the rate limiting step is the release of hydrolysis products (ADP or Pé), with rate constants which may depend on the strain experienced by the myosin heads (Homsher et al. 1997). The calculations made here are based on the results of simultaneous measurements of sarcomere shortening velocity, force, power output and ATPase rate in contracting muscle fibres. These values provide a consistent data set for calculating the energetics of contraction and to test our understanding of energy transduction in muscle. Bershitsky, S., Tsaturyan, A., Bershitskaya, O., Mashanov, G., Brown, P., Webb, M. & Ferenczi, M. A. (1996). Mechanical and structural properties underlying contraction of skeletal muscle fibers after partial EDC cross-linking. Biophysical Journal 71, 1462—1474. Blinks, J. R. (1965). Influence of osmotic strength on cross-section and volume of isolated single muscle fibres. Journal of Physiology 177, 42—57. Bottinelli, R., Canepari, M., Pellegrino, M. A. & Reggiani, C. (1996). Force—velocity properties of human skeletal muscle fibres: myosin heavy chain isoform and temperature dependence. Journal of Physiology 495, 573—586. Brenner, B. (1988). Effect of Ca¥ on cross-bridge turnover kinetics in skinned single rabbit psoas fibers: implications for regulation of muscle contraction. Proceedings of the National Academy of Sciences of the USA 85, 3265—3269.
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