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ABSTRACT |
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 TopAbstract IntroductionMethodsResultsDiscussionReferences |
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1. The steady state rate of ATP utilisation by single permeabilised fibres from rabbit psoas muscle immersed in silicone oil was measured using a linked enzyme assay that coupled ADP production to the oxidation of NADH.
2. At sarcomere length 2.5 
m, at 10 °C, the rate of ATP utilisation in relaxing conditions was 6 ± 1 M s-1 (mean ± S.E.M., n = 8 fibres); during isometric contraction it was 310 ± 10 M s-1 (mean ± S.E.M., n = 11). Assuming a myosin active site concentration of 150 M, these values correspond to rates of ATP utilisation per active site of about 0.04 and 2.1 s-1, respectively.
3. The rate of ATP utilisation in relaxing conditions was independent of sarcomere length in the range 2.5-4.0 m. The rate of ATP utilisation during isometric contraction had a dependence on resting sarcomere length similar to that of isometric force in the range 2.5-4.0 m, but was less strongly dependent on sarcomere length than was isometric force in the range 1.5-2.5 m.
4. The rate of ATP utilisation in relaxing conditions had a Q10 of 2.5 in the temperature range 7-25 °C, but this increased to 9.7 in the range 25-35 °C, suggesting that some active force may have been generated in relaxing solution at temperatures above 25 °C.
5. The rate of ATP utilisation during isometric contraction had a Q10 of 3.6 throughout the temperature range 7-25 °C; this was similar to the Q10 for isometric force at low temperature (3.5 at 7-10 °C) but much larger than that for isometric force at higher temperature (1.3 at 20-25 °C).
6. Application of the NADH-linked assay to single muscle fibres in oil improves the effective sensitivity and time resolution of the method, and allows continuous measurements of the rate of ADP production during active contraction.
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INTRODUCTION |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Muscle contraction is powered by the free energy of ATP hydrolysis, which is converted to mechanical work by myosin and actin. According to the standard model of muscle contraction, one molecule of ATP is hydrolysed each time a myosin cross-bridge attaches to an actin filament, executes a force-generating working stroke, then detaches from the actin filament (A. F. Huxley, 1957, 1974; H. E. Huxley, 1969). This mechanical cycle is generally considered to be tightly coupled to a biochemical cycle in which ATP binds to the active site of myosin, the bond between its 
and 
phosphates is hydrolysed, and the hydrolysis products, inorganic phosphate (Pi) and ADP, are released sequentially from the active site (Lymn & Taylor, 1971; Trentham et al. 1976; Eisenberg & Greene, 1980).
Mechanical-chemical coupling in muscle has been extensively studied by mechanical measurements on demembranated fibres, in which the composition ([ATP], [ADP], [Pi], ionic strength, etc.) of the solutions bathing the myofibrils can be controlled, or rapidly perturbed by pulsed photolysis of caged precursor molecules (Hibberd & Trentham, 1986; Brenner, 1987; Goldman, 1987). These studies suggested a link between the release of Pi from the active site of myosin and the formation of a strongly bound myosin-actin complex or the execution of the working stroke in an actively contracting fibre. ADP release from the active site would subsequently permit rapid ATP binding, which weakens the binding of myosin to actin, leading to detachment and thereby permitting muscle fibre shortening (ibid.).
Efficient mechanical-chemical coupling requires a reciprocal set of relationships in which the mechanical state of the muscle influences the rates of the biochemical transitions. For example, tight coupling between detachment of myosin from actin and ADP release predicts that the rate of ADP release should be accelerated by shortening, which is expected to increase the detachment rate (Huxley, 1957). Consistent with this prediction, shortening leads to an increased rate of ATP utilisation and rate of energy liberation by muscle, the Fenn effect (Fenn, 1923). On the other hand, detailed quantitative analyses of mechanical, energetic and biochemical data suggest that the tight-coupling model may be an oversimplification, and that detachment can occur without ADP release (Cooke et al. 1994; Piazzesi & Lombardi, 1995).
Direct measurements of the rate and extent of the transitions in the actomyosin ATPase cycle in a contracting muscle fibre would seem to be required for a better understanding of the mechanism of mechanical- chemical coupling. A method for continuous measurement of Pi release in muscle fibres, using a fluorescent phosphate binding protein, was recently described (He et al. 1997, 1999). In the present work we studied ADP release in single muscle fibres using a linked-enzyme assay to couple ADP production to the oxidation of NADH, the concentration of which was measured by fluorescence. This assay has been widely used to measure ADP production in the solution bathing demembranated muscle fibres (e.g. Glyn & Sleep, 1985; Potma et al. 1994). The sensitivity and time resolution of the method were greatly improved by Stephenson et al. (1989), who immersed single fibres in silicone oil and measured NADH fluorescence from within the fibre volume. This avoids delays due to diffusion from the fibre to the bathing solution and the dilution effect of the large bath:fibre volume ratio.
Despite its apparent advantages, this technique seems to have been neglected since its original description. In the present paper we used it to measure the steady state rate of ADP production in single demembranated fibres from rabbit psoas muscle. We measured the sarcomere length and temperature dependence of this rate in relaxation and during isometric contraction. Preliminary results of this work have been presented to The Physiological Society (Hilber et al. 1999). The accompanying paper (Sun et al. 2001) describes a further development of the technique and its application to measure the extra ADP release due to active shortening.
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METHODS |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Fibre preparation and mounting
Adult New Zealand White rabbits were killed by sodium pentobarbitone injection (200 mg kg-1 I.V.). Small fibre bundles were dissected from the psoas muscle, demembranated, and stored for up to 6 weeks in relaxing solution containing 50 % (v/v) glycerol at -20 °C as described previously (Sabido-David et al. 1998). Single fibre segments 2.5-4 mm long were dissected from a bundle in the storage solution on a cooled microscope stage. The ends of the segment were held in T-shaped aluminium foil clips (Goldman & Simmons, 1984), and the regions adjacent to the clips were fixed with 0.1 % glutaraldehyde in rigor solution, to minimise end compliance (Chase & Kushmerick, 1988). Fibre segments were then mounted horizontally between a fixed hook and another hook connected to a force transducer (AE801; Aksjeselskapet Mikro-elektronikk, Horten, Norway), and immersed in relaxing solution in one of five 40 l glass troughs mounted circumferentially around a circular copper plate. The temperature of the plate was measured with a thermistor (Thermometrics, Edison, NJ, USA) and controlled within ± 0.5 °C by varying the flow of cold nitrogen or hot air onto the plate/trough assembly. The temperature of the experimental trough was determined with a small thermocouple after each measurement of ATP utilisation. Fibre dimensions at slack length were determined using the eyepiece micrometer of a stereo microscope. Fibre cross-sectional area was estimated from mean fibre diameter. Sarcomere length was measured by laser diffraction in the relaxed fibre and during activation at 10 °C at the start of each experiment. Sarcomere shortening on activation was less than 0.1 m. The solution bathing the fibre was changed in about 1 s by motorised rotation of the copper plate, combined with a synchronised vertical movement which raised the fibre from one trough and lowered it into another.
Assay for ATP utilisation and experimental solutions
The rate of ATP utilisation by the muscle fibres was measured by a NADH-linked assay (Glyn & Sleep, 1985; Stephenson et al. 1989; Potma et al. 1994), in which hydrolysis of ATP to ADP and Pi by the fibre is coupled by pyruvate kinase and lactate dehydrogenase to oxidation of NADH, as follows:
ATP  ADP + Pi,
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Phosphoenolpyruvate + ADP pyruvate + ATP,
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Pyruvate + NADH + H+ lactate + NAD+.
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All experimental solutions contained 5 mM Mg-ATP, 1 mM free Mg2+, and 25 mM imidazole, except where noted. The pH was adjusted to 7.1 at each experimental temperature. Ionic strength was adjusted to 150 mM using potassium propionate. The relaxing solution also contained 5 mM EGTA. The activating solution contained 5 mM Ca-EGTA (pCa 4.5). The pre-activating solution contained 0.2 mM EGTA. For measurements of ATP utilisation at 10 °C, the solutions also contained 250 units ml-1 pyruvate kinase (PK; Sigma, cat. no. P-9136), 250 units ml-1 lactate dehydrogenase (LDH; Sigma, cat. no. L-1254), 5 mM NADH, 10 mM phosphoenolpyruvate (PEP, trisodium salt; Sigma), and 0.1 mM P 1,P 5-di(adenosine-5') pentaphosphate (Sigma). Enzyme units refer to the manufacturer's specification for 37 °C, pH 7.5. There was no significant effect of PK and LDH concentration (250, 500 or 1000 units ml-1) on the isometric rate of ATP utilisation at 10 °C. For experiments involving activation at temperatures greater than 10 °C (Fig. 5 and 6), PK and LDH concentrations were 500 units ml-1 and [NADH] and [PEP] were 7.5 and 15 mM, respectively.
NADH fluorescence measurements
The central ca 1 mm of a muscle fibre segment was illuminated via an objective lens (Zeiss Fluar X 10, N.A. 0.50) using a Zeiss epifluorescence condenser with HBO 100 W lamp and an excitation filter of wavelength 365 nm; full width at half-maximum, 11 nm. Photobleaching was minimised by blocking the illumination by a shutter except during fluorescence recording periods. About 5 % of the excitation light was diverted to a photomultiplier (R4632; Hamamatsu Photonics K.K., Japan) for continuous measurement of its intensity. The rest of the excitation light was reflected into the objective by a 395 nm dichroic mirror. Fluorescent light collected by the objective passed through the dichroic mirror and a 420 nm long-pass barrier filter. About 10 % of this light was reflected by a pellicle beamsplitter and used to view the fibre through a X 8 eyepiece, and the remainder passed to another R4632 photomultiplier for intensity measurement. The output of this photomultiplier was divided by that from the incident light photomultiplier in order to remove fluctuations in incident light intensity. Force and fluorescence signals were recorded using a PC-based data acquisition system (AT-MIO-16E-2 card and LabVIEW 5.0; National Instruments, Austin, TX, USA) at 1 kHz sample rate.
Experimental protocols
Fibres were loaded with PK and LDH, but not NADH, for 60 min in relaxing solution. The fibre was transferred to silicone oil (Dow Corning, 10 centistokes), and background fluorescence (which was subtracted from all subsequent fluorescence measurements) was recorded. The fibre was returned to aqueous solution and incubated for about 5 min in a relaxing solution containing all the linked-assay components, including 5 mM NADH, then re-immersed in silicone oil and its fluorescence measured. This measurement was used to calibrate subsequent fluorescence changes in terms of change in NADH concentration and, stoichiometrically, ADP production by the muscle fibre. Resting ATP utilisation was routinely recorded by the method described in Fig. 1A, and subsequently subtracted from all measurements of active ATP utilisation in the presence of Ca2+.
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RESULTS |
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Continuous measurements of ATP utilisation at rest and during active contraction
Single demembranated fibres from rabbit psoas muscle were pre-incubated in NADH, phosphoenolpyruvate (PEP), pyruvate kinase (PK), and lactate dehydrogenase (LDH) in relaxing solution, then transferred to a bath of silicone oil (see Methods for details). The concentration of NADH in a central 1 mm segment of the fibre was determined from its fluorescence. In relaxing conditions NADH fluorescence decreased slowly and continuously (Fig. 1A). Part of this decrease is due to photobleaching, the effect of which was eliminated by measuring the change in NADH fluorescence during a ca 20 s period during which the illumination was blocked (between vertical arrows in Fig. 1A). The NADH concentration decreased by 7.8 ± 0.8 M s-1 (mean ± S.E.M., 8 fibres) in this period at sarcomere length 2.5 m, at 10 °C. When PEP, PK and LDH were absent, [NADH] still decreased by 2.0 ± 0.4 M s-1. This residual decrease may be due to diffusion of NADH out of the recording region, or to other reactions in the fibre that remove NADH. The difference between the rates of [NADH] decrease observed in the presence and absence of PEP, PK and LDH, 5.8 ± 0.9 M s-1, was taken as the best estimate of the rate of oxidation of NADH that is coupled to the ATP utilisation by resting fibres. Addition of 10 M cyclopiazonic acid (CPA), which inhibits the sarcoplasmic reticulum Ca2+-ATPase (Kurebayashi & Ogawa, 1991), had no significant effect on the resting rate of ATP utilisation in three fibres, showing that the measured activity is likely to be due to myosin. Assuming that the concentration of myosin heads in the fibre is 150 M, the resting rate of ATP utilisation corresponds to a turnover rate of 0.04 s-1 per myosin head.
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A, force and NADH fluorescence traces from a resting fibre immersed in silicone oil. To eliminate the effects of photobleaching, the excitation light was blocked for about 20 s (arrows), and the resting rate of ATP utilisation was calculated from the change in NADH fluorescence during this period. B, force and NADH fluorescence traces during an active isometric contraction. The fibre was maximally Ca2+ activated; after force had reached a plateau it was transferred into silicone oil, and then the shutter was opened (upwards arrow). After all the NADH had been oxidised the fibre was transferred to relaxing solution. The slopes of the dashed lines in A and B represent the rate of ATP utilisation. Temperature, 10 °C.
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When a fibre that had been loaded with the NADH assay system was Ca2+ activated, then transferred to silicone oil, NADH fluorescence decreased rapidly (Fig. 1B). In these conditions photobleaching and processes other than the linked assay that remove NADH make negligible contributions to the observed fluorescence changes. The rate of decline of NADH fluorescence remained constant during the activation while [NADH] was greater than about 0.5 mM, and the rate of ATP utilisation by the fibre was estimated by linear regression of the fluorescence trace in this period (dashed line). The force remained roughly constant during the entire period when fluorescence was measured, and the force recorded with the fibre in silicone oil was close to that observed while it was in the bath of activating solution (Fig. 1B).
The rate of ATP utilisation during isometric contraction at sarcomere length 2.5 m, at 10 °C, was 310 ± 10 M s-1 (mean ± S.E.M., 11 fibres). This corresponds to a turnover rate of 2.1 s-1 per myosin head, about 50 times that observed in the resting fibre under the same conditions.
Sarcomere length dependence of the rate of ATP utilisation
The rate of ATP utilisation by resting fibres was independent of sarcomere length in the range 2.5-4.0 m (Fig. 2A). At sarcomere length 2.5 m there should be almost complete overlap between myosin- and actin-containing filaments, whereas at 4.0 m the overlap between them should be abolished (Page & Huxley, 1963). Thus the present results show that the rate of ATP utilisation by myosin in relaxing conditions is independent of the degree of overlap between myosin and actin filaments.
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Data in A are from a randomised sequence of sarcomere lengths in fibres that had not been activated at the time of the measurement. Force data were normalised by the active isometric value at 2.5
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In contrast, the rate of ATP utilisation during isometric contraction was strongly dependent on sarcomere length in the range 2.5-4.0 m (Fig. 2B and Fig. 3). The rate of ATP utilisation at sarcomere length 4.0 m was only about 20 % of that at 2.5 m, and the dependence of the rate of ATP utilisation on sarcomere length in this range was similar to that of the isometric force. This dependence is expected if both ATP utilisation and force depend on overlap between myosin- and actin-containing filaments. A small overlap-independent component of ATP utilisation cannot be excluded by the present results, but some or all of the residual ATP utilisation observed at sarcomere length 4.0 m may be related to sarcomere length inhomogeneity.
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m, 1.5 m and 3.5 m
NADH fluorescence was recorded during consecutive isometric contractions of a single muscle fibre at three different sarcomere lengths. The fibre was transferred from activating solution into silicone oil at time zero. Sarcomere length was measured in relaxing solution.
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In the sarcomere length range 1.5-2.5 m, the rate of ATP utilisation during active contraction was less steeply dependent on sarcomere length than was the force (Fig. 2B). The rate of ATP utilisation at 1.5 m was 77 % of that at 2.5 m, whereas active force at 1.5 m was only 41 % of that at 2.5 m. Thus, on the ascending limb of the force-sarcomere length relationship, at sarcomere lengths < 2.5 m, the coupling ratio between active force and ATP utilisation is not constant, in contrast with the almost constant coupling between these quantities on the descending limb of the force-sarcomere length relationship, at sarcomere lengths > 2.5 m (Fig. 2B).
Temperature dependence of the rate of ATP utilisation
The rate of ATP utilisation in relaxing conditions increased reversibly with temperature in the range 7-35 °C (Fig. 4B). A semi-logarithmic plot of the resting rate of ATP utilisation against temperature (Fig. 4C) suggests that their relationship can be described by separating the temperature range into regions above and below 25 °C. In the range 7-25 °C, the resting rate of ATP utilisation had a Q10 of 2.5. In the range 25-35 °C, the rate of ATP utilisation in relaxing solution was much more sensitive to temperature, and the Q10 was 9.7. The force recorded in relaxing solution also increased dramatically in this temperature range (Fig. 4A), suggesting that some active force may be generated under these conditions (Ranatunga, 1994).
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Force and ATP utilisation data in A and B were binned in temperature ranges 6.5-12.5, 12.5-17.5, 17.5-22.5, 22.5-27.5, 27.5-32.5 and 32.5-37.5 °C. The data are means ± S.E.M. from 13-19 measurements in six fibres. ATP utilisation data from individual fibres are plotted with different symbols on a logarithmic scale in C, together with linear fits to the data in the regions above and below 25 °C. Sarcomere length, 2.5
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The rate of ATP utilisation during maximal Ca2+ activation was also strongly dependent on temperature in the range 7-25 °C (Fig. 5 and Fig. 6), and these data were accurately described by a Q10 value of 3.6 over the entire temperature range studied (Fig. 6D). The rate of ATP utilisation was much more temperature sensitive than the active force (Fig. 6C and A, respectively), but the force data could not be described by a single Q10 value. Q10 values for force in the temperature ranges 7-10, 10-15, 15-20 and 20-25 °C were estimated from quadratic fits of the force-temperature data from each fibre, as 3.5 ± 0.7, 2.3 ± 0.2, 1.7 ± 0.1 and 1.3 ± 0.1 (means ± S.E.M., n = 5), respectively. Thus at low temperature (< 10 °C) force and ATP utilisation had a similar Q10, but there was a progressive discrepancy as temperature was increased.
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The fibre was immersed in silicone oil at time zero. Sarcomere length, 2.5
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A and C, force and rate of ATP utilisation, respectively, grouped in temperature ranges 6.5-12.5, 12.5-17.5, 17.5-22.5 and 22.5-27.5 °C. The data are means ± S.E.M. from 11-15 measurements in five fibres. B and D, force and the rate of ATP utilisation, respectively, on a logarithmic scale with individual fibres plotted with different symbols. In four of the fibres the sequence of observations was low to high to low temperature; in the other (
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The relationship between active force and temperature appeared to be completely reversible in the temperature range 7-20 °C, but after either one or two activations at higher temperatures (24-28 °C) active force declined by 24 ± 9 % (mean ± S.E.M., n = 5). The extent of force loss varied between fibres, and two out of the five fibres studied with this protocol showed no significant force decrease. In all fibres activation at 24-28 °C had no effect on the rate of ATP utilisation during subsequent activations at lower temperatures; the average decrease in the rate of ATP utilisation was 3 ± 8 % (n = 5). Thus the estimate of Q10 for ATP utilisation is not affected by the irreversible force loss in activations at the higher temperatures. Q10 for the active force was also unaffected; in the temperature range 15-20 °C, for example, Q10 for the active force before activation at 24-28 °C was 1.7 ± 0.1 (mean ± S.E.M., n = 5); afterwards it was 1.9 ± 0.1.
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DISCUSSION |
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ATP utilisation in relaxing conditions
The rate of ATP utilisation by rabbit psoas fibres in relaxing conditions was estimated as about 6 M s-1 at 10 °C after correction for the effects of photobleaching and processes other than the linked assay which remove NADH from the recording region (Fig. 1A). ATP utilisation by relaxed fibres was unaffected by inhibition of the sarcoplasmic reticulum Ca2+-ATPase, and its most likely origin is the myosin ATPase. Assuming a myosin active site concentration of 150 M, the observed rate corresponds to 0.04 s-1 per active site. The corresponding rate at 20 °C was 0.10 s-1 per active site (Fig. 4), which is close to the value reported using a phosphate binding protein, 0.11 s-1 per active site at 20 °C (He et al. 1997). These rates are also close to those reported for isolated myosin subfragment-1, the head domain of myosin that contains the active site, and for suspensions of myofibrils from rabbit psoas muscle in similar solutions at 20 °C, 0.08 and 0.07 s-1 per active site, respectively (Herrmann et al. 1992, 1994). The Q10 for the steady state ATPase activity of these two preparations, 2.4 (calculated from Fig. 6 of Herrmann et al. 1992) is similar to that, 2.5, observed here for the temperature range 7-25 °C (Fig. 4C).
These comparisons suggest that the ATP utilisation in relaxed demembranated muscle fibres is predominantly due to the myosin ATPase. However, contributions from other ATPases, or more likely from a population of myosin heads that utilise ATP more rapidly because of loss or proteolysis of some of the regulatory proteins, cannot be excluded. Support for this possibility comes from measurements of the rate of release of bound ADP from relaxed myofibrils using a fluorescent ATP analogue, which was only 0.03 s-1 per active site at 25 °C (Myburgh et al. 1995). The steady state rate of ATP utilisation measured in relaxed demembranated muscle fibres should probably be considered as an upper limit for the rate of ATP utilisation by native myosin in resting intact muscle.
ATP utilisation in relaxed fibres was independent of sarcomere length in the range 2.5-4.0 m (Fig. 2A). Thus there was no detectable effect of overlap between myosin and actin filaments on the rate of ATP utilisation in relaxing conditions at 0.15 M ionic strength, in which conditions little actin-myosin interaction is expected. There was also no sign of the enhanced ATP utilisation at long sarcomere length that might be expected from the so-called Feng effect (Feng, 1932; Clinch, 1968), the increase in resting heat production seen on stretch of some frog muscles. The absence of such an effect in the present experiments suggests that the Feng effect is either not present in rabbit psoas muscle, or requires the presence of an intact sarcolemma or sarcoplasmic reticulum.
Increasing the temperature of relaxed fibres above 25 °C produced a dramatic increase in the rate of ATP utilisation (Fig. 4B and C), and the force measured in relaxing solution also increased (Fig. 4A). The latter phenomenon has been interpreted in terms of a population of actively cycling cross-bridges resulting from Ca2+-independent activation of the actin-containing filaments in this temperature range (Ranatunga, 1994). The increased rate of ATP utilisation provides general support for this interpretation, but the fraction of actively cycling cross-bridges could be very small. The force in relaxing solution at 35 °C, about 0.5 N cm-2 (Fig. 4A), was less than 2 % of that in activating conditions at 25 °C (the highest temperature studied in activating conditions, Fig. 6A), and the rate of ATP utilisation in relaxing conditions at 35 °C is only about 5 % of that expected in activating conditions at the same temperature (Fig. 6).
If the rate of ATP utilisation in relaxing conditions (Fig. 4C) were extrapolated to the physiological temperature of 39 °C for rabbits, it would correspond to 6 s-1 per active site. Considerations of resting metabolic rate make it very unlikely that such a high rate could occur in resting muscles in vivo (Myburgh et al. 1995). This suggests that the physiological regulatory mechanism has not been completely preserved in the demembranated rabbit psoas muscle fibre preparation.
ATP utilisation during isometric contraction
The steady state rate of ATP utilisation during isometric contraction was about 50 times faster than that observed in relaxing conditions (Fig. 1). The isometric rate of ATP utilisation was reduced at sarcomere lengths greater than the optimal for isometric force production, 2.5 m (Fig. 2B). In the sarcomere length range 2.5-4 m, the rate of ATP utilisation during isometric contraction decreased linearly with increasing sarcomere length, like the isometric force, as shown previously in rat and toad fibres (Stephenson et al. 1989). The decrease is expected from the smaller fraction of myosin cross-bridges that can interact with actin when the overlap between myosin and actin filaments is reduced, and shows that ATP utilisation during isometric contraction is predominantly due to the interaction of myosin cross-bridges with actin filaments. Less than 20 % of the maximum isometric ATP utilisation and active force remained at sarcomere length 4.0 m, where overlap between myosin and actin filaments should be abolished (Page & Huxley, 1963), but this may be due to residual overlap in a small fraction of sarcomeres as a result of sarcomere length non-uniformity.
At sarcomere lengths less than the optimal for isometric force, the rate of ATP utilisation was smaller at shorter sarcomere lengths (Fig. 2B). This effect was not seen in demembranated fibres from rat extensor digitorum longus muscle in the same sarcomere length range (Stephenson et al. 1989), but has been observed in skinned cardiac muscle preparations (Kentish & Stienen, 1994). The isometric rate of heat production increases with increasing sarcomere length in this range in some fast muscles of the frog but not in others (Elzinga et al. 1984). Thus the relationship between isometric ATP utilisation and sarcomere length at lengths below the optimal for isometric force seems to vary between muscle types, for unknown reasons. On the other hand, in all these studies, the force was more sensitive to sarcomere length in this range than was the rate of ATP utilisation (Fig. 2B). Thus, in addition to the decreased rate of cross-bridge cycling at shorter sarcomere lengths evidenced by the lower rate of ATP utilisation in some preparations, there is a more general mechanism which reduces force more than ATP utilisation. This may be due to opposing forces associated with filament compression or with other myofibrillar proteins, or to the double overlap of actin filaments at sarcomere lengths less than 2.0 m, which would lead to interactions between myosin cross-bridges and actin filaments of the wrong polarity. Such interactions may utilise ATP but not contribute to force generation.
At sarcomere length 2.5 m the rate of ATP utilisation during isometric contraction can be considered to arise from myosin cross-bridges interacting with correctly oriented and fully activated actin filaments. The steady state rate of ATP utilisation at 10 °C was 310 ± 10 M s-1, corresponding to 2.1 s-1 per active site assuming the concentration of the latter to be 150 M. In the temperature range 7-25 °C, the rate was accurately described by a Q10 of 3.6 (Fig. 6D). This relationship can be used to compare the present results with those of previous measurements of the steady state rate of ATP utilisation based on NADH oxidation in the solution bathing rabbit psoas fibres at various experimental temperatures. Thus Brenner (1988) reported 1.0 s-1 per active site at 5 °C (cf. 0.9 s-1 from Fig. 6D), Glyn & Sleep (1985) and Potma et al. (1994) reported 1.8 s-1 and 2.3 s-1, respectively, at 15 °C (cf. 3.1 s-1 from Fig. 6D) and Kawai et al. (1990) reported 3.6 s-1 at 20 °C (cf. 5.9 s-1 from Fig. 6D). The agreement between the present and previous results is reasonably good, but the present method measures higher rates of ATP utilisation at the higher temperatures studied. Consistent with this, the Q10 found here, 3.6 (Fig. 6D), is higher than values based on NADH oxidation in the bathing solution of about 2 in the range 10-30 °C in rabbit psoas fibres (Zhao & Kawai, 1994), and 2.6 in the range 12-30 °C in skinned fibres from human muscle (Stienen et al. 1996). The lower values of Q10 and of the rate of ATP utilisation at higher temperatures in the previous experiments may be due to diffusion of NADH into the fibre becoming rate limiting. This limitation is avoided by measuring [NADH] within the fibre volume, as in the present experiments. Extrapolation of the present data to 39 °C, the physiological temperature for rabbits, predicts a rate of ATP utilisation during isometric contraction of 67 s-1 per active site.
The steady state rate of ATP utilisation measured here (5.9 s-1 at 20 °C; Fig. 6D) is much lower than the initial rate following release of ATP from caged ATP measured using a phosphate binding protein, 41 s-1 (He et al. 1997, 1998). The rate of ATP utilisation in those experiments progressively decreased after ATP release, but the steady state rate could not be measured because of saturation of the phosphate binding protein. The rate of ATP utilisation in the period from 0.3 to 1.5 s after release of tritiated ATP from caged [3H]ATP was measured by rapid freezing and analysis of [3H]ADP in fibre extracts as 1.9 s-1 per active site at 12 °C (Ferenczi et al. 1984; Ferenczi, 1986), similar to the value estimated here for this temperature, 2.1 s-1 (Fig. 6D). The cause of the progressive decrease in the rate of ATP utilisation after release of ATP from caged ATP is unknown, although accumulation of ADP (He et al. 1998) and transient shortening during the initial period when the rate of ATP utilisation is high (He et al. 1999) may contribute.
It is instructive to compare the rate of ATP utilisation of isometrically contracting muscle fibres with the ATPase properties of purified myosin and actin in solution (Brenner, 1987; Goldman, 1987). The comparison is complicated, however, by the fact that myosin and actin are largely dissociated at experimentally accessible actin concentrations in solutions of physiological ionic strength. One approach to this problem is to use myosin subfragment-1 (the myosin head domain, subfragment-1 or S-1) which has been chemically cross-linked to actin. At 4-5 °C the steady state rate of ATP utilisation per active site (kcat) for cross-linked acto-S-1 in solutions similar to those used here is 1.1-1.8 s-1 (Brenner & Eisenberg, 1986; Herrmann et al. 1994), similar or up to 2 times larger than the steady rate of ATP utilisation in muscle fibres, 0.9 s-1 (Fig. 6D). There is a clearer discrepancy at higher temperatures: kcat for cross-linked acto-S-1 is 15 s-1 at 20 °C (Herrmann et al. 1994), cf. 5.9 s-1 in fibres (Fig. 6D), and 49 s-1 at 25 °C (Brenner & Eisenberg, 1986), cf. 11.2 s-1 in fibres (Fig. 6D). Q10 for kcat of cross-linked acto-S-1 is 4.5-5.9 (Brenner & Eisenberg, 1986; Herrmann et al. 1994), which is higher than that for the steady state rate of ATP utilisation in an isometrically contracting muscle fibre, 3.6 (Fig. 6D).
These differences have been widely interpreted as showing that the rate-limiting step of the acto-myosin ATPase is different in solution and in an isometrically contracting muscle fibre. The rate-limiting step in solution under conditions that promote a high degree of association of myosin and actin is likely to be the ATP cleavage step (Rosenfeld & Taylor, 1984; White et al. 1997), whereas the rate-limiting step in an isometric fibre may be ADP release or an adjacent isomerisation (Hibberd & Trentham, 1986; Goldman, 1987; Brenner, 1987). The slower rate of the latter transition in an isometric fibre could be explained as a consequence of mechanical strain in the myosin head; this would be absent in solution, leading to a greater rate of ADP release, which might no longer be rate limiting. This general scheme could also explain the higher isometric tension generated at higher temperatures (Fig. 6A); if the ATP cleavage step has a higher Q10 than the ADP release step, as suggested by the comparison of the Q10 values for the rate-limiting steps in solution and in isometrically contracting fibres, a higher fraction of the myosin heads would be expected to be in the force-generating product-bound states at higher temperatures.
These arguments based on the comparison between ATPase rates in an isometric fibre and in cross-linked acto-S-1 in solution have two general weaknesses. First, cross-linked acto-S-1 may not be a good model for the ATPase activity of native myosin heads in a muscle fibre, so direct comparison of the absolute rates may be misleading. Second, in converting the rates of ATP utilisation measured in the fibre into 'per active site' units for comparison with solution data it was implicitly assumed that all the myosin heads in the muscle fibre (total concentration 150 M) can contribute to ATP utilisation during isometric contraction. If some of the heads cannot do so, for example if the two heads of one myosin molecule are not simultaneously active, or because of steric constraints associated with the actin-myosin filament lattice, the turnover rates per active myosin head during isometric contraction would have been underestimated. Since the discrepancy between the rate of ATP utilisation in the fibre based on 100 % active heads and kcat of cross-linked acto-S-1 in the same ionic conditions and in the temperature range 5-25 °C is only a factor of 2-4, these two factors could have a significant effect on the comparison.
The method applied here to measure the rate of ATP utilisation in muscle fibres, using the NADH-linked assay with fibres immersed in silicone oil (Stephenson et al. 1989), has some advantages over other available methods. NADH concentrations of the order of 10 mM can be used, giving sufficient time for the establishment of the steady state without significant substrate depletion or indicator saturation (which limits experiments with the phosphate binding protein). The solution conditions of the NADH-linked assay are close to physiological, and the assay acts as an ATP regenerating system, keeping the [ADP] within the fibre low and substituting in this respect for the physiological action of creatine kinase. Again this contrasts with the phosphate binding protein assay, in which ADP accumulates but [Pi] is held at unphysiologically low levels.
Two potential limitations of the NADH-linked assay method applied to fibres immersed in oil are the progressive build-up of Pi within the fibre, and the possibility that the pyruvate kinase and lactate dehydrogenase reactions fail to keep up with the rate of ADP production. [Pi] could increase by as much as 7.5 mM during the present measurements; this could depress the active force, but is unlikely to produce significant errors in the rate of ATP utilisation, which is almost unaffected by 30 mM Pi (Potma & Stienen, 1996; He et al. 1997). Three lines of evidence show that the NADH-linked assay is fast enough to accurately report the rate of ATP utilisation observed during isometric contraction. First, increasing the enzyme concentrations by a factor of four had no effect on the measured rates (see Methods). Second, a rate of ATP utilisation about 10 times faster than the isometric rates found here is reported by the NADH-linked assay method during rapid shortening (Sun et al. 2001). Third, cuvette assays of the pyruvate kinase and lactate dehydrogenase used in the fibre experiments (He et al. 1997; Sun et al. 2001) showed that the maximum turnover rates of both enzymes are greater than the rates of ATP utilisation reported in the present experiments.
We conclude that the application of the NADH-linked assay to fibres immersed in silicone oil gives an accurate and versatile measure of the steady state rate of ATP utilisation by demembranated muscle fibres. In the following paper (Sun et al. 2001) this approach is used to characterise the rate of ATP utilisation during active shortening.
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Acknowledgements
This work was supported by the Wellcome Trust, UK. K.H. was supported by a fellowship (J1504-BIO) from FWF, Austria. We thank Dr J. Sleep for advice on the NADH-linked assay and for helpful comments on the manuscript.
Corresponding author
M. Irving: School of Biomedical Sciences, King's College London, New Hunt's House, Guy's Campus, London SE1 1UL, UK.
Email: malcolm.irving{at}kcl.ac.uk
Author's present address
K. Hilber: Institut für Pharmakologie, Universität Wien, Währingerstrasse 13A, A-1090 Vienna, Austria.
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) and rate of ATP utilisation (
) were normalised by the corresponding values at sarcomere length 2.5