Skip to main content
NCBI home page
The Journal of Physiology logoLink to The Journal of Physiology
. 2001 Mar 15;531(Pt 3):781–791. doi: 10.1111/j.1469-7793.2001.0781h.x

Effect of active shortening on the rate of ATP utilisation by rabbit psoas muscle fibres

Y-B Sun 1, K Hilber 1, M Irving 1
PMCID: PMC2278485  PMID: 11251058

Abstract

  1. The rate of ATP utilisation during active shortening of single skinned fibres from rabbit psoas muscle at 10 °C was measured using an NADH-linked assay. Fibres were immersed in silicone oil and illuminated with 365 nm light. The amounts of NADH and carboxytetramethylrhodamine (CTMR) in the illuminated region of the fibre were measured simultaneously from fluorescence emission at 425–475 and 570–650 nm, respectively. The ratio of these two signals was used to determine the intracellular concentration of NADH, and thus the ATP utilisation, without interference from movements of the fibre with respect to the measuring light beam.

  2. The total extra ATP utilisation due to shortening (ΔATP) was determined by extrapolation of the steady isometric rates before and after shortening to the mid-point of the shortening period. ΔATP had a roughly linear dependence on the extent of shortening in the range 1–15% fibre length (L0) at a shortening velocity of 0.4 L0 s−1 from initial sarcomere length 2.7 μm. For shortening of 1%L0, ΔATP was 21 ± 1 μm (mean ±s.e.m., n = 3).

  3. The mean rate of ATP utilisation during ramp shortening of 10%L0 had a roughly linear dependence on shortening velocity in the range 0.05–1.2 L0 s−1. During unloaded shortening at 1.2 L0 s−1 the mean rate of ATP utilisation was 1.7 mm s−1, about 9 times the isometric rate. ΔATP was roughly independent of shortening velocity, and was 84 ± 9 μm (mean ±s.e.m., n = 6) for shortening of 10%L0.

  4. The implications of these results for mechanical-chemical coupling in muscle are discussed. The total ATP utilisation associated with shortening of 1%L0 is only about 17% of the concentration of the myosin heads in the fibre, suggesting that during isometric contraction either less than 17% of the myosin heads are attached to actin, or that heads can detach without commitment to ATP splitting. The fraction of myosin heads attached to actin during unloaded shortening is estimated from the rate of ATP utilisation to be less than 7%.

The preceding paper (Hilber et al. 2001) described measurements of the steady state rate of ATP utilisation during isometric contraction of skeletal muscle fibres, and its dependence on sarcomere length and temperature. Isometric ATP utilisation represents the metabolic cost of maintaining the isometric tension. No external work is done under these conditions, and the energy produced by ATP splitting is all liberated as heat.

In the present paper we describe the effect of active shortening on the rate of ATP utilisation. During active shortening part of the free energy from ATP splitting is converted by the muscle into mechanical work, and an analysis of how work production is related to the rate of ATP utilisation is central to understanding the mechanism of mechanical-chemical coupling in muscle. We made continuous measurements of ATP utilisation during shortening of single demembranated fibres from rabbit psoas muscle using an NADH-linked fluorescence assay applied to fibres immersed in silicone oil (Stephenson et al. 1989). This approach allows ATP utilisation to be measured with high sensitivity and time resolution within the fibre volume (Hilber et al. 2001). However, its application to shortening muscle presents a technical challenge, because shortening leads to an increase in the number of sarcomeres in the measuring light beam, producing an artefactual increase in NADH fluorescence. We overcame this problem by including a second fluorometric indicator, carboxytetramethylrhodamine (CTMR), in the intracellular solutions. CTMR can be excited at the same wavelength as NADH, but fluoresces at a longer wavelength. By simultaneously recording fluorescence from NADH and CTMR, effects due to changes in the number of sarcomeres in the measuring light beam can be eliminated, and the change in NADH concentration due to ATP utilisation can be accurately determined.

Some preliminary results of these experiments have been presented (Sun et al. 1999a, b).

METHODS

Demembranated fibres from rabbit psoas muscle were prepared, stored and mounted as described in the previous paper (Hilber et al. 2001); adult New Zealand White rabbits were killed by sodium pentobarbitone injection (200 mg kg−1i.v.). The end regions of the fibres were fixed with glutaraldehyde to reduce end compliance (Chase & Kushmerick, 1988); the length of the unfixed region was 2.3-3.0 mm. Fibre segments were attached via aluminium T-clips to a force transducer (AE801; Aksjeselskapet Mikro-elektronikk, Horten, Norway) at one end, and to a loudspeaker-type motor constructed by Professor V. Lombardi (Lombardi & Piazzesi, 1990) at the other end. The sarcomere length was measured by laser diffraction and set to 2.7 μm in relaxing solution. The experimental temperature was 10.0 ± 0.5 °C.

The experimental solutions were also as specified in the previous paper (Hilber et al. 2001), except that the NADH assay solutions contained additionally 0.2 mm carboxytetramethylrhodamine (CTMR; C-300, Molecular Probes, Eugene, OR, USA). All measurements of ATP utilisation were made using 1000-1500 units ml−1 pyruvate kinase (PK; Sigma, cat. no. P-9136) and lactate dehydrogenase (LDH; Sigma, cat. no. L-1254), 7.5 mm NADH and 15 mm phosphoenolpyruvate (Sigma). Enzyme units refer to the manufacturer's specification for pH 7.5 and 37 °C. The activities of the PK and LDH used in the present experiments were measured at 10 °C, pH 7.1 by monitoring absorbance at 340 nm in a cuvette containing 125 μm NADH, 50 mm imidazole, and 10 mm potassium propionate. For the PK assay, 0.12 units ml−1 PK and 12 units ml−1 LDH, 1 mm phosphoenolpyruvate and 10 mm MgCl2 were added to the cuvette, and the PK reaction was initiated by adding 1 mm ADP. PK activity in these conditions was 12.5% of the manufacturer's specification for 37 °C, pH 7.5. LDH activity at 10 °C, pH 7.1, measured at 0.24 units ml−1 with 5 mm pyruvate, was 22% of the value specified for 37 °C, pH 7.5.

The fluorescence from NADH and CTMR in muscle fibres was measured using a modified Zeiss epifluorescence microscope (Fig. 1) with HBO 100 W lamp controlled by an AttoArc adjustable power unit (Zeiss no. 4191759042). The excitation light passed through a slit aperture and 365 nm interference filter; full width at half-maximum (FWHM) 11 nm. The intensity of the excitation light was monitored by reflecting about 5% of the illumination to a photomultiplier (R4632; Hamamatsu Photonics K.K., Japan), and this signal was used to correct for fluctuations in incident light intensity. The rest of the excitation light was reflected by a 395 nm dichroic mirror through an objective lens (Zeiss Fluar x 10, N.A. 0.50) to illuminate a 0.5-0.8 mm region of the fibre segment, normally chosen between the centre of the segment and the force transducer end. Fluorescent light was collected by the same objective lens, and passed through the 395 nm dichroic mirror and 420 nm long-pass barrier filter. A pellicle beamsplitter was used to view fibre fluorescence via a x 8 ocular. The rest of the fluorescent light was further separated by a 480 nm dichroic mirror. The reflected component passing through a 450 nm interference filter (50 nm FWHM) is due to NADH fluorescence, and the transmitted component passing through a 610 nm interference filter (75 nm FWHM) is mainly due to CTMR fluorescence (Fig. 1, inset). The intensities of these two components were measured with R4632 photomultipliers. The optical signals, force and motor position were filtered with 8-pole 500 Hz Bessel filters and sampled at 1 kHz by a PC-based data acquisition system (AT-MIO-16E-2 DAQ board and LabVIEW software; National Instruments, Austin, TX, USA).

Figure 1. Experimental set-up for simultaneous measurement of NADH and CTMR fluorescence.

Figure 1

Open in a new tab

See text for details. The inset shows normalised fluorescence emission spectra of 0.2 mm NADH and 0.2 μm CTMR in 10 mm imidazole, 2.5 mm EGTA, 1 mm MgCl2, ionic strength 150 mm, pH 6.8, 25 °C, measured in a 1 cm cuvette with 365 nm excitation.

Fibres were incubated for 60 min in a relaxing solution containing pyruvate kinase, lactate dehydrogenase and phosphoenolpyruvate (Hilber et al. 2001). Background fluorescence was measured in the NADH and CTMR channels for subtraction from subsequent measurements. The fibres were bathed in the same solution plus 7.5 mm NADH for about 5 min, and fluorescence was measured in both channels again. The NADH emission spectrum is broad (Fig. 1, inset), so some NADH fluorescence is recorded in the CTMR channel. With the standard photomultiplier voltages used during these experiments (800 and 750 V for the NADH and CTMR channels, respectively), the ratio (C) of the NADH fluorescence recorded in the CTMR channel to that in the NADH channel was 0.115 ± 0.002 in 19 fibres. CTMR (0.2 mm) was added to the solution bathing the fibres, and the fibres were incubated in this solution for 5 min before measurements of ATP utilisation.

Experimental protocols for measuring ATP utilisation during active contraction were as described previously (Hilber et al. 2001), but extra precautions were taken in order to avoid potential artefacts due to fibre movement. Fluorescence was recorded from a clean and uniform region of the fibre. Immediately before transfer to the trough containing silicone oil, the motorised trough changer was used to lightly blot the actively contracting fibre onto a small piece of filter paper that had been soaked in activating solution. This procedure prevented small droplets of aqueous solution adhering to the fibre in the oil trough after successive transfers of a fibre between oil and aqueous media, and reproducibly minimised the amount of aqueous solution transferred to the oil trough with the fibre. The steady active isometric tension during the first activation in oil, 116.5 ± 6.5 kN m−2 at sarcomere length 2.7 μm in 12 fibres, was the same as that measured in activating solution. Experiments were terminated after 20-37 activations, when active tension was about 70% of that in the first activation. Ramp shortening was applied about 10 s after transfer of fibres to the oil trough.

Results are given as means ±s.e.m., with n representing the number of fibres.

RESULTS

Measurement of ATP utilisation during fibre shortening

When a relaxed fibre containing the NADH assay constituents and immersed in silicone oil was allowed to shorten by 10% of its initial length (L0) from sarcomere length 2.9 μm, the fluorescence recorded from NADH increased (Fig. 2A). The increase is due to a larger number of NADH-containing sarcomeres being in the illuminating light beam after the shortening. This effect must be eliminated if the NADH-linked assay is to be used for accurate measurements of ATP utilisation during shortening. To this end we included a second fluorometric indicator, carboxytetramethylrhodamine (CTMR), in the assay solutions. CTMR was chosen because it can be excited at the same wavelength as NADH, has a high quantum yield, and does not bind strongly to fibre constituents. As expected, CTMR fluorescence also increased during shortening of the relaxed fibre (Fig. 2A). In principle, the ratio of the NADH and CTMR signals should give a continuous measure of NADH concentration which is independent of movements of the fibre with respect to the measuring beam. In practice, a correction had to be applied for the contribution (C) of NADH fluorescence to the CTMR signal (see Methods; Fig. 1, inset), so [NADH] was estimated as:

graphic file with name tjp0531-0781-m1.jpg (1)

where FNADH and FCTMR are the fluorescence signals from NADH and CTMR channels, respectively, C is a spectrophotometric constant (0.115) measured in fibres containing NADH but not CTMR (see Methods), and K is a calibration constant measured in relaxed fibres that had been equilibrated with 7.5 mm NADH. The corrected [NADH] signal calculated in this way was not affected by shortening of a relaxed fibre by 10%L0 (Fig. 2A).

Figure 2. Measurement of ATP utilisation during shortening.

Figure 2

Open in a new tab

Shortening of 10%L0 was imposed from sarcomere length 2.9 μm in relaxing solution (A) and from 2.7 μm during active contraction (B). Traces labelled CTMR and NADH show the output of the photomultipliers recording fluorescence at 610 and 450 nm (Fig. 1); the initial values were 6.2 and 5.2 V, respectively, at sarcomere length 2.9 μm in A, and 6.7 and 5.6 V at sarcomere length 2.7 μm in B. Traces labelled ‘Corrected [NADH]’ show [NADH] in the fibre volume estimated as described in Results (eqn (1)). The force baseline is indicated by the lower end of the calibration bar. Fibre cross-sectional area, 3100 μm2.

When shortening of 10%L0 was applied from sarcomere length 2.7 μm during maximal Ca2+ activation (Fig. 2B), both the CTMR and the NADH signals decreased slowly during isometric contraction, and increased during shortening. The steady decrease in the NADH signal during isometric contraction is due to oxidation of NADH in the linked assay as a result of ADP production by myosin cross-bridges interacting with actin filaments. The CTMR signal also decreased slightly during the isometric period because of the small contribution of NADH fluorescence to the CTMR channel. The corrected [NADH] signal decreased at a steady rate during isometric contraction and at a faster rate during active shortening (Fig. 2B). Control experiments in which lactate dehydrogenase was omitted from the assay solutions so that ADP production was no longer linked to the oxidation of NADH, or in which pyruvate kinase, lactate dehydrogenase and phosphoenolpyruvate were omitted and 10 mm phosphocreatine and 1 mg ml−1 creatine kinase were used to rephosphorylate ADP, showed no change in the corrected [NADH] signal when the same shortening ramp was applied to actively contracting fibres in oil (data not shown). Thus the faster rate of decrease of the corrected [NADH] signal during active shortening when all components of the NADH-linked assay are present (Fig. 2B) is due to a greater rate of ADP production during shortening.

The corrected [NADH] signals were analysed by linear regression of the data from three periods: isometric pre-shortening, during shortening, and isometric post-shortening (dashed lines in Fig. 2B), under the assumption that there is a constant rate of ATP utilisation in each period, leading to a constant rate of ADP production and a constant rate of decrease in [NADH]. This assumption is examined in the Discussion. For each trace the extra ATP utilisation due to shortening (ΔATP) was also calculated as the difference between the regression lines in the pre- and post-shortening isometric periods extrapolated to the mid-point of the shortening period. This procedure accounts for the dependence of ATP utilisation on sarcomere length, assuming that the contribution of the isometric ATP utilisation during the shortening period is the mean of those at the pre- and post-shortening lengths.

Effect of extent of shortening on ATP utilisation

ATP utilisation was measured during active shortening of up to 15%L0 at a velocity of 0.4 L0 s−1 (Fig. 3). For the smallest extent of shortening studied, 1%L0, force was still falling rapidly at the end of the imposed shortening. The 25 ms shortening period was too short to allow an accurate measurement of the rate of ATP utilisation during the shortening, but the extra ATP utilisation due to shortening (ΔATP) was measured from the offset between the pre- and post-shortening regression lines as 20.7 ± 0.9 μm (n = 3). Assuming that the myosin head concentration in the fibre is 150 μm, this corresponds to 14% of the myosin heads in the fibre splitting an extra ATP molecule as a result of the shortening.

Figure 3. ATP utilisation for different extents of shortening.

Figure 3

Open in a new tab

Length, force and corrected [NADH] signals for shortening of 1, 2.5, 5, 10 and 15%L0 (A to E, respectively) at a velocity of 0.4 L0 s−1. Each trace was averaged from 14-33 runs in 3-7 fibres. Dashed lines on the [NADH] traces were obtained by linear regression before, during and after the shortening period. Fibre cross-sectional area, 3800 ± 400 μm2.

For extents of shortening of 2.5%L0 or greater, the average rate of ATP utilisation could be measured during the shortening period, and this rate decreased with increasing extent of shortening in the range 5-15%L0 (Fig. 4A). The extra ATP utilisation due to shortening (ΔATP) increased with increasing extent of shortening (Fig. 4B), and these data were reasonably well fitted by a straight line. The regression line did not pass through the origin, however, and intersected the ΔATP axis at 12.3 μm (95% confidence limits 3.1-21.5 μm). ATP utilisation is not directly proportional to the extent of shortening; there is an extra ATP cost for small extents of shortening which may be associated with the initial fall and subsequent recovery of force.

Figure 4. Dependence of ATP utilisation on extent of shortening.

Figure 4

Open in a new tab

A, rate of ATP utilisation during the shortening period. The dashed line is the isometric rate averaged from pre- and post-shortening measurements. B, extra ATP utilisation due to shortening (ΔATP). The slope of the regression line is 6.7 μm%L0−1. The data are means ±s.e.m. from the same fibres as in Fig. 3; n = 7 except for the point at 1%L0, for which n = 3.

Effect of shortening velocity on ATP utilisation

Shortening velocity is expected to have a substantial effect on the rate of ATP utilisation, because myosin cross-bridges should detach more rapidly from actin filaments at higher velocities (Huxley, 1957). If detachment is tightly coupled to ATP hydrolysis, the rate of ATP utilisation should therefore increase with increasing velocity. The mechanical power output of the muscle, on the other hand, has a biphasic dependence on velocity, being zero during isometric contraction and at the velocity of unloaded shortening (V0) with a maximum value at about one-third V0 (Hill, 1938; He et al. 1999). It is therefore of interest to characterise the rate of ATP utilisation over the whole range of velocities from zero (isometric) to V0.

V0 was measured in activating solution at 10 °C using the slack test (Edman, 1979). Typically four different amplitudes of quick release were imposed during active isometric contraction from an initial sarcomere length of 2.7 μm, and the time from the start of the release to the start of force redevelopment, the slack period, was measured in each case. The amplitude of release was linearly related to the slack period. V0, the slope of this relationship, was 1.19 ± 0.03 L0 s−1 (n = 4). The series compliance of the fibre preparation, determined as the intercept on the amplitude axis, was 2.74 ± 0.12%L0 (n = 4). In two of the four fibres, V0 was also measured in releases from sarcomere length 2.5 μm, with similar results.

The rate of ATP utilisation was measured during shortening of 10%L0 at velocities from 0.05 to 1.2 L0 s−1 (Fig. 5A-F, respectively), corresponding to 0.04-1.0 V0. The rate of ATP utilisation during isometric contraction at sarcomere length 2.7 μm before the imposed shortening, 181 ± 16 μm s−1 (n = 6), was slightly less than that, 197 ± 18 μm s−1, at sarcomere length 2.43 μm after shortening. The difference is consistent with the linear dependence of the isometric rate of ATP utilisation on the overlap between myosin and actin filaments (Stephenson et al. 1989). During the shortening period the rate of ATP utilisation at a given shortening velocity appeared to be roughly constant, although the data are too noisy to eliminate the possibility of a brief lag between the start of shortening and the increase in the rate of ATP utilisation. Similarly, although there was no evidence for extra ATP utilisation after the end of shortening, a short period of delayed ATP utilisation cannot be excluded.

Figure 5. ATP utilisation for different shortening velocities.

Figure 5

Open in a new tab

Length, force and corrected [NADH] signals for shortening of 10%L0 at velocities of about 0.05, 0.1, 0.2, 0.4, 0.8 and 1.2 L0 s−1 (A to F, respectively). Each trace was averaged from 11-14 runs in six fibres. Dashed lines on [NADH] traces were obtained by linear regression before, during and after the shortening period. Fibre cross-sectional area, 3200 ± 200 μm2.

The rate of ATP utilisation during shortening clearly increased with increasing shortening velocity (Fig. 5), and the relationship was roughly linear (Fig. 6A). During unloaded shortening, at 1.2 L0 s−1, the rate of ATP utilisation was 1.70 ± 0.29 mm s−1 (n = 6), which is about 9 times faster than the isometric rate. Assuming that the myosin head concentration is 150 μm, the rate of ATP utilisation at V0 was 11.3 s−1 per myosin head.

Figure 6. Dependence of ATP utilisation on shortening velocity.

Figure 6

Open in a new tab

A, rate of ATP utilisation during shortening. The dashed line shows the isometric rate averaged from the pre-and post-shortening measurements B, extra ATP utilisation due to shortening (ΔATP). C, total ATP utilisation associated with shortening. The data are means ±s.e.m. from the six fibres in Fig. 5.

The extra ATP utilisation as a result of shortening (ΔATP) was almost independent of shortening velocity throughout the range from 0.05 to 1.2 L0 s−1 (Fig. 6B). The average value for all velocities was 84 ± 9 μm from the six fibres. Thus, shortening by 10%L0 at any velocity from about 0.04 V0 to V0 incurs an extra ATP cost that is equivalent to 0.56 ATP per myosin head. However, because the duration of the shortening is longer at slower velocities, it is also important to consider the total amount of ATP utilisation during the shortening period (Fig. 6C). The difference between total (Fig. 6C) and extra ATP utilisation (Fig. 6B) corresponds to the isometric rate of ATP utilisation, which makes a small contribution at V0, but a large contribution at 0.04 V0. Thus the total ATP utilisation during shortening is much larger at slower velocities (Fig. 6C).

Mechanical work and efficiency

The fall of force during shortening of 10%L0 showed two temporal components at all velocities (Fig. 5), an initial fast component followed by a slow linear decrease. The mean force during the linear phase is shown as a function of velocity in Fig. 7A (open circles). The Hill equation (Hill, 1938) was fitted to these force-velocity data, and Vmax estimated from the fitted parameters was 1.30 ± 0.07 L0 s−1. This value, measured in the conditions used for the NADH-linked assay with fibres immersed in silicone oil, is not significantly different from the value of V0 measured by the slack test in activating solution, 1.19 ± 0.03 L0 s−1.

Figure 7. Mechanical work and efficiency.

Figure 7

Open in a new tab

A: •, average force during shortening; ○, average force during the slow linear component of force decrease during shortening. The line shows a fit of the Hill equation (Hill, 1938) to the latter data. Fitted parameters: Vmax, 1.30 ± 0.07 L0 s−1; a/P0, 0.09 ± 0.01. B, efficiency during shortening calculated from the average force during shortening (▪) and average force during the slow linear component (□), as described in the text. The data are means ±s.e.m. from the six fibres in Fig. 5.

Because the extent of shortening was constant in this experiment, the mechanical work performed by the fibre during shortening (Fig. 7A; right-hand ordinate) is proportional to the fibre force during shortening (Fig. 7A; left-hand ordinate). The constant of proportionality was determined from the force per cross-sectional area and the fractional length change during shortening. The total mechanical work output of the fibre (Fig. 7A, filled circles) was calculated from the average force during shortening, and therefore includes the work done by passive elastic structures during the period at the start of shortening when force is decreasing. These elastic structures are re-extended by about the same amount when force redevelops after shortening, as a result of work done on them by the myosin cross-bridges. Therefore this estimate of total mechanical work output represents the net work done by the cross-bridges as a result of the imposed shortening, which may be compared directly with the total ATP utilisation during shortening (Fig. 6C).

The relationship between mechanical work output (Fig. 7A) and total ATP utilisation during shortening (Fig. 6C) was used to calculate the efficiency with which the muscle fibre converts the free energy of ATP hydrolysis to mechanical work, under the assumption that the molar free energy of ATP splitting is -50 kJ (Woledge et al. 1985). The efficiency (Fig. 7B) had a biphasic dependence on shortening velocity, with a maximum value of 0.41 (based on the slow linear component of force during shortening; open squares), or 0.46 (based on average force during shortening; filled squares), at 0.1-0.2 L0 s−1, where force was 30-50% of its isometric value.

DISCUSSION

Measurement of the rate of ATP utilisation during shortening using two fluorescent indicators

The general advantages and limitations of the NADH-linked assay method for measurements of the steady state rate of ATP utilisation in demembranated single muscle fibres immersed in silicone oil were considered in the preceding paper (Hilber et al. 2001), where we concluded that the method accurately reports the rate of ATP utilisation during active isometric contraction. The assay is not affected by substrate depletion or product accumulation. Application of the method to actively shortening fibres in the present paper presented new problems related to the fibre movement in the measuring beam, and raised the question of whether the assay is sufficiently rapid to measure the much faster rate of ATP utilisation observed during a brief period of rapid shortening.

Movement of the muscle fibre with respect to the measuring light beam is a general problem for quantitative photometric measurements with intracellular indicators. It is particularly serious for the intracellular NADH-linked assay used here because small changes in [NADH] are measured against a relatively high background concentration. For example, shortening of the fibre by 10% of its initial length (L0) may increase the amount of NADH in the measuring beam by about the same percentage, producing a change in NADH fluorescence that is larger than that due to the increased ATP utilisation during the shortening (Fig. 2). We corrected for this effect using simultaneous fluorescence measurements from a second indicator, carboxytetramethylrhodamine (CTMR), which was excited by the same light beam as the NADH. This procedure should remove artefacts due to longitudinal movement or shortening of the fibre, and to spatial non-uniformity of fibre cross-section or incident light intensity. The method was tested by applying length changes to relaxed fibres (Fig. 2A), in which the rate of ATP utilisation is very low and not affected by fibre length (Hilber et al. 2001), and to actively contracting fibres that contained NADH and CTMR but not the coupling enzymes.

This method gave a highly reproducible measure of the extra ATP utilisation due to active shortening (ΔATP). For example, ΔATP for shortening of 10%L0 had a standard error of about 20 μm (Fig. 6B), much smaller than the artefactual apparent increase in [NADH] which might be expected from this extent of shortening, about 500 μm, estimated as 10% of total [NADH] at the time of the measurement. Judged by these criteria, the CTMR method successfully removed the artefactual changes in NADH fluorescence produced by fibre shortening.

The second issue raised at the start of this section is whether the NADH assay is sufficiently rapid to measure accurately the ATP utilisation during rapid shortening. The corrected [NADH] signals show a sharp transition between a constant rate of decrease during isometric contraction and a faster rate during shortening. The rate of ATP utilisation appeared to be approximately constant during the shortening period (Figs 3 and 5), although a lag of about 20 ms at the start of shortening cannot be ruled out at the current signal:noise level. At the end of the shortening period the lower isometric rate of [NADH] decrease was re-established with no measurable delay.

The absence of a substantial lag in the [NADH] signal is also shown by the comparison of the rate of decrease measured by linear regression of the signal during the shortening period itself (Figs 4A and 6A) with the total extra ATP utilisation due to shortening (ΔATP) measured as the difference between the steady pre- and post-shortening isometric rates of ATP utilisation extrapolated to the middle of the shortening period (Figs 4B and 6B). The largest discrepancy was observed at the fastest shortening velocity, 1.2 L0 s−1 (Fig. 5F). In this case the rate of ATP utilisation estimated by linear regression of [NADH] during the shortening period was 1.70 mm s−1 (Fig. 6A) and ΔATP was 88 μm (Fig. 6B). Subtracting the mean isometric rate, 0.19 mm s−1, from the total rate during shortening gives the rate of extra ATP utilisation during shortening as 1.51 mm s−1. The duration of shortening was 83 ms, so the extra ATP utilisation estimated from these data is 126 μm, slightly larger than ΔATP estimated by extrapolating the isometric rates. A difference in the opposite direction would have been produced by a lag between ATP utilisation and the change in the [NADH] signal, since a lag would reduce the average rate during the shortening period but have little or no effect on the difference between the pre- and post-shortening isometric rates.

The maximum rate of ATP utilisation measured here, 1.70 mm s−1 during shortening at 1.2 L0 s−1 (Fig. 6A), is similar to the maximum turnover rate expected for the concentrations of pyruvate kinase and lactate dehydrogenase used in the assay, 1000-1500 units ml−1. After allowing for the different temperature and pH (see Methods), the expected maximum turnover rate for pyruvate kinase in the conditions of the fibre experiments is 2.1-3.1 mm s−1, and the corresponding rate for lactate dehydrogenase is 3.5-5.2 mm s−1. These calculations suggest that the maximum rate of ATP utilisation measured in the fibre assay might be limited to some extent by the turnover rate of the coupling enzymes, in apparent contradiction to the absence of a substantial lag in the [NADH] transients. One possible explanation is that the concentration of pyruvate kinase and lactate dehydrogenase in the fibres may have become substantially greater than that in the loading solution during the 60 min loading period as a result of binding to fibre constituents.

Comparison with previous estimates of the rate of ATP utilisation during shortening

The extra ATP utilisation due to shortening was measured previously in small bundles of fibres from rabbit psoas muscle at 15 °C using an NADH-linked absorbance assay in the bathing solution (Potma & Stienen, 1996). The changes in NADH absorbance were delayed by about 1 s after the shortening period, but the extra ATP utilisation due to shortening (ΔATP) was determined as the difference between regression lines fitted to the pre- and post-shortening isometric rates, as in the present work (Fig. 4B and 6B). ΔATP for shortening of 5%L0, the smallest extent of shortening for which measurements were made, at ∼5 L0 s−1, was 78 μm, slightly larger than that determined here (49 ± 4 μm) for the same extent of shortening at 0.4 L0 s−1, 10 °C (Fig. 4B). The relationship between ΔATP and extent of shortening in the fibre bundles saturated for shortening of more than 10%L0, in contrast to the more linear relationship observed here (Fig. 4B). The difference may be associated with the greater series compliance of the fibre bundle preparation, about 7.5%L0, cf. 2.7%L0 here, or with the incomplete force redevelopment after the larger extents of shortening in that preparation.

ΔATP has also been measured in single fibres from fast skeletal muscles of the rat using the NADH-linked absorbance assay in the bathing solution (Reggiani et al. 1997). ΔATP was about 200 μm for shortening of 20%L0 at velocities in the range 0.2-2.0 L0 s−1 at 12 °C. Extrapolation of the present data for shortening at 0.4 L0 s−1, 10 °C (Fig. 4B) to 20%L0 gives a similar estimate of ΔATP, about 150 μm. Thus the values of ΔATP measured here appear to be broadly similar to those determined previously in fast fibres of mammalian skeletal muscle from measurements of NADH absorbance in the bathing solutions, at least within the variation that might be expected from the differences in the preparations and experimental conditions.

The improved sensitivity and time resolution of the present method also allowed the rate of ATP utilisation to be measured during the shortening period itself (Figs 4A and 6A), and these rates can be compared directly with those measured using a phosphate binding protein in single fibres from rabbit psoas muscle by He et al. (1999). These authors report a rate of ATP utilisation of 2.7 mm s−1 during shortening of about 7%L0 at a velocity greater than 1 L0 s−1 at 12 °C. Here we measured 1.7 mm s−1 for shortening of 10%L0 at 1.2 L0 s−1 at 10 °C (Fig. 6A). The difference between the rates measured by the two methods can probably be accounted for by the smaller shortening distance (cf. Fig. 4A) and higher temperature in the phosphate binding protein study. There is a discrepancy between the rates of ATP utilisation measured during either isometric contraction or slow shortening in the two studies. This is related to the higher rate of isometric ATP utilisation observed transiently after ATP release from caged ATP in the phosphate binding protein experiments (He et al. 1997), which may be at least partly explained by sarcomere shortening during the initial phase of the nominally isometric contraction (He et al. 1999).

The rate of ATP utilisation during shortening had a roughly linear dependence on shortening velocity (Fig. 6A). A roughly linear relationship between the rate of ATP utilisation and shortening velocity was also reported for skinned muscle fibres of the rat (Reggiani et al. 1997). These linear relationships are in marked contrast to the biphasic relationship between the total rate of energy liberation and shortening velocity in frog muscle (Hill, 1938, 1964; Linari & Woledge, 1995). This is surprising, because the total rate of energy liberation, measured as the rate of heat plus work production, is expected to be proportional to the rate of ATP utilisation. However, the dependence of the total rate of energy liberation on shortening velocity in mouse EDL muscle (Barclay, 1996) is more nearly linear than that in frog muscle. These comparisons suggest that ATP utilisation may have a different dependence on shortening velocity in amphibian and mammalian muscles. Since this relationship is critical for testing models of mechanical- chemical coupling in muscle (Huxley, 1957; Piazzesi & Lombardi, 1995), this possibility merits further study.

Implications for mechanical-chemical coupling

The present results demonstrate a clear dependence of the rate of ATP utilisation on the mechanical state of the muscle fibre. When shortening was imposed, the rate of ATP utilisation increased promptly to up to 9 times the isometric rate, and at the end of shortening the isometric rate was quickly re-established (Figs 3 and 5). These results are consistent with a model in which the detachment of myosin heads from actin is rate limiting for ATP utilisation under isometric conditions, and in which shortening increases the rate of detachment and thus the rate of ATP utilisation (Huxley, 1957). The linear relationship between the rate of ATP utilisation and shortening velocity found here is consistent with a simple scheme in which detachment remains rate limiting during rapid shortening in these conditions, in contrast with models that were developed to describe the biphasic relationship between the rate of energy liberation and shortening velocity in frog muscle (e.g. Huxley, 1957; Piazzesi & Lombardi, 1995), in which the effective attachment rate is reduced during rapid shortening.

Some general conclusions about mechanical-chemical coupling in this model can be derived from the present results by comparing the measured rate of ATP utilisation with the expected detachment rate. A lower limit for the detachment rate can be estimated as the relative sliding velocity (V) between the actin and myosin filaments, divided by the maximum distance over which a myosin head can remain attached to actin (D). Several lines of evidence suggest that D is about 10 nm. The myosin head is 16 nm long (Rayment et al. 1993), and three different conformations of the head with different nucleotide analogues at the active site have been described (Rayment et al. 1993; Dominguez et al. 1998; Houdusse et al. 1999). Comparison of these structures suggests that release of the ATP hydrolysis products from the active site may be coupled to a structural change corresponding to a displacement of about 10 nm between the myosin and actin filaments. This value is also consistent with the transient mechanical response of active muscle fibres to small length steps (Huxley & Simmons, 1971) and, within a factor of two, with mechanical studies of isolated myosin fragments interacting with actin filaments in vitro (e.g. Finer et al. 1994; Molloy et al. 1995; Kitamura et al. 1999).

The total rate of ATP utilisation during shortening at 1.2 L0 s−1 was 1.7 ± 0.29 mm s−1 (Fig. 6), which corresponds to 11.3 ± 1.9 s−1 per myosin head, assuming that the concentration of myosin heads in the fibre is 0.15 mm. During shortening at this velocity, V is 1.2 x 1350 = 1620 nm s−1, so with D = 10 nm the detachment rate must be at least 162 s−1. This is about 15 times the rate of ATP utilisation normalised by the total concentration of myosin heads in the muscle fibre, 11.3 s−1. Thus, if detachment is tightly coupled to ATP utilisation, less than 7% of the myosin heads in the fibre can be attached to actin during rapid shortening. Similar or lower estimates of this quantity have been made previously based on measurements of the rate of ATP utilisation during rapid shortening of intact frog sartorius muscles (Homsher et al. 1981) and fast and slow skinned fibres from rat skeletal muscle (Reggiani et al. 1997).

A similar argument can be made for slower shortening, for example at about 0.4 L0 s−1, where the efficiency of energy transduction is close to its maximum value (Fig. 7B). At this velocity, the extra ATP utilisation due to shortening of 10%L0, involving filament sliding of 135 nm, was about 80 μm (Figs 4B and 6B). The isometric rate of ATP utilisation, 190 μm s−1, contributes a further ca 48 μm during the shortening period, so the total ATP utilisation was 128 μm (Fig. 6C), or 0.85 per myosin head. Assuming D = 10 nm and tight coupling of detachment and ATP utilisation as before, the fraction of myosin heads attached during shortening at this velocity must be less than 0.85 x 10/135 = 6%.

This type of argument can also be used to estimate the fraction of heads attached to actin during isometric contraction. Shortening of 1%L0, corresponding to filament sliding of 13.5 nm, produced an extra ATP utilisation (ΔATP) of 20.7 ± 0.9 μm (Fig. 4B). The isometric rate of ATP utilisation contributes a further 4.8 μm during the 25 ms shortening period. If myosin heads can stay attached to actin for only 10 nm of filament sliding, then all the myosin heads that were attached before the 13.5 nm shortening must have been detached by the imposed filament sliding. If detachment is tightly coupled to ATP utilisation, an upper limit for the fraction of myosin heads that were attached during isometric contraction, calculated by including the isometric component of ATP utilisation, is (20.7 + 4.8)/150 = 17%. This estimate depends critically on the value of D. If the applied length step was in fact smaller than D, some heads would have remained attached to actin and therefore would not have been counted by the measurement of ΔATP. However, ΔATP for a shortening step of 2.5%L0, corresponding to filament sliding of 34 nm, was still only 25.9 ± 2.4 μm, and the isometric component would add 11.9 μm. In this case the total ATP utilisation corresponds to 25% of the myosin heads in the fibre. Since D is almost certainly smaller than 34 nm, this result strongly suggests that, if ATP utilisation is tightly coupled to detachment, the fraction of myosin heads attached during isometric contraction at the relatively low temperature of 10 °C used in the present experiments must be considerably less than 25%.

The above estimates of the fraction of myosin heads attached to actin were all based on the assumption of 1:1 coupling between detachment and commitment to ATP utilisation. It is possible that detachment of myosin heads from actin can occur without ADP release, at least in some conditions (Cooke et al. 1994; Piazzesi & Lombardi, 1995). Such decoupling seems more likely to occur during rapid shortening, when the mechanical work output is small, or during stretch, when work is done on the fibre, rather than during moderate speed shortening when work is produced with relatively high efficiency.

The fraction of myosin heads attached to actin during isometric contraction of rabbit psoas fibres has also been estimated to be less than 25% from the orientation of probes attached to the myosin heads (Cooke et al. 1982; Hopkins et al. 1998; Corrie et al. 1999). Considerably higher values for the fraction of attached heads have been estimated by comparing the stiffness of muscle fibres during isometric contraction and in rigor, under the assumption that all heads contribute to stiffness in the latter state. However, early estimates based on stiffness measurements were artefactually high because they did not take into account the compliance of the myofilaments. When myofilament compliance is allowed for, the fraction of myosin heads attached to actin during isometric contraction of intact fibres from frog muscle estimated from stiffness measurements is less than 43% (Linari et al. 1998). The fraction of heads attached to actin in active muscle may vary between species, and the fraction attached during active contraction of rabbit psoas muscle at physiological temperatures could be higher than that estimated here for 10°C.

Acknowledgments

This work was supported by the Wellcome Trust. K.H. was supported by a fellowship (J1504-BIO) from FWF, Austria. We are very grateful to Dr U. A. van der Heide for his suggestion of the dual indicator technique to remove movement artefacts, and to Professor V. Lombardi for the generous gift of the loudspeaker motor.

References

  1. Barclay CJ. Mechanical efficiency and fatigue of fast and slow muscles of the mouse. Journal of Physiology. 1996;497:781–794. doi: 10.1113/jphysiol.1996.sp021809. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Chase PB, Kushmerick MJ. Effects of pH on contraction of rabbit fast and slow skeletal muscle fibers. Biophysical Journal. 1988;53:935–946. doi: 10.1016/S0006-3495(88)83174-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Cooke R, Crowder MS, Thomas DD. Orientation of spin labels attached to cross-bridges in contracting muscle fibers. Nature. 1982;300:776–778. doi: 10.1038/300776a0. [DOI] [PubMed] [Google Scholar]
  4. Cooke R, White H, Pate E. A model of the release of myosin heads from actin in rapidly contracting muscle fibers. Biophysical Journal. 1994;66:778–788. doi: 10.1016/s0006-3495(94)80854-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Corrie JET, Brandmeier BD, Ferguson RE, Trentham DR, Kendrick-Jones J, Hopkins SC, van der Heide UA, Goldman YE, Sabido-David C, Dale RE, Criddle S, Irving M. Dynamic measurement of myosin light-chain domain tilt and twist in muscle contraction. Nature. 1999;400:425–430. doi: 10.1038/22704. [DOI] [PubMed] [Google Scholar]
  6. Dominguez R, Freyzon Y, Trybus KM, Cohen C. Crystal structure of a vertebrate smooth muscle myosin motor domain and its complex with the essential light chain: visualisation of the pre-power stroke state. Cell. 1998;94:559–571. doi: 10.1016/s0092-8674(00)81598-6. [DOI] [PubMed] [Google Scholar]
  7. Edman KAP. The velocity of unloaded shortening and its relation to sarcomere length and isometric force in vertebrate muscle fibres. Journal of Physiology. 1979;291:143–159. doi: 10.1113/jphysiol.1979.sp012804. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Finer JT, Simmons RM, Spudich JA. Single myosin molecule mechanics: piconewton forces and nanometer steps. Nature. 1994;368:113–119. doi: 10.1038/368113a0. [DOI] [PubMed] [Google Scholar]
  9. He Z-H, Chillingworth RK, Brune M, Corrie JET, Trentham DR, Webb MR, Ferenczi MA. ATPase kinetics on activation of rabbit and frog permeabilized isometric muscle fibres: a real time phosphate assay. Journal of Physiology. 1997;501:125–148. doi: 10.1111/j.1469-7793.1997.125bo.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. He Z-H, Chillingworth RK, Brune M, Corrie JET, Webb MR, Ferenczi MA. The efficiency of contraction in rabbit skeletal muscle fibres, determined from the rate of release of inorganic phosphate. Journal of Physiology. 1999;517:839–854. doi: 10.1111/j.1469-7793.1999.0839s.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Hilber K, Sun Y-B, Irving M. Effects of sarcomere length and temperature on the rate of ATP utilisation by rabbit psoas muscle fibres. Journal of Physiology. 2001;531:771–780. doi: 10.1111/j.1469-7793.2001.0771h.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Hill AV. The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society. 1938;126:B136–195. [Google Scholar]
  13. Hill AV. The effect of load on the heat of shortening of muscle. Proceedings of the Royal Society. 1964;159:B297–318. doi: 10.1098/rspb.1964.0004. [DOI] [PubMed] [Google Scholar]
  14. Homsher E, Irving M, Wallner A. High-energy phosphate metabolism and energy liberation associated with rapid shortening in frog skeletal muscle. Journal of Physiology. 1981;321:423–436. doi: 10.1113/jphysiol.1981.sp013994. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Hopkins SC, Sabido-David C, Corrie JET, Irving M, Goldman YE. Fluorescence polarization transients from rhodamine isomers on the myosin regulatory light chain in skeletal muscle fibers. Biophysical Journal. 1998;74:3093–3110. doi: 10.1016/S0006-3495(98)78016-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Houdusse A, Kalabokis VN, Himmel D, Szent-Györgyi AG, Cohen C. Atomic structure of scallop myosin subfragment S1 complexed with MgADP: a novel conformation of the myosin head. Cell. 1999;97:459–470. doi: 10.1016/s0092-8674(00)80756-4. [DOI] [PubMed] [Google Scholar]
  17. Huxley AF. Muscle structure and theories of contraction. Progress in Biophysics and Biophysical Chemistry. 1957;7:255–318. [PubMed] [Google Scholar]
  18. Huxley AF, Simmons RM. Proposed mechanism of force generation in striated muscle. Nature. 1971;233:533–538. doi: 10.1038/233533a0. [DOI] [PubMed] [Google Scholar]
  19. Kitamura K, Tokunaga M, Iwane AH, Yanagida T. A single myosin head moves along an actin filament with regular steps of 5. 3 nm. Nature. 1999;397:129–134. doi: 10.1038/16403. [DOI] [PubMed] [Google Scholar]
  20. Linari M, Dobbie I, Reconditi M, Koubassova N, Irving M, Piazzesi G, Lombardi V. The stiffness of skeletal muscle in isometric contraction and rigor: the fraction of myosin heads bound to actin. Biophysical Journal. 1998;74:2459–2473. doi: 10.1016/S0006-3495(98)77954-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Linari M, Woledge RC. Comparison of energy output during ramp and staircase shortening in frog muscle fibres. Journal of Physiology. 1995;487:699–710. doi: 10.1113/jphysiol.1995.sp020911. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Lombardi V, Piazzesi G. The contractile response during steady lengthening of stimulated frog muscle fibres. Journal of Physiology. 1990;431:141–171. doi: 10.1113/jphysiol.1990.sp018324. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Molloy JE, Burns JE, Kendrick-Jones J, Tregear RT, White DCS. Movement and force produced by a single myosin head. Nature. 1995;378:209–212. doi: 10.1038/378209a0. [DOI] [PubMed] [Google Scholar]
  24. Piazzesi G, Lombardi V. A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophysical Journal. 1995;68:1966–1979. doi: 10.1016/S0006-3495(95)80374-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Potma EJ, Stienen GJM. Increase in ATP consumption during shortening in skinned fibres from rabbit psoas muscle: effects of inorganic phosphate. Journal of Physiology. 1996;496:1–12. doi: 10.1113/jphysiol.1996.sp021660. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Rayment I, Rypniewski WR, Schmidt-Base K, Smith R, Tomchick DR, Benning MM, Winkelmann DA, Wesenberg G, Holden HM. Three-dimensional structure of myosin subfragment-1: a molecular motor. Science. 1993;261:50–58. doi: 10.1126/science.8316857. [DOI] [PubMed] [Google Scholar]
  27. Reggiani C, Potma EJ, Bottinelli R, Canepari M, Pellegrino MA, Stienen GJM. Chemo-mechanical energy transduction in relation to myosin isoform composition in skeletal muscle fibres of the rat. Journal of Physiology. 1997;502:449–460. doi: 10.1111/j.1469-7793.1997.449bk.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Stephenson DG, Stewart AW, Wilson GJ. Dissociation of force from myofibrillar MgATPase and stiffness at short sarcomere lengths in rat and toad skeletal muscle. Journal of Physiology. 1989;410:351–366. doi: 10.1113/jphysiol.1989.sp017537. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Sun Y-B, Hilber K, Irving M. An improved method for continuous measurements of ATP hydrolysis during active shortening of single muscle fibers. Biophysical Journal. 1999a;76:34a. [Google Scholar]
  30. Sun Y-B, Hilber K, Irving M. Effect of active shortening on the ATPase activity of single fibres from rabbit psoas muscle. Journal of Physiology. 1999b;515.P doi: 10.1111/j.1469-7793.2001.0781h.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Woledge RC, Curtin NC, Homsher E. Energetic Aspects of Muscle Contraction. London: Academic Press; 1985. [PubMed] [Google Scholar]

Articles from The Journal of Physiology are provided here courtesy of The Physiological Society

RESOURCES