The efficiency of contraction in rabbit skeletal muscle fibres, determined from the rate of release of inorganic phosphate

Abstract

1. The relationship between mechanical power output and the rate of ATP hydrolysis was investigated in segments of permeabilized fibres isolated from rabbit psoas muscle.

2. Contractions were elicited at 12 °C by photolytic release of ATP from the P³-1-(2-nitrophenyl)ethyl ester of ATP (NPE-caged ATP). Inorganic phosphate (P_i) release was measured by a fluorescence method using a coumarin-labelled phosphate binding protein. Force and sarcomere length were also monitored.

3. ATPase activity was determined from the rate of appearance of P_i during each phase of contraction. The ATPase rate was 10.3 s⁻¹ immediately following release of ATP and 5.1 s⁻¹ during the isometric phase prior to the applied shortening. It rose hyperbolically with shortening velocity, reaching 18.5 s⁻¹ at a maximal shortening velocity > 1 ML s⁻¹ (muscle lengths s⁻¹).

4. Sarcomeres shortened at 0.09 ML s⁻¹ immediately following the photolytic release of ATP and at 0.04 ML s⁻¹ prior to the period of applied shortening. The high initial ATPase rate may be largely attributed to initial sarcomere shortening.

5. During shortening, maximal power output was 28 W l⁻¹. Assuming the free energy of hydrolysis is 50 kJ mol⁻¹, the efficiency of contraction was calculated from the power output at each shortening velocity. The maximum efficiency was 0.36 at a shortening velocity of 0.27 ML s⁻¹, corresponding to a force level 51 % of that in the isometric state.

6. At the maximal shortening velocity, only 10 % of the myosin heads are attached to the thin filaments at any one time.

The mechanical efficiency of muscle contraction is the ratio of work performed to the chemical energy produced by the hydrolysis of ATP. Chemical energy which is not converted into work or absorbed by the reaction is lost as heat. The efficiency of contraction is zero when no work is produced, either because the muscle does not shorten, i.e. during isometric contractions, or when the force produced by the muscle is zero, as is the case when the muscle is allowed to shorten under zero load. In the latter case, the shortening velocity is the maximum which the muscle can achieve. It is also necessary to consider the internal work which does not translate into macroscopic movement, but which may be relevant to considerations of efficiency. Here we have precisely determined the work resulting from the actomyosin ATPase activity, without interference from the effects of tendon elasticity and of ATP hydrolysis due to activation of the muscle machinery, namely calcium release and re-uptake by the sarcoplasmic reticulum. This was achieved by using segments of permeabilized muscle fibres obtained from the rabbit psoas muscle and initiating contraction by the photolytic release of ATP from the P³-1-(2-nitrophenyl)ethyl ester of ATP (NPE-caged ATP; Ferenczi et al. 1984) in the presence of a saturating concentration of calcium (32 μm). The ability of the muscle fibres to perform work was measured by recording the force response during a period of applied constant velocity shortening. The ends of such fibre segments may be damaged at their point of attachment to the apparatus, resulting in local stretching during force development. So we measured the sarcomere length in the segment during contraction and shortening, thus providing a direct measurement of the shortening velocity of the sarcomeres.

The other aspect of efficiency calculations is the determination of chemical energy utilized. For this, we used a fluorescence assay which is sensitive to the amount of inorganic phosphate (P_i) released in the muscle fibre by the hydrolysis of ATP (He et al. 1997). The advantages of this assay over other methods are its high sensitivity and millisecond time resolution. Here, P_i binds to a phosphate binding protein (PBP) which has been labelled with a coumarin fluorophore, N-(2-[1-maleimidyl]ethyl)-7-diethylaminocoumarin-3-carboxamide (MDCC) (Brune et al. 1994, 1998). The labelled protein, MDCC-PBP, binds P_i tightly and rapidly, resulting in a 5-fold enhancement of fluorescence under our experimental conditions (He et al. 1997, 1998b).

The calculation of efficiency also requires a value for the amount of energy released by the hydrolysis of ATP and available for conversion into work. In the experiments shown here, changes in the ATP concentration after its photolytic release were minimized by the use of creatine kinase to regenerate hydrolysed ATP.

Previous work on intact frog muscles has shown that the efficiency of contraction depends on the shortening velocity, with a maximum efficiency of approximately 0.5 for a shortening velocity of 1/3 of that under zero load (V_max) (for review, see Woledge et al. 1985). We explore here the efficiency in permeabilized muscle fibres, where only the actomyosin ATPase is present. In our assay system where P_i binds tightly to MDCC-PBP, the P_i concentration during the measurement period is low (< 1 μm) compared with that found in vivo (∼1 mM). We discuss the role of P_i concentration on the power output and efficiency of contraction (Pate et al. 1998).

ATP hydrolysis during contraction under isometric conditions is a substantial fraction of that seen under conditions of maximal power output, even though no external work is performed under isometric conditions. From the energetics point of view, ATP hydrolysed during isometric contractions is wasted. This waste appears even more significant in the light of the experiments of He et al. (1997) who showed that in the first few hundred milliseconds of isometric contraction, the ATPase rate is very much higher than that encountered during the steady phase of contraction. We compare here the ATPase rates measured during shortening and during the initial phases of isometric contraction with a view to understanding the mechanism that may be responsible for the initial high ATPase rate and for its subsequent decline.

The results of preliminary experiments published previously were carried out with muscle fibres at a sarcomere length of 3.0 μm but with no sarcomere monitoring (He et al. 1998a). However at such a sarcomere length the muscle fibre segments exhibit resting tension, which affects the shortening behaviour of the fibres (Edman, 1979) and the calculations of efficiency. Here we show more extensive results using an initial sarcomere length of 2.7 μm, where little resting tension is seen (Stephenson & Williams, 1982), thus allowing more direct evaluation of the work performed and efficiency of contraction.

METHODS

Muscle fibres

Muscle fibre bundles were obtained from the psoas muscle of 5 kg Large Lops rabbits. The animals were killed by placing them in a chamber with a rising concentration of CO₂ followed by exsanguination, according to Home Office guidelines. The bundles were tied in situ to wood applicator sticks to maintain their in vivo length and permeabilized as described previously with glycerol and Triton X-100 (Thirlwell et al. 1994; He et al. 1997, 1998b). The bundles were kept at −18°C for up to 3 weeks. Single muscle fibre segments were dissected from the bundles on a cooled stage (5°C) of a dissecting microscope. The ends of the ∼3 mm-long muscle fibre segments were attached to aluminium foil T-shaped clips and cross-linked with glutaraldehyde to reduce the compliance of the attachment regions (Chase & Kushmerick, 1988; Thirlwell et al. 1994; He et al. 1997, 1998b). The fibre segments had a mean cross-sectional area of 6.7 × 10⁻⁹ m² (s.d.= 2.0 × 10⁻⁹ m² for 16 fibres) with a range of 4.1 × 10⁻⁹ to 11.9 × 10⁻⁹ m².

The apparatus

The muscle fibres were mounted horizontally in the apparatus based on a Zeiss ACM microscope (Oberkochen, Germany) described previously (He et al. 1997), but modified to incorporate a motor which allowed the muscle fibres to shorten at a pre-set speed (He et al. 1998a) and a sarcomere measurement system briefly described previously (He et al. 1998a,b). One end of the fibre segment was attached through the T-clip to a hook formed from 100 μm-diameter stainless steel wire glued to a force transducer (AE801, SensoNor, Horten, Norway). The other end was similarly fixed to the motor.

Changing the muscle length

The motor (Fig. 2 in He et al. 1998a) which was constructed from a commercial loudspeaker coil (RS Components, Corby, UK, 8 Ω, 40 mm diameter) allowed the application of length changes of up to 1 mm in 1 ms. Smaller steps (up to 50 μm) were complete in 0.2 ms.

Figure 2. Three consecutive contractions, a, b and c, initiated by the photolytic release of ≈1.5 mM ATP from 5 mM NPE-caged ATP in a single muscle fibre segment.

The layout of the figure is the same as that of Fig. 1. In each contraction, 0.4 s after the photolytic release of ATP, the fibre segment was subjected to shortening periods with shortening velocities, in chronological order, of 0.395 (a), 0.202 (b) and 0.612 (c) ML s⁻¹. The amplitude of the shortening was 7 % in each case. Fibre dimensions: cross-sectional area 5.30 × 10⁻⁹ m², initial length of fibre segment 2.3 mm, initial sarcomere length 2.7 μm.

Fibre troughs and laser-flash photolysis

The muscle fibres were incubated in one of a set of six 20 μl troughs (2 mm × 10 mm × 1 mm) cut into a circular, stainless steel, temperature-controlled rotating stage (see Fig. 1 in He et al. 1998a). The hooks holding the fibre were horizontal and emerged through slits in the ends of the trough. Surface tension prevented the solution from leaking out of the ends of the troughs. Five of the six troughs contained the incubating solutions, so that fibres could be easily transferred from one solution to the other. The first trough had a fused silica front window (2 mm × 8 mm × 0.5 mm) to allow illumination of the fibre by light pulses from a frequency-doubled ruby laser (Type QSR 2, Innolas UK, Rugby, UK) used for photolysing NPE-caged ATP. The light pulses from the laser (30 ns long, 50–100 mJ pulse at a wavelength of 347 nm) were adjusted with a fused silica cylindrical lens to illuminate the whole length of the fibre segment in the horizontal plane, but not the T-clips or attachment hooks. This trough contained low-viscosity silicone fluid (Dow Corning 200/10cs, BDH Ltd, Dagenham, UK). The fluid was prevented from escaping through the ends of the trough by water droplets at each end of the trough, kept in place by surface tension. A single laser pulse caused the photolytic release of 1.5 mM ATP in a fibre pre-incubated with 5 mM NPE-caged ATP and immersed in silicone fluid, as determined previously (He et al. 1997).

Figure 1. Contraction of a muscle fibre following the photolytic release of ATP from NPE-caged ATP.

The muscle fibre is initially in rigor, and immersed in silicone fluid. At time zero, a pulse of laser light causes photolysis of NPE-caged ATP, releasing ≈1.5 mM ATP. A shows the position of the motor which controls the length of the fibre segment. 0.3 s after the laser pulse, the motor allows the fibre segment to shorten at 1.28 mm s⁻¹, for a total distance of 0.162 mm. B shows that photolytic release of ATP initially caused a fall in tension, and then a rise to an isometric plateau of approximately 150 kN m⁻². When the fibre segment was allowed to shorten, tension rapidly fell to a new level which, during the period of steady shortening, averaged 29.1 % of the isometric value prior to the shortening period. After the shortening period, force redeveloped rapidly to a new isometric plateau, slightly higher than the value reached at 0.3 s. C shows the fluorescence signal, calibrated in terms of the amount of P_i bound to MDCC-PBP. The muscle fibre had been incubated in solution containing 1.2 mM MDCC-PBP. The raw fluorescence signal and that corrected for the aci-nitro decay transient are superimposed. The inset in C shows the raw and corrected traces on an expanded scale. The thin line is the raw signal, the thicker line is the signal corrected for the aci-nitro decay. The straight line segments marked a, b and c in the main panel C show linear regressions to parts of the fluorescence signal to show derivation of the ATPase rate constants during the first turnover, during the isometric phase prior to the shortening phase and during the shortening phase. The rate constant is obtained from calculation of the gradient of the line segments. D shows the sarcomere diffraction signal indicating the sarcomere length of the fibre segment. Fibre dimensions: cross-sectional area 8.60 × 10⁻⁹ m², initial length of fibre segment 2.2 mm, initial sarcomere length 2.7 μm.

Sarcomere length measurements

A 5 mm-wide wedge-shaped fused silica block inserted into the back wall of the trough allowed illumination of the fibre with the beam from a He-Ne laser (wavelength 632.8 nm, 1 mm diameter beam, 5 mW, model LGK 7634, Zeiss, Oberkochen, Germany) to obtain diffraction orders produced by the sarcomeres. Fused silica was preferable to glass because of its higher thermal conductivity. The He-Ne light was expanded by a 14 mm focal length (FL) glass plano-convex lens (this, and subsequently mentioned lenses were obtained from Coherent-Ealing Ltd, Watford, UK) and focused by a 60 mm FL plano-convex lens onto the plane of the photodiode described below. The beam was 1 mm high, extended 2.1 mm along the fibre and illuminated the fibre normally, in a plane at 5 deg to that of the frequency-doubled light so that the non-diffracted beam emerged from the fibre through the front window below the frequency-doubled beam. For a sarcomere length of 2.7 μm, the light from each of the first orders of diffraction emerged at an angle of 13.55 deg with respect to the zero order. As the scattering effect of the fibre spread the diffracted beam in the vertical plane, a bi-convex cylindrical lens (40 mm FL made up of two plano-convex 80 mm FL lenses) was used to collect each diffracted beam and to focus it to a spot onto one of two 9 mm-long position-sensitive photodiodes (PS-100-10; Quantrad, Santa Clara, CA, USA). An electrical signal was obtained from each edge of the position-sensitive diodes. The sum of these signals indicated the intensity of the light falling on the photodiode whereas the difference was sensitive to the position of the diffraction spot. The ratio of the difference to the sum of the output signals was used in the measurements as it varies linearly with the position of the centroid of the light falling on the diode. The degradation of the diffraction signal was shown by a decrease in the summed signal. The lenses and photodiodes were mounted on an horizontal arc centred on the middle of the fibre at a radius of 170 mm. Micrometer screws allowed each photodiode to be moved horizontally, tangentially to the circular track, with 10 μm precision. For each fibre, only the brighter of the two diffracted first-order beams was used. At the beginning of each experiment, the photodiode signal was adjusted to zero by moving the photodiode along the track to centre the diffraction spot and the corresponding sarcomere length of the fibre was measured through the microscope using bright-field illumination with a ×40 0.75 NA water-immersion objective lens and a ×10 eyepiece (both from Zeiss). After adjustment of the electrical signal to zero, calibration of the sarcomere length signal was achieved for each fibre by recording the photodiode electrical signal in response to movement of the photodiode by a known distance along the track. The change in electrical signal achieved by moving the photodiode, for example, by 1 mm in the direction away from the zero order was equivalent to the change in electrical signal resulting from movement of the diffraction spot by the sarcomeres shortening from a length of 2.70 μm to 2.64 μm. The sarcomere signal was sharpest and brightest in fresh fibres, and deteriorated after each photolytically induced contraction. Some recovery of the signal occurred during the relaxation phase after each contraction. The sarcomere signal also gradually deteriorated during each contraction, so that in some cases, only the first few hundred milliseconds following photolytic release of ATP produced reliable measurements of sarcomere length. In some traces, a slow drift in the sarcomere signal can be attributed to deterioration of the sarcomere signal rather than to sarcomere shortening, as evidenced by an accompanying decrease in the intensity of the sarcomere signal. The slow drift seen in Fig. 1D after the period of steady shortening is an example of this.

Data collection

Fluorescence, force, motor output signal and sarcomere length signals were collected using a 12-bit analog-to-digital circuit operated at a minimum of 1 kHz (Computerscope, R.C. Electronics EGAA Computerscope, Goletta, CA, USA in an Intel Pentium 133 MHz computer). A chart recorder continuously monitored the force and fluorescence signal as a means of evaluating the state of the fibres. The fluorescence signal was converted into the amount of P_i released by the fibres as explained below.

Solutions

The experimental solutions were described previously (He et al. 1997) and consisted of ‘relaxing’, ‘activating’, ‘loading’ and ‘rigor’ solutions. The ionic strength of all solutions was calculated to be 0.15 M. The pH was adjusted to 7.1 at 20°C. Care was taken to minimize contamination of the solutions with P_i.

Relaxing solution consisted of 60 mM TES, 10 mM EGTA, 1 mM free Mg²⁺, 5 mM MgATP (6.2 mM total ATP), 10 mM glutathione, with ionic strength adjusted with potassium propionate. Calcium-free rigor solution was identical to relaxing solution, except for the omission of ATP and contained 4 units ml⁻¹ apyrase (Martin & Barsotti, 1994; He et al. 1997) to remove ADP contamination in the fibre and ‘P_i-mop’ (namely 1 mM 7-methylguanosine, 0.5 units ml⁻¹ purine nucleoside phosphorylase) to remove P_i contamination (Brune et al. 1994). Calcium-containing rigor solution was identical to calcium-free rigor except that the free calcium concentration was 32 μm achieved by addition of Ca-EGTA and there was no apyrase and no P_i-mop. Loading solution contained 60 mM TES, 10 mM EGTA, 1 mM free Mg²⁺, 40 mM glutathione, 32 μm free Ca²⁺, 1.2 mM MDCC-PBP, 5 mM NPE-caged ATP (pre-treated with 10 units ml⁻¹ apyrase to remove ADP contamination: the final apyrase concentration in the loading solution was 0.0013 units ml⁻¹), 10 mM creatine phosphate, 4 mg ml⁻¹ creatine kinase obtained from chicken breast (338 units mg⁻¹ at pH 7.1 and 25°C; Bershitsky et al. 1996) and P_i-mop.

Protocol

Muscle fibres were transferred from the dissecting stage to the apparatus by means of a small glass rod and the fibre and T-clips were attached to the tension transducer and motor hooks in a trough containing relaxing solution. The temperature of the microscope stage was adjusted to 12°C and all subsequent steps and measurements were carried out at this temperature. Sarcomere length was adjusted to 2.7 μm and the width and depth of the fibre were measured whilst immersed in relaxing solution using the water-immersion objective lens (Blinks, 1965). The regions of the fibre which had been exposed to glutaraldehyde during the fixation procedure could be seen as they were less iridescent than the non-fixed central region. The length of the central region was measured as it is needed for calculation of the length change and shortening velocity. On average the central region prior to shortening had a length of 2.21 mm (s.d.= 0.25 for 16 fibres), with a range of 1.96 to 3.00 mm. At this temperature and sarcomere length, the isometric force level reached during activation (190 kN m⁻², s.d.= 40 kN m⁻², n = 41), was 17 % lower than at 2.4 μm and 15°C (He et al. 1998b) and resulted in less degradation of the sarcomere signal. The ATPase activity was also slower, thus allowing more time before saturation of the MDCC-PBP with P_i. At this sarcomere length, the percentage of myosin heads in the overlap zone between the thick and thin filaments is 93 % of maximal, assuming a linear force-length relationship giving 100 and 0 % overlap at sarcomere lengths of 2.6 and 4.0 μm, respectively, as is the case for rat fast- and slow-twitch muscles (Page & Huxley, 1963; Stephenson & Williams, 1982). Each fibre was incubated for 30 min in relaxing solution containing 1 % (v/v) Triton X-100 (He et al. 1998b) to remove membrane and membrane protein remnants and to improve its transparency. Fibres were washed twice in relaxing solution and the sarcomere length was checked again. The sarcomere diffraction signal was optimized by fine alignment of the He-Ne laser and a sarcomere length calibration was obtained as described above. The fibre was transferred to a trough containing calcium-free rigor solution for 10 min in which rigor tension developed. The fibre was transferred for 5 min into calcium-containing rigor solution and then for 7–10 min to a trough containing loading solution. Finally the fibre was transferred to the trough containing silicone fluid. The epifluorescence head of the microscope was lowered so that the objective lens made contact with the silicone fluid and the shutter for the fluorescence excitation light was opened. A few seconds later, a pulse of near-UV laser light illuminated the fibre to induce contraction by the photolytic release of ATP from caged ATP. At a predetermined time following photolysis (usually 0.4 s) an electrical signal was applied to the motor to cause shortening of the muscle fibre. The applied velocity of shortening varied from zero to 1.5 muscle lengths s⁻¹ (ML s⁻¹), where the muscle length is the central, iridescent portion of the fibre segment (see above). The extent of applied shortening was ∼161 μm, corresponding to a change in fibre length of 7.4 ± 0.1 % (n = 41, mean ± one standard error of the mean with n equal to the number of measurements), over which filament overlap increases from 93 to 100 %. At the end of the shortening phase, the epifluorescence microscope head was lifted, the fibre was transferred to relaxing solution and returned to its initial length, then transferred to rigor solution. The whole procedure was repeated up to five times with variations in the speed of the applied length change.

Derivation of ATPase activity from fluorescence measurements

ATPase activity was calculated from the change in fluorescence of the P_i-sensitive fluorescent protein MDCC-PBP diffused into the muscle fibre. The 400 μm-long centre section of the fibre segment was illuminated at 420 nm through the ×40 objective lens using the light from a tungsten lamp mounted in the epifluorescence mode on the ACM microscope as described previously (He et al. 1997, 1998a,b) where details of the filter sets are given. Background fluorescence was low because the muscle fibre was immersed in silicone fluid during these measurements. Fluorescence was collected by the objective and its intensity at 470 nm was measured by a photomultiplier tube (EMI 9924QB or 9824B) operating at 500 V cathode voltage and mounted above the fibre on the microscope head (He et al. 1997). Calibration procedures as well as the sensitivity and linearity of the measurements were described previously (He et al. 1997). The concentration of MDCC-PBP considered here is that of the active protein, ∼75 % of the total protein. This value was determined for each batch by P_i titration (He et al. 1997). As described in He et al. (1998b), the concentration of P_i and hence the rate of P_i release was derived from the fluorescence signal after subtraction of the fluorescence background, recorded during a period before the laser fired. The concentration of P_i released by the fibre was related to the amplitude of the fluorescence signal by:

(1)

where [P_i] was the concentration of P_i (mM) released in the fibre and indicated MDCC-PBP-bound P_i (mM), F_t was the amplitude of the fluorescence signal at time t, F_min was the fluorescence signal prior to photolytic release of ATP and F_max was the fluorescence signal when all the MDCC-PBP was saturated with P_i. F_t, F_min and F_max were in arbitrary units, which in practice were the photomultiplier tube voltages after amplification. The above relationship did not hold when the amount of P_i released was close to, or exceeded, the amount of MDCC-PBP in the fibre. The ATPase rate constant was derived from the gradient of the fluorescence signal calibrated in terms of P_i concentration.

Transient artefact caused by photolysis of caged ATP

A short-lived artefact (< 1 ms) was seen on some of the fluorescence, tension and motor traces at the time of the laser flash, and was caused by scattered light from the laser pulse being detected by the motor photodiode and the photomultiplier tube. A further light artefact present on the fluorescence signal immediately following photolysis was caused by a short-lived aci-nitro intermediate formed as an intermediate of NPE-caged ATP photolysis which absorbed light at 420 nm (Corrie et al. 1992). At 12°C, the aci-nitro intermediate decayed with a rate constant of ∼46 s⁻¹ (He et al. 1998a). The fluorescence traces after photolysis were corrected by adding to the signal a rising exponential process with a rate constant of 46 s⁻¹ starting at the time of the laser pulse, with an amplitude adjusted so that the lowest value for the fluorescence signal after correction was equal to the average of the fluorescence signal prior to photolysis (He et al. 1998b). The mean amplitude of the aci-nitro signal correction corresponded to 0.130 ± 0.005 mM P_i (n = 41) in the fluorescence signal, approximately 10 % of the total fluorescence change. This amplitude corresponds to that measured directly in control experiments in which fluorescence changes were observed following photolysis of NPE-caged ATP in the presence of MDCC-PBP saturated with P_i. Correction for absorption by the aci-nitro intermediate resulted in measurements of the initial ATPase rate constants during the first turnover which were 18 % slower than when the correction was not applied (see Fig. 1C). The correction was not applied in the work of He et al. (1997) as it was deemed small compared with the overall signal. Better characterization of the artefact now allows for systematic correction (He et al. 1998a,b). Absorption by the aci-nitro intermediate only affected ATPase measurements in the first 100 ms following photolytic liberation of caged ATP.

Effect of shortening

In experiments where muscle fibres were subjected to applied shortening, further geometric factors needed consideration: the effect of change in volume due to shortening, and the change in filament overlap.

It was assumed that fibres immersed in silicone fluid maintained a constant volume during shortening. However, the reduction in fibre length during shortening increased the proportion of the muscle fibre illuminated by the light used for excitation of MDCC-PBP fluorescence, in proportion to the extent of shortening, and consequently, an increase in the intensity of the fluorescence signal was recorded. Calculated from the extent of applied shortening, the fibre volume in the field of view after fibre shortening was, on average, 7.4 ± 0.1 % (n = 41) larger than before the shortening. Control experiments with relaxed muscle fibres containing 1.2 mM MDCC-PBP and >1.2 mM total P_i subjected to shortenings showed that an increase in fluorescence could be detected during the length change. For an applied shortening of 7 %, the fluorescence increased 6.1 % (n = 2). This effect was largely corrected for by the fact that F_max (eqn (1)) was measured for the fibre at the shorter sarcomere length.

A further change resulting from shortening fibres was the change in overlap between the thick and thin filaments during the experiments, which caused an increase in the fraction of actin-activated myosin heads. The sarcomere shortening of 7.4 % from 2.7–2.5 μm increased the fraction of myosin heads in the overlap region from 93 to 100 %, assuming full overlap at 2.6 μm and no overlap at 4.0 μm. The actin-activated active site concentration, namely the concentration of myosin subfragment 1 heads in the whole volume of the sarcomeres, at full overlap was 0.15 mM (He et al. 1997). If we consider that at full overlap, this concentration is that in the overlap region, the active site concentration changed from 0.14 to 0.15 mM in the course of the shortening. The ATPase rate constant during shortening was obtained by dividing the gradient of the fluorescence trace (expressed in mM s⁻¹) by the average of the active site concentration at the beginning and end of the shortening period, i.e. 0.145 mM. For the isometric phase prior to shortening, the ATPase rate in mM s⁻¹ was divided by the active site concentration prior to shortening (namely 0.14 mM) and, for the isometric phase following shortening, an active site concentration of 0.15 mM was used. In practice, the corrections for fibre volume and change in overlap were found to be small relative to the changes caused by shortening. Derivation of total energy utilization by the fibre, as used for computation of the fibre efficiency, did not require normalization of ATP hydrolysis per myosin head, and was not affected by the change in overlap.

RESULTS

Response to the photolytic release of ATP and to muscle shortening

Figure 1 shows an example of the experimental traces following the photolytic release of ATP from 5 mM NPE-caged ATP in a permeabilized muscle fibre of the rabbit psoas muscle in the presence of calcium and MDCC-PBP at 12°C. Prior to the laser pulse, the muscle fibre was in the rigor state in silicone fluid as the final incubation solution did not contain ATP. The panels in Fig. 1 show, from top to bottom, the overall fibre length, force, P_i bound to MDCC-PBP (derived from the intensity of the MDCC-PBP fluorescence signal) and sarcomere length (derived from the position of the first-order diffraction). Force (B) initially decreased as myosin heads detached, and then rose to an isometric plateau; 0.3 s after the laser flash, the motor hook moved at a steady velocity of 1.28 mm s⁻¹ (A), corresponding to 0.58 muscle lengths s⁻¹ (ML s⁻¹). Force decreased rapidly to reach a relatively steady level of 43 kN m⁻², 29 % of the isometric level. After the end of the shortening period, tension rose to an isometric level of 166 kN m⁻², 12 % higher than prior to the shortening phase, slightly higher than the increase of 7 % expected as a result of the increase in filament overlap.

The inset in Fig. 1C containing the MDCC-PBP fluorescence shows the observed signal at the time of the laser flash (thin line in the inset). The bold line in the inset shows how the trace was corrected when the transient increase in absorption caused by the appearance of the aci-nitro intermediate of NPE-caged ATP photolysis was taken into account (see Methods). The main panel C shows that fluorescence increased after the photolytic release of ATP. The rate of increase diminished with time during the isometric phase. When the fibre shortened, fluorescence increased more rapidly. After shortening, the rate of increase diminished again. The slowing of the fluorescence signal occurred even though considerable force development took place. This situation was markedly different from that at time zero, when both force and fluorescence increased rapidly. The fluorescence signal continued to rise until saturation of MDCC-PBP with P_i. The tight binding of P_i to MDCC-PBP ensures that the fluorescence rise remains linearly related to P_i concentration until close to saturation (He et al. 1997). Once MDCC-PBP was saturated, further ATP hydrolysis was not reported by the fluorescence signal even though P_i generation continued.

The line segments in Fig. 1C are linear regressions to parts of the fluorescence signal from which the ATPase rate constants were derived. During the first turnover of the ATPase, namely for P_i < 0.14 mM, the concentration of active sites for a fibre at a sarcomere length of 2.7 μm, the rate was 1.67 mM s⁻¹. During the isometric phase prior to shortening and during the shortening phase, the ATPase rates were 1.04 and 2.46 mM s⁻¹, respectively.

In Fig. 1D, regression lines to the sarcomere length during the first turnover of the ATPase and during the shortening period show the initial shortening to occur at 0.15 ML s⁻¹ and 0.69 ML s⁻¹, respectively. The slow drift in the sarcomere signal after the period of shortening is probably caused mainly by deterioration of the sarcomere signal, rather than by actual shortening (see Methods).

Figure 2 shows one experiment in which three consecutive contractions were elicited by photolysis of NPE-caged ATP in a single muscle fibre segment. Unusually, an adequate sarcomere signal was maintained throughout each contraction of this fibre. For each of the three consecutive contractions (a, b, c), shortening of the fibre was induced by motor movements at speeds of 0.91, 0.46 and 1.41 mm s⁻¹, and which correspond to 0.40, 0.20 and 0.61 ML s⁻¹, respectively. The isometric tensions prior to the release (P_o) were 219, 207 and 227 kN m⁻², respectively, and during the shortening period, force dropped to P/P_o values 0.40, 0.74 and 0.26 of the respective isometric values. The fluorescence signal (after correction for the initial aci-nitro transient) shows remarkable reproducibility in the first 0.4 s following the photolytic release of ATP. The ATPase rate constants in the first turnover were 13.8, 14.4 and 14.3 s⁻¹ for an active site concentration of 0.14 mM. Immediately prior to the shortening phase, the ATPase rate constants were 6.1, 5.6 and 6.4 s⁻¹, respectively. During shortening, the ATPase rate constants were 6.0, 11.5 and 13.7 s⁻¹, respectively, calculated for an active site concentration of 0.145 mM, the average concentration of myosin heads in the overlap region during the shortening phase. Immediately following the photolytic release of ATP the sarcomeres shortened slightly, probably at the expense of the damaged ends of the muscle segments. During the periods of applied shortening, the sarcomere signal reported shortening velocities of 0.51 (a), 0.23 (b) and 0.57 (c) ML s⁻¹, compared with imposed shortening velocities of 0.40, 0.20 and 0.61 ML s⁻¹, respectively, as reported above.

In a series of 41 measurements, the mean isometric force prior to the period of applied shortening was 190 ± 6 kN m⁻² (range 101 to 292 kN m⁻²). This value is 17 % less than the value of 230 ± 11 kN m⁻² reported by He et al. (1998b) at a sarcomere length of 2.4 μm and 15°C under otherwise identical conditions. Taking the standard errors into account, the measurements here are 6.5 to 28 % less than the value of 230 kN m⁻². For a linear length-tension relation in permeabilized fibres, force should be 7 % less at a sarcomere length of 2.7 μm than at 2.4 μm.

The time course of force development following the photolytic release of NPE-caged ATP was examined. The time course was fitted by three exponential processes after normalization of the force rise so that the isometric force level immediately prior to the shortening ramp was assigned a value of 1. The initial rate of force decrease, attributed to initial cross-bridge detachment, was fitted by a rate constant of 243 s⁻¹ (s.d.= 130 s⁻¹, n = 12), with an amplitude equal to the average rigor force (25 % of the final isometric level). The subsequent rate of tension rise was described by two rate constants of 17.2 s⁻¹ (s.d.= 2.5 s⁻¹) and 2.6 s⁻¹ (s.d.= 0.5 s⁻¹) while the amplitude of the faster phase of tension rise was, on average, 96 % of the total rise. The determination of the rate constant describing the initial decrease in force suffers from the jerk in the tension trace which often accompanies the laser flash. The time course of force redevelopment following the period of shortening was consistently fitted by a single exponential process with a rate constant of 20.7 s⁻¹ (s.d.= 2.4 s⁻¹, n = 11). The rate of force redevelopment is close to the fast phase of force development following the photolytic release of ATP. The rate of force redevelopment did not appear to depend on the force level reached at the end of the shortening phase.

The ATPase rate constant during the first turnover was 10.3 ± 0.3 s⁻¹ (s.d.= 2.2 s⁻¹; n = 41) for an active site concentration of 0.14 mM. The mean ATPase rate constant in the period immediately prior to the period of applied length change was 5.1 ± 0.2 s⁻¹ (s.d.= 1.2 s⁻¹).

Sarcomere length change at the beginning of the contraction

Figures 1 and 2 show that the sarcomere length changes in the few hundred milliseconds following photolytic release of ATP, in spite of attempts to reduce the fibre compliance by glutaraldehyde fixation of the fibre ends. The velocity of sarcomere length change during the first turnover is shown in Fig. 3. In 9 of 29 measurements where the sarcomere signal was reliable, the sarcomeres were found to lengthen. On average, the sarcomere length changed during the first turnover of the ATPase with a mean velocity of 0.09 ± 0.03 ML s⁻¹ (n = 29) in the direction of sarcomere shortening, covering a range of velocities from 0.50 to −0.15 ML s⁻¹ (i.e. lengthening) and a median shortening velocity of 0.07 ML s⁻¹. During the first turnover the ATPase rate constant averaged 10.7 ± 0.4 s⁻¹ (n = 29) for these fibres when referred to an active site concentration in the overlap region of 0.14 mM. By comparison, the mean shortening velocity immediately prior to the period of rapid shortening was 0.05 ± 0.01 ML s⁻¹ (n = 29) with a median value of 0.04 ML s⁻¹.

Figure 3. Relationship between sarcomere shortening velocity and the ATPase rate during the first turnover following photolytic release of ATP.

The ATPase rate was calculated in 29 experiments from the rate of change of MDCC-PBP fluorescence. The mean ATPase rate was 10.7 ± 0.4 s⁻¹. Sarcomere velocity was determined from the rate of change in position of the first-order diffraction spot during the same period. Sarcomeres were found to shorten in 20 cases and to lengthen in 9 cases during the first turnover, with a mean velocity of 0.09 ± 0.03 ML s⁻¹ in the direction of shortening.

Comparison of the extent of shortening reported by the motor and sarcomere length signals during shortening

Figure 4 shows the measured sarcomere shortening velocity as a function of the shortening velocity applied to the fibre by movement of the motor, for 15 experiments where the sarcomere signal was maintained during the period of shortening. The linear fit through the data is shown (constrained through the origin). The gradient is 1.09 ± 0.05 (mean ± one standard error of the mean) for twelve degrees of freedom. Data for applied shortening faster than 1 ML s⁻¹ were not included in the regression as muscle fibres may have been slack at these high shortening velocities. These results show that the applied length changes were faithfully reflected in the sarcomere signal, for the fibres where a sarcomere signal was recorded. Most of the data in Fig. 4 were obtained for the first shortening to which each fibre was subjected, as in subsequent shortenings the sarcomere signal was more diffuse. The implication of these results is that compliance of the muscle fibre ends during shortening does not markedly affect our measurement of the shortening velocity.

Figure 4. Relationship between the applied velocity of shortening and the sarcomere shortening velocity measured from the rate of change of the position of the first-order diffraction spot.

The straight line is the regression line constrained through the origin for all data points for applied shortening velocities of < 1 ML s⁻¹. The gradient of the line is 1.09 ± 0.05 (n = 12).

Effect of the timing of the shortening phase

We compared the shortening velocity and ATPase rates obtained for shortening periods applied either 0.2 or 0.4 s after the photolytic release of ATP (Fig. 5). The isometric tension values prior to the shortening phase were 215 and 223 kN m⁻², respectively. P/P_o values during the shortening were 0.364 and 0.375, respectively. The ATPase rate constants for the first experiment, measured by linear regression as described above (Fig. 1), were 11.8, 7.3 and 17.5 s⁻¹ during the first turnover, immediately prior to the shortening phase and during shortening, respectively. In the second contraction, the respective ATPase rate constants were 12.9, 6.4 and 16.4 s⁻¹. When compared with the ATPase rate before shortening, the ATPase rate increased during shortening by factors of 2.40 and 2.56 in the first and second contractions, respectively. The higher increase in ATPase rate during the second contraction is explained by some gradual slowing of the ATPase rate during the isometric phase. The experiment demonstrated that the timing of the shortening phase has little effect on the shortening velocity or on the ATPase rate during shortening. It also showed that the force level and the ATPase rate during the period immediately prior to the shortening phases changed by less than 15 % in the period 0.2–0.4 s after the photolytic release of ATP, indicating that a near-steady state was reached, a situation markedly different from observations at a sarcomere length of 2.4 μm (He et al. 1997), where no steady phase in the ATPase was seen. This effect of sarcomere length is demonstrated later.

Figure 5. Time course of tension and fluorescence change in response to shortening periods imposed at different times.

Two consecutive contractions initiated by photolytic release of ATP are shown. In the first contraction, a period of shortening at a velocity of 0.50 ML s⁻¹ was applied 0.2 s after the photolytic release of ATP. In the second contraction, the shortening period at the same velocity was applied 0.4 s after photorelease. The amplitude of the shortening was 8.3 % of the fibre length in each case. Fibre dimensions: cross-sectional area 5.0 × 10⁻⁹ m², initial length of fibre segment 1.96 mm, initial sarcomere length 2.7 μm. The sarcomere signals for this fibre were too diffuse to be meaningful and are not shown.

Force-velocity curve and power output

The applied shortening velocity had a marked effect on the tension level during shortening (Fig. 2). This force-velocity relationship is shown in Fig. 6. The force level was calculated as the average force obtained once the initial force decrease had ended. The force-velocity relationship was fitted with Hill's hyperbolic equation (1938):

where P was the force during shortening at a shortening velocity V. P_o, the force level immediately prior to shortening, was 190 kN m⁻². The maximal shortening velocity (at P = 0), V_max=bP_o/a, and a and b were constants to the hyperbola. The fit gave a/P_o= 0.42, b = 0.51 and V_max= 1.21 ML s⁻¹. The data obtained for applied shortening velocities of 1.3 and 1.53 ML s⁻¹ were not included in the fit as the fibres may have been slack during the shortening period.

Figure 6. Relationship between the applied shortening velocity and force, measured from the average value during the phase of steady shortening.

The thin line was a fit to Hill's force-velocity relationship as described in the text, using for P_o the mean value for all fibres of 190 kN m⁻², with best-fit values of 0.42 and 0.51 for a/P_o and b, respectively, giving an extrapolated maximal shortening velocity of 1.21 ML s⁻¹ at P = 0. The thick line is the best fit according the theory of A. F. Huxley (1957) as explained in the text, with f₁= 20.7 s⁻¹, g₁= 118 s⁻¹ and g₂= 342 s⁻¹.

The relationship was also fitted according to the theory of A. F. Huxley (1957) where f₁, g₁ and g₂ are rate constants for myosin head attachment, for myosin head detachment in regions of positive strain (in the direction of shortening) and for myosin head detachment in regions of negative strain, respectively, using the equation:

where h is the myosin head attachment range and s is the sarcomere length (Simmons & Jewell, 1974). Using s = 2.55 μm and h = 9 nm (Goldman & Huxley, 1994), a value for f₁=k₂= 20.7 s⁻¹, the rate constant describing force redevelopment following shortening as a reasonable estimate for the rate of myosin head attachment, and V_max= 1.21 as derived from Hill's force-velocity curve giving g₂=V_maxs/h = 342 s⁻¹, a best fit was obtained for g₁ of 118 s⁻¹.

The mechanical power produced by the fibres at a given shortening velocity given by P×V is plotted in Fig. 7, together with the power curve calculated from the best fit to the force-velocity relationship. Maximum power of 28 W l⁻¹ was achieved at a shortening velocity of 0.42 ML s⁻¹ and P/P_o of 0.35. The scatter in the data shown in Figs 6 and 7 is in part a consequence of the imprecision in the value for fibre cross-sectional area based on the microscopical measurement of fibre depth and width.

Figure 7. Relationship between the power output and the applied shortening velocity.

The power output was obtained by multiplying the average force during the shortening period by the average shortening velocity. The power (W) is force (N) × velocity (m s⁻¹). Here we used force in kN m⁻² and shortening velocity in ML s⁻¹, where ML had dimensions of reciprocal length, so that power was kN m⁻²× m⁻¹ s⁻¹, or kN m⁻³ s⁻¹, corresponding to N l⁻¹ s⁻¹, namely W l⁻¹. The continuous line was calculated from the values of a/P_o and b obtained from the fit to the force-velocity relationship in Fig. 6.

ATPase rate as a function of shortening velocity

The relationship between the ATPase rate constant and the shortening velocity is shown in Fig. 8. The ATPase rate in the isometric fibres, immediately prior to the phase of applied shortening (V = 0) was 0.71 ± 0.02 mM s⁻¹ (n = 41), corresponding to 5.1 ± 0.2 s⁻¹ for 0.14 mM active sites. As mentioned above, the fibres are not in a true isometric state at this time because some sarcomere shortening still takes place, at a mean velocity of 0.04 ML s⁻¹. The ATPase increased approximately linearly with shortening velocity up to 0.6 ML s⁻¹ and appeared to plateau at higher velocities. The maximal ATPase rate for applied shortening velocities of 1 ML s⁻¹ and above was 18.5 ± 0.6 s⁻¹ (n = 3), after considering that the average sarcomere length during shortening resulted in an active site concentration of 0.145 mM (see Methods). The ATPase activity during fast shortening was 3.6-fold greater than during isometric contraction. There was no evidence of a decrease in ATPase rate at high shortening velocities. A hyperbola is shown through the data to describe the relationship (see legend to Fig. 8).

Figure 8. Relationship between the ATPase rate constant and the applied shortening velocity.

The ATPase rate constant was obtained from the gradient of the fluorescence signal during the shortening period, as described for Fig. 1, and was divided by the mean active site concentration during the shortening phase, namely 0.145 mM. These data are shown as the filled circles. The square symbol at a shortening velocity of zero was the mean rate constant obtained for the nominally isometric phase immediately prior to the shortening phase (5.1 ± 0.2 s⁻¹, n = 41). The error bars are shown inside the square symbol. The continuous line is the best fit of the data to a hyperbola corresponding to the equation:

where V is the applied shortening velocity in ML s⁻¹, 5.1 s⁻¹ is the ATPase rate constant in the isometric state and 18.7 s⁻¹ is the ATPase rate constant above that in the isometric state for shortening at infinite velocity.

Efficiency of muscle contraction

The ratio of power output to the energy released by ATP hydrolysis is shown in Fig. 9, using 50 kJ mol⁻¹ for the free energy of ATP hydrolysis (Kushmerick & Davies, 1969; Woledge et al. 1985). This value was obtained from the free energy of phosphocreatine breakdown in muscle under in vivo conditions, and may be lower than the correct value for our experimental conditions where P_i concentration is low. Efficiency was zero where no work was performed, namely during isometric contraction or shortening at zero load.

Figure 9. Relationship between the efficiency of contraction and the applied shortening velocity.

The efficiency of contraction is the ratio of energy output and energy input. Energy output (in W l⁻¹) is the data shown in Fig. 7. Energy input is the ATP consumed (in mM s⁻¹) multiplied by the free energy of hydrolysis (50 kJ mol⁻¹). The energy input can be converted from the data shown in Fig. 8 by multiplying the rate constant by the mean active site concentration of 0.145 mM. The continuous line is that calculated by obtaining the ratio of the calculated relationships in Figs 7 and 8. From the continuous line, a maximal efficiency of 0.36 is obtained at 0.27 ML s⁻¹, corresponding to P/P_o= 0.51.

Using the hyperbolic fit shown in Fig. 8, and the relationship for power output derived from Hill's force- velocity curve, a mean efficiency curve was calculated. This is shown as the continuous line in Fig. 9. From this curve, a maximal efficiency of 0.36 was derived at a shortening velocity of 0.27 ML s⁻¹, corresponding to P/P_o= 0.51.

Effect of temperature and sarcomere length on the ATPase rate constant in the first turnover

The ATPase rate constant measured after the photolytic release of ATP has been found to decrease with time (He et al. 1997) and with the amount of ATP hydrolysed (He et al. 1998b). The decrease was found to be affected by the sarcomere length, since in experiments at long sarcomere length the ATPase rate appears to reach a relatively constant value after an initial rapid phase (see Figs 1, 2 and 5). We investigated the time course of the ATPase at sarcomere lengths of 2.4 and 2.7 μm. In Fig. 10, tension (A), fluorescence change (B) and ATPase rate constants (C) are shown in a series of experiments. It can be seen from panel B that, at a sarcomere length of 2.7 μm, the fluorescence shows a break in its time course approximately 0.2 s after photolytic release of ATP, whereas at a sarcomere length of 2.4 μm there is no such break: the ATPase rate decays continuously. This difference is emphasized in C where the ATPase rate constant was obtained by calculating the gradient of the fluorescence signal (B) over 60 ms periods. At a sarcomere length of 2.7 μm, the ATPase rate constant remains almost unchanged from 0.2 to 0.6 s after photolytic release of ATP, whereas at a sarcomere length of 2.4 μm the ATPase rate constant decays continuously. Although it is initially faster than at 2.7 μm, it becomes slower after ∼0.5 s and the two traces cross over. The period of constant ATPase rate is a feature of the conditions used here (2.7 μm and 12°C). At the same sarcomere length, but at 15°C, the period of steady ATPase rate is not so clear (data not shown). The ATPase rate in the first turnover is also sensitive to temperature. At a sarcomere length of 2.4 μm, the ATPase rate increased from 15.2 ± 0.7 to 19.8 ± 2.2 s⁻¹ (n = 5) when temperature was raised from 12 to 15°C. At a sarcomere length of 2.7 μm, the same temperature rise caused the ATPase rate constant during the first turnover to increase from 10.5 ± 1.0 to 15.4 ± 1.8 s⁻¹ (n = 5). A temperature rise of only 3°C increases the rate constants by factors of 1.3 and 1.47 for sarcomere lengths of 2.4 and 2.7 μm, respectively.

Figure 10. Relationship between force, P_i release and the ATPase rate constant at sarcomere lengths of 2.4 and 2.7 μm.

Muscle fibres at 12 °C were exposed to photolytically released ATP from NPE-caged ATP as described previously. The initial sarcomere length was either 2.4 μm (a, thin lines) or 2.7 μm (b, thick lines). The data shown are the mean of five experiments (2.4 μm) and three experiments (2.7 μm). Experiments at 15 °C were also carried out in the same fibres, but these results are not shown, although the ATPase rate constants in the first turnover are given in the text. Tension is shown in A and the concentration of P_i bound to MDCC-PBP is shown in B, as calculated from the fluorescence signal, after correction for the aci-nitro decay. The derivative of the fluorescence signal is shown in C, by calculating the gradient of the fluorescence signal over 60 ms periods, and by dividing the gradient by the active site concentration (0.14 mM for 2.7 μm and 0.15 mM for 2.4 μm). The derivative is much noisier than the fluorescence data, particularly near time 0, where the flash artefact greatly perturbs the time course. It can be seen that at 2.7 μm, the ATPase rate constant remains relatively constant between 0.2 and 0.6 s, at 5.2 s⁻¹.

DISCUSSION

The ATPase rate constant during the first turnover of the ATPase

The experiments were carried out on muscle fibres which had been treated with Triton X-100 as well as permeabilized by treatment with glycerol. In consequence, the ATPase activity remaining in the muscle fibre is attributed solely to that of the actomyosin, as was shown previously (He et al. 1997) on the basis of its sarcomere length dependence, Ca²⁺ sensitivity and resistance to sarcoplasmic ATPase inhibitors. At 12°C, the mean ATPase rates during the first turnover were 10.3 s⁻¹, when referred to an active site concentration of 0.14 mM, at a sarcomere length of 2.7 μm and 15.2 s⁻¹ at 2.4 μm. This latter value is slightly lower than that reported earlier (18.8 s⁻¹) for psoas muscle fibres at 12°C and a sarcomere length of 2.4 μm, referred to an active site concentration of 0.15 mM (He et al. 1997). At 15°C and a sarcomere length of 2.4 μm, the ATPase rate during the first turnover (19.8 s⁻¹) is lower than the value of 31.5 s⁻¹ reported by He et al. (1998b). The high temperature sensitivity of the ATPase in this range and possible variations between fibres may explain this difference.

Decay of the ATPase rate constant following photolysis of caged ATP

He et al. (1997, 1998b) reported a high initial ATPase rate which gradually declines during the first few hundred milliseconds following the photolytic release of ATP in isometrically contracting muscle fibres. He et al. (1998b) showed that the ATPase rate constant decayed gradually with time for both soleus and psoas muscle fibres, and that the decay was less marked in the presence of ADP. We show here that the decay in the ATPase rate constant depends on experimental conditions, in that, at a long sarcomere length (2.7 μm) and at 12°C, a period is seen during which the ATPase rate constant remains relatively constant, as reported previously (Fig. 7 of He et al. 1997). Here, we use the period of steady ATPase to apply length changes, and to study the corresponding changes in ATPase rate. The conditions are therefore useful in that the observed changes in response to shortening are largely independent of the time when the shortening was applied. The difference in behaviour seen at short and long sarcomere lengths in rabbit fibres may be related to the extent and the time course of fibre shortening seen at different lengths.

Relationship between the ATPase rate constant during the first turnover, in the isometric state and that seen during filament sliding

We investigate below the effect of sarcomere shortening on the ATPase rate in the early phases of contraction, when the fibre length is constant. The high ATPase rate seen previously during the first turnover (He et al. 1997, 1998b) was not thought to be attributable to sarcomere shortening in the initial phases of contraction, but in those experiments sarcomere length measurements were not performed. Here, we show sarcomere length measurements from the same region of the fibre from which fluorescence signals are obtained. Although the diffraction signal indicated that sarcomere length changes occurred following the photolytic release of ATP, the signal was variable, sometimes showing either lengthening or shortening. In most cases, the velocity of sarcomere shortening was slow and would not be expected to cause a large acceleration in the ATPase rate, unlike that seen in response to applied shortening. For shortening to account for the ATPase rate in the first turnover, it can be calculated from the hyperbola in Fig. 8 that the shortening velocity during the first turnover should be 0.22 ML s⁻¹. The mean of the data in Fig. 3 (0.09 ML s⁻¹) argues against this possibility. However, the hyperbola in Fig. 8 shows that shortening at a velocity of 0.09 ML s⁻¹ during the nominally isometric phase of contraction is accompanied by an ATPase rate of 8 s⁻¹, 22 % less than the measured value of 10.3 s⁻¹. The difference between the observed ATPase rate constant and the ATPase rate constant which can be explained by a period of shortening is therefore small and it cannot be excluded that our sarcomere measurements fail to report precisely the nature of sarcomere shortening in the field of view. For example, the laser diffraction signal provides a mean shortening velocity, but the presence of a small fraction of rapidly shortening sarcomeres may increase the ATPase rate and not be detected by our apparatus. It may also be that some sarcomere jitter, or individual sarcomeres shortening rapidly at the expense of their neighbours accounts for an increase in ATPase rate. More recent experiments using video-microscopy of muscle fibres during experiments have confirmed the accuracy of our laser diffraction method, but do not improve the spatial resolution of the measurements and do not exclude local shortening.

However, if the ATPase rate during the first turnover was higher than in the steady state because of transient shortening, the mean shortening velocity during the first turnover (0.09 ML s⁻¹, n = 29) would cause an increase in the ATPase rate from 5.1 to 8.0 s⁻¹ (calculated from the hyperbola to the data shown in Fig. 8). This value is less than the actual ATPase rate in the first turnover (10.7 s⁻¹) 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⁻¹. 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⁻¹ for nominally isometric fibres corresponds to shortening at 0.05 ML s⁻¹, but extrapolation of the hyperbola in Fig. 8 to an extension velocity of 0.05 ML s⁻¹ results in an ATPase activity of 3.1 s⁻¹. 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 (18.7/5.1) to 6.0 (18.7/3.1).

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 P_i 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⁻¹ 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⁻¹) is 2–5 times faster than that measured by others, e.g. 1.27 s⁻¹ in the presence of 3 mM P_i at 10°C (Cooke et al. 1988), 1.8 s⁻¹ at 15°C (Glyn & Sleep, 1985) and 2.1 s⁻¹ 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 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 V_max is 3–4 times higher than that immediately prior to the period of applied shortening (5.0 vs. 18.5 s⁻¹), similar to the 2.7-fold 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 a/P_o, although combinations of the values for (f₁+g₁) or for g₂ also describe it (Simmons & Jewell, 1974). The value for a/P_o of 0.42 is higher (force-velocity relationship is less curved), and V_max is lower than that found by others under similar conditions. For example Cooke et al. (1988) obtained 0.23 and 1.6 ML s⁻¹ for a/P_o and V_max, respectively, at 10°C and Sweeney et al. (1988) obtained V_max of 2.1 ML s⁻¹ 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 mM or less (Thirlwell et al. 1995). The 3.5 mM 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 a/P_o found here compared with that in the literature. Using the same preparation at 10°C and the same technique, He et al. (1998a) obtained a value for a/P_o 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 V_max obtained by extrapolation (1.45 ML s⁻¹), and because the initial sarcomere length was 3.0 μm, where resting tension contributes to the restoring force during shortening.

A difference between our work and that of others is that here the presence of MDCC-PBP results in a low concentration of P_i during the measurements (< 1 μm). However, Cooke et al. (1988) showed that in the concentration range 3–20 mM, P_i did not alter a/P_o or V_max, although an effect of P_i on a/P_o and V_max is possible at P_i < 3 mM. However, isometric force is sensitive to P_i concentration (Pate et al. 1998), thus explaining the high isometric force obtained here at low P_i concentration (< 1 μm) compared with that where P_i is not removed from the experimental solution (e.g. 124.5 kN m⁻² in Sweeney et al. 1988 compared with 190 kN m⁻² here).

Power output and efficiency of contraction

The maximal power output of 28 W l⁻¹ measured here at 12°C is higher than that measured at the same temperature in rat fast muscle fibres (9.6 W l⁻¹; Reggiani et al. 1997) or in human type IIB fibres (3.5 W l⁻¹; Bottinelli et al. 1996). Potma & Stienen (1996) measured ∼20 W l⁻¹ at a shortening velocity of 1 ML s⁻¹ 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⁻¹, dropping to less than 13 W l⁻¹ at 10°C, with a Q₁₀ 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⁻¹. 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 P_i in the solution. In our work the P_i concentration was very low (< 1 μm) 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 P_i 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 mM P_i 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 μm.

Step size, duty ratio and myosin head interaction distance with actin

The maximum ATPase rate of 18.5 s⁻¹ at 12°C is comparable to that obtained by Ma & Taylor (1994) in shortening myofibrils of rabbit psoas muscle at 20°C (22 s⁻¹), but faster than their value at 10°C (6.5 s⁻¹). The direct measurement of the ATPase in shortening muscle fibres obtained here can be used to estimate the distance travelled by myosin heads for each ATP hydrolysed. At V_max, 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, is given by d =V/k where V is the shortening velocity (in nm s⁻¹) and k is the maximum myosin head cycling rate (18.5 s⁻¹). For V_max= 1.21 ML s⁻¹ at 12°C and a sarcomere length of 2.7 μm, each half-sarcomere shortens at 1633 nm s⁻¹, giving a myosin head travel distance of 88.3 nm per ATP (1633/18.5). 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 (9/88.3) (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 P_i), 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.