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

8978 

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 

effectsoftendonelasticityandofATPhydrolysisdueto 

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 PÅ-1- 

Journal of Physiology (1999), 517.3, pp. 839—854 839 

The efficiency of contraction in rabbit skeletal muscle fibres, 

determined from the rate of release of inorganic phosphate 

Zhen-He He, Rodney K. Chillingworth, Martin Brune, John E. T. Corrie, 

Martin R. Webb and Michael A. Ferenczi 

National Institute for Medical Research, The Ridgeway, Mill Hill, London NW7 1AA, UK 

(Received 18 November 1998; accepted after revision 26 February 1999) 

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 PÅ-1-(2nitrophenyl)ethyl 

ester of ATP (NPE-caged ATP). Inorganic phosphate (Pé) 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 Pé during each phase of 

contraction. The ATPase rate was 10·3 s¢ immediately following release of ATP and 5·1 s¢ 

during the isometric phase prior to the applied shortening. It rose hyperbolically with 

shortening velocity, reaching 18·5 s¢ at a maximal shortening velocity > 1 ML s¢ (muscle 

lengths s¢). 

4. Sarcomeres shortened at 0·09 ML s¢ immediately following the photolytic release of ATP 

and at 0·04 ML s¢ 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¢. Assuming the free energy of 

hydrolysis is 50 kJ mol¢, 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¢, 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 

filamentsatanyonetime. 

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(2-nitrophenyl)ethyl ester of ATP (NPE-caged ATP; 

Ferenczi et al. 1984) in the presence of a saturating 

concentration of calcium (32 ìÒ). 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 (Pé) 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, Pé 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,

840 

1998). The labelled protein, MDCC-PBP, binds Pé 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 1Ï3 of that under zero load (Vmax)(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 Pé 

binds tightly to MDCC-PBP, the Pé concentration during the 

measurement period is low (< 1 ìÒ) compared with that 

found in vivo (•1 mÒ). We discuss the role of Pé 

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 

moresignificantinthelightoftheexperimentsofHeet 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 3·0ìm 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 ìm, 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 COµ followed by 

exsanguination, according to Home Office guidelines. The bundles 

Z.-H. He and others 




J. Physiol. 517.3 

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 crosssectional 

area of 6·7 ² 10¦Í mÂ (s.d. = 2·0 ² 10¦Í mÂ for 16 fibres) 

with a range of 4·1 ² 10¦Í to 11·9 ² 10¦Í mÂ. 

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 100ìmdiameter 

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. 2inHeet al. 1998a) which was constructed from a 

commercial loudspeaker coil (RS Components, Corby, UK, 8 Ù, 

40 mm diameter) allowed the application of length changes of up to 

1 mm in 1 ms. Smaller steps (up to 50 ìm) were complete in 0·2 ms. 

Fibre troughs and laser-flash photolysis 

The muscle fibres were incubated in one of a set of six 20 ìl troughs 

(2mm²10mm²1mm) cut into a circular, stainless steel, 

temperature-controlled rotating stage (see Fig. 1inHeet 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 ²8mm²0·5mm) toallow 

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 200Ï10cs, 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 mÒ ATP in a fibre pre-incubated with 5 mÒ NPE-caged ATP 

and immersed in silicone fluid, as determined previously (He et al. 

1997). 

Sarcomere length measurements 

A5mm-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

J. Physiol. 517.3 Efficiency of muscle contraction 

841 

obtained from Coherent-Ealing Ltd, Watford, UK) and focused by 

a60mm 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 ìm, 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 biconvex 

cylindrical lens (40 mm FL made up of two plano-convex 

80 mm FL lenses) was used to collect each diffracted beam and to 

focusittoaspotontooneoftwo9mm-long position-sensitive 

photodiodes (PS-100-10; Quantrad, Santa Clara, CA, USA). An 

electrical signal was obtained from each edge of the positionsensitive 

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 ìm 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 ² 40 0·75 NA water-immersion objective lens 

and a ² 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 ìm to 2·64 ìm. 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 

Pé 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 Ò. The pH was adjusted to 7·1 at 20 °C. Care was taken to 

minimize contamination of the solutions with Pé. 

Relaxing solution consisted of 60 mÒ TES, 10 mÒ EGTA, 1 mÒ 

free Mg¥, 5 mÒ MgATP (6·2 mÒ total ATP), 10 mÒ glutathione, 

with ionic strength adjusted with potassium propionate. Calciumfree 

rigor solution was identical to relaxing solution, except for the 

omission of ATP and contained 4 units ml¢ apyrase (Martin & 

Barsotti, 1994; He et al. 1997) to remove ADP contamination in the 

fibre and ‘Pé-mop’ (namely 1 mÒ 7-methylguanosine, 0·5 units ml¢ 

purine nucleoside phosphorylase) to remove Pé contamination 

(Brune et al. 1994). Calcium-containing rigor solution was identical 

to calcium-free rigor except that the free calcium concentration was 

32 ìÒ achieved by addition of Ca-EGTA and there was no apyrase 

and no Pé-mop. Loading solution contained 60 mÒ TES, 10 mÒ 

EGTA, 1 mÒ free Mg¥, 40 mÒ glutathione, 32 ìÒ free Ca¥, 

1·2 mÒ MDCC-PBP, 5 mÒ NPE-caged ATP (pre-treated with 

10 units ml¢ apyrase to remove ADP contamination: the final 

apyrase concentration in the loading solution was 0·0013 units ml¢), 

10 mÒ creatine phosphate, 4 mg ml¢ creatine kinase obtained 

from chicken breast (338 units mg¢ at pH 7·1 and 25 °C; Bershitsky 

et al. 1996) and Pé-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 ìm 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 nonfixed 

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¦Â, s.d. =40kNm¦Â, 

n= 41), was 17% lower than at 2·4 ìm 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 Pé. 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 ìm, respectively, as is the case for rat fastand 

slow-twitch muscles (Page & Huxley, 1963; Stephenson & 

Williams, 1982). Each fibre was incubated for 30 min in relaxing 

solution containing 1 % (vÏv) 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

842 

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¢ (ML s¢), where the muscle length is the 

central, iridescent portion of the fibre segment (see above). The 

extent of applied shortening was •161 ìm, 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 Pé-sensitive fluorescent protein MDCC-PBP diffused into the 

muscle fibre. The 400 ìm-long centre section of the fibre segment 

was illuminated at 420 nm through the ² 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 

500V 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 Pé titration 

(He et al. 1997). As described in He et al. (1998b), the concentration 

of Pé and hence the rate of Pé release was derived from the 

fluorescence signal after subtraction of the fluorescence background, 

recorded during a period before the laser fired. The concentration of 

Pé released by the fibre was related to the amplitude of the 

fluorescence signal by: 

[Pé] = (Ft − Fmin) ² [MDCC-PBP]Ï(Fmax − Fmin), (1) 

where [Pé] was the concentration of Pé (mÒ) released in the fibre and 

indicated MDCC-PBP-bound Pé (mÒ), Ft wastheamplitudeofthe 

fluorescence signal at time t, Fmin was the fluorescence signal prior 

to photolytic release of ATP and Fmax was the fluorescence signal 

when all the MDCC-PBP was saturated with Pé. Ft, Fmin and Fmax 

were in arbitrary units, which in practice were the photomultiplier 

tube voltages after amplification. The above relationship did not 

hold when the amount of Pé 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 Pé 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 acinitro 

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¢ (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¢ 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 mÒ Pé (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 Pé. 

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 acinitro 

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 mÒ 

MDCC-PBP and >1·2 mÒ total Pé 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 Fmax (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 actinactivated 

myosin heads. The sarcomere shortening of 7·4 % from 

2·7—2·5 ìm increased the fraction of myosin heads in the overlap 

region from 93 to 100 %, assuming full overlap at 2·6 ìm and no 

overlap at 4·0 ìm. 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 mÒ (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 mÒ in the course of the shortening. The ATPase 

rate constant during shortening was obtained by dividing the 

gradient of the fluorescence trace (expressed in mÒ s¢) by the 

average of the active site concentration at the beginning and end of


843 

the shortening period, i.e. 0·145 mÒ. For the isometric phase prior 

to shortening, the ATPase rate in mÒ s¢wasdividedbytheactive 

site concentration prior to shortening (namely 0·14 mÒ) and,for 

the isometric phase following shortening, an active site 

concentration of 0·15 mÒ 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 mÒ NPEcaged 

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. 1show,fromtopto 

bottom, the overall fibre length, force, Pé 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¢ (A), corresponding 

to 0·58 muscle lengths s¢ (ML s¢). Force decreased rapidly 

to reach a relatively steady level of 43 kN m¦Â, 29 % of the 

isometric level. After the end of the shortening period, 

tension rose to an isometric level of 166 kN m¦Â, 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 Pé. The tight binding of Pé to 

MDCC-PBP ensures that the fluorescence rise remains 

linearly related to Pé 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 Pé 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 Pé < 0·14 mÒ, the concentration of 

active sites for a fibre at a sarcomere length of 2·7 ìm, the 

rate was 1·67 mÒ s¢. During the isometric phase prior to 

shortening and during the shortening phase, the ATPase 

rates were 1·04 and 2·46 mÒ s¢, 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¢ 

and 0·69 ML s¢, 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¢, and 

which correspond to 0·40, 0·20 and 0·61 ML s¢, respectively. 

The isometric tensions prior to the release (Pï) were 219, 

207 and 227 kN m¦Â, respectively, and during the 

shortening period, force dropped to PÏPï 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¢ for an active 

site concentration of 0·14 mÒ. Immediately prior to the 

shortening phase, the ATPase rate constants were 6·1, 5·6 

and 6·4 s¢, respectively. During shortening, the ATPase 

rate constants were 6·0, 11·5 and 13·7 s¢, respectively, 

calculated for an active site concentration of 0·145 mÒ, 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¢, compared with imposed 

shortening velocities of 0·40, 0·20 and 0·61 ML s¢, 

respectively, as reported above. 

In a series of 41 measurements, the mean isometric force 

prior to the period of applied shortening was 190±6kN 

m¦Â (range 101 to 292 kN m¦Â). This value is 17 % less than 

thevalueof230±11kNm¦ÂreportedbyHeet al. (1998b) 

at a sarcomere length of 2·4 ìm 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¦Â. For a linear length—tension 

relation in permeabilized fibres, force should be 7 % less at a 

sarcomere length of 2·7 ìm than at 2·4 ìm.

844 


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 mÒ 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¢, 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¦Â. 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 Pé bound to MDCC-PBP. The muscle 

fibre had been incubated in solution containing 1·2 mÒ 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 ² 10¦Í mÂ, initial length of fibre segment 2·2 mm, initial sarcomere length 2·7 ìm. 




J. Physiol. 517.3


845 

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 crossbridge 

detachment, was fitted by a rate constant of 243 s¢ 

(s.d. = 130 s¢, 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¢ (s.d. = 2·5 s¢) and 2·6 s¢ (s.d. = 0·5 s¢) 

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¢ 

(s.d. = 2·4 s¢, 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 

didnotappeartodependontheforcelevelreachedatthe 

end of the shortening phase. 

The ATPase rate constant during the first turnover was 

10·3 ± 0·3 s¢ (s.d. = 2·2 s¢; n =41) for an active site 

concentration of 0·14 mÒ. The mean ATPase rate constant 

in the period immediately prior to the period of applied 

length change was 5·1 ± 0·2 s¢ (s.d. = 1·2 s¢). 

Figure 2. Three consecutive contractions, a, b and c, initiated by the photolytic release of 

•1·5 mÒ ATPfrom5mÒ NPE-caged ATP in a single muscle fibre segment 

ThelayoutofthefigureisthesameasthatofFig. 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¢. The amplitude of the shortening was 7 % in each case. 

Fibre dimensions: cross-sectional area 5·30 ² 10¦Í mÂ, initial length of fibre segment 2·3 mm, initial 

sarcomere length 2·7 ìm. 



by guest on March 5, 2013

846 

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¢. Sarcomere velocity was determined 

fromtherateofchangeinpositionofthefirst-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¢ in the direction of shortening. 

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¢ (n = 29) in the direction of sarcomere 

shortening, covering a range of velocities from 0·50 to 

−0·15 ML s¢ (i.e. lengthening) and a median shortening 

velocity of 0·07 ML s¢. During the first turnover the 

ATPase rate constant averaged 10·7 ± 0·4 s¢ (n = 29) for 

these fibres when referred to an active site concentration in 

the overlap region of 0·14 mÒ. By comparison, the mean 

shortening velocity immediately prior to the period of rapid 

shortening was 0·05 ± 0·01 ML s¢ (n = 29) with a median 

value of 0·04 ML s¢. 

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¢ 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


847 

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¦Â, respectively. PÏPï 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¢ 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¢. 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 ìm 

(He et al. 1997), where no steady phase in the ATPase was 

seen. This effect of sarcomere length is demonstrated later. 

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 

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¢ 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 ² 10¦Í mÂ, initial length of fibre segment 1·96 mm, initial sarcomere length 2·7 ìm. The sarcomere 

signals for this fibre were too diffuse to be meaningful and are not shown. 




848 

fitted with Hill’s hyperbolic equation (1938): 

Pïb −aV 

P = –––––, 

V+b 

where P was the force during shortening at a shortening 

velocity V. Pï, the force level immediately prior to 

shortening, was 190 kN m¦Â. The maximal shortening 

velocity (at P = 0), Vmax = bPïÏa, and a and b were constants 

to the hyperbola. The fit gave aÏPï = 0·42, b = 0·51 and 

Vmax = 1·21 ML s¢. The data obtained for applied 

shortening velocities of 1·3 and 1·53 ML s¢ were not 

included in the fit as the fibres may have been slack during 

the shortening period. 

The relationship was also fitted according to the theory of 

A. F. Huxley (1957) where f1, g1 and gµ 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: 

V 1 fÔ+gÔÂV 

P=Pï(1−– (1−e ÖÏV 

Ö 2 gµ Ö 

)(1+–(– ––)–)), 

where h is the myosin head attachment range and s is the 

sarcomere length (Simmons & Jewell, 1974). Using 

s = 2·55 ìm and h = 9 nm (Goldman & Huxley, 1994), a 

value for f1 = kµ = 20·7 s¢, the rate constant describing 

force redevelopment following shortening as a reasonable 

estimate for the rate of myosin head attachment, and 



Vmax = 1·21 as derived from Hill’s force—velocity curve 

giving gµ =VmaxsÏh = 342 s¢, a best fit was obtained for g1 

of 118 s¢. 

The mechanical power produced by the fibres at a given 

shortening velocity given by P²V 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¢ 

was achieved at a shortening velocity of 0·42 ML s¢ and 

PÏPï 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. 

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 mÒ s¢ (n = 41), 

corresponding to 5·1 ± 0·2 s¢ for 0·14 mÒ 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¢. The ATPase 

increased approximately linearly with shortening velocity 

up to 0·6 ML s¢ and appeared to plateau at higher 

velocities. The maximal ATPase rate for applied shortening 

velocities of 1 ML s¢ and above was 18·5 ± 0·6 s¢ (n = 3), 

after considering that the average sarcomere length during 

shortening resulted in an active site concentration of 

0·145 mÒ (see Methods). The ATPase activity during fast 

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 Pï the mean 

value for all fibres of 190 kN m¦Â, with best-fit values of 0·42 and 0·51 for aÏPï andb, respectively, giving 

an extrapolated maximal shortening velocity of 1·21 ML s¢ at P =0.Thethicklineisthebestfit 

according the theory of A. F. Huxley (1957) as explained in the text, with f1 = 20·7 s¢, g1 = 118 s¢ and 

gµ = 342 s¢. 





849 

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). 

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¢ 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 

ourexperimentalconditionswherePéconcentrationislow. 

Efficiency was zero where no work was performed, namely 

during isometric contraction or shortening at zero load. 

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¢, corresponding to PÏPï = 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 

sarcomerelength,sinceinexperimentsatlongsarcomere 

length the ATPase rate appears to reach a relatively 

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) ² velocity (m s¢). Here 

we used force in kN m¦Â and shortening velocity in ML s¢, 

where ML had dimensions of reciprocal length, so that power 

was kN m¦Â ² m¢ s¢, or kN m¦Å s¢, corresponding to 

N l¢ s¢, namely W l¢. The continuous line was calculated 

fromthevaluesofaÏPïandbobtained from the fit to the 

force—velocity relationship in Fig. 6. 

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 mÒ. 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¢, 

n = 41). The error bars are shown inside the square symbol. 

Thecontinuouslineisthebestfitofthedatatoahyperbola 

corresponding to the equation: 

Y = 5·1 + 18·7 ² 1·94 ² VÏ(1 + 1·94 ² V), 

where V is the applied shortening velocity in ML s¢, 5·1 s¢ 

is the ATPase rate constant in the isometric state and 

18·7 s¢ is the ATPase rate constant above that in the 

isometric state for shortening at infinite velocity. 




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¢) is the data shown in 

Fig. 7. Energy input is the ATP consumed (in mÒ s¢) 

multiplied by the free energy of hydrolysis (50 kJ mol¢). 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 mÒ. 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¢, 

corresponding to PÏPï = 0·51.

850 

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 ìm. 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 ìm, 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 ìm 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 ìm, 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 ìm 

the ATPase rate constant decays continuously. Although it 

Figure 10. Relationship between force, Pé release and the ATPase rate constant at sarcomere 

lengths of 2·4 and 2·7 ìm 

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 ìm (a, thin lines) or 2·7 ìm (b, thick lines). The data 

shown are the mean of five experiments (2·4 ìm) and three experiments (2·7 ìm). 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 andtheconcentrationofPé 

bound to MDCC-PBP is shown in B, as calculated from the fluorescence signal, after correction for the acinitro 

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 mÒ for 2·7 ìm and 0·15 mÒ for 2·4 ìm). 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 ìm, the ATPase rate constant remains relatively constant between 0·2 and 0·6 s, at 5·2 s¢. 





851 

is initially faster than at 2·7 ìm, 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 ìm 

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 ìm, 

the ATPase rate increased from 15·2 ± 0·7 to 19·8 ± 2·2 s¢ 

(n = 5) when temperature was raised from 12 to 15 °C. At a 

sarcomere length of 2·7ìm, 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¢ (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 ìm, respectively. 

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, Ca¥ 

sensitivity and resistance to sarcoplasmic ATPase inhibitors. 

At 12 °C, the mean ATPase rates during the first turnover 

were 10·3 s¢, when referred to an active site concentration 

of 0·14 mÒ, at a sarcomere length of 2·7 ìm and 15·2 s¢ at 

2·4 ìm. This latter value is slightly lower than that reported 

earlier (18·8 s¢) for psoas muscle fibres at 12 °C and a 

sarcomere length of 2·4 ìm, referred to an active site 

concentration of 0·15 mÒ (He et al. 1997). At 15 °C and a 

sarcomere length of 2·4 ìm, the ATPase rate during the 

first turnover (19·8 s¢) is lower than the value of 31·5 s¢ 

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 ìm) and at 12 °C, a period is seen during which the 

ATPase rate constant remains relatively constant, as 

reported previously (Fig. 7ofHeet 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¢. The mean of the data in Fig. 3 (0·09 ML s¢) 

argues against this possibility. However, the hyperbola in 

Fig. 8 shows that shortening at a velocity of 0·09 ML s¢ 

during the nominally isometric phase of contraction is 

accompanied by an ATPase rate of 8 s¢, 22 % less than the 

measured value of 10·3 s¢. The difference between the 

observed ATPase rate constant and the ATPase rate 

constant which can be explained by a period of shortening is 

thereforesmallanditcannotbeexcludedthatoursarcomere 

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 videomicroscopy 

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¢, n = 29) would cause an increase in 

the ATPase rate from 5·1 to 8·0 s¢ (calculated from the 

hyperbola to the data shown in Fig. 8). This value is less

852 

than the actual ATPase rate in the first turnover (10·7 s¢) 

for these same 29 experiments. 

As reported earlier, some shortening does take place in the 

period immediately prior to the period of applied 

shortening, with a mean shortening velocity of 0·05 ML s¢. 

If the muscle fibres were extended at this velocity during 

this period, sarcomere shortening would be abolished. 

Hence, the measured ATPase activity of 5·1 s¢ for 

nominally isometric fibres corresponds to shortening at 

0·05 ML s¢, but extrapolation of the hyperbola in Fig. 8to 

an extension velocity of 0·05 ML s¢ results in an ATPase 

activity of 3·1 s¢. This latter value may be the true 

isometric ATPase. If this were the case, the acceleration of 

the ATPase activity of isometric muscle fibres produced by 

shortening would increase from a factor of 3·7 (18·7Ï5·1) to 

6·0 (18·7Ï3·1). 

The period immediately prior to the period of applied 

shortening, which in most cases was set at 0·4 s after 

photolysis, is that which most closely resembles the steady, 

isometric state because Pé release and force levels are 

relatively constant at this time. We use the term isometric 

to describe this phase, but the slow shortening which we 

observe shows that this isometric phase is not truly a steady 

state. The ATPase rate during the first turnover was 

typically twice as high as that in this isometric phase (for 41 

experiments the ratio was 2·06 ± 0·06). 

The ATPase rate constant in the first turnover is about half 

the ATPase rate constant measured at the maximal 

shortening velocity (10·3 vs. 18·5 s¢ for 41 measurements) 

and is not fully accounted for by initial sarcomere 

shortening, suggesting that the mechanism underlying the 

initial ATPase rate is not equivalent to that responsible for 

the acceleration of the ATPase during shortening at a 

constant velocity. The initial ATPase rate accompanies a 

period of rapid force development. A similar rapid rise in 

force is seen at the end of the period of rapid shortening, 

but here the ATPase rate is slower than during the 

shortening phase or than during the initial phase of 

contraction. Instead, at the end of the shortening phase the 

ATPase rate is similar to the slower rate seen immediately 

prior to the period of applied shortening (Figs 1, 2 and 5). 

As discussed in He et al. (1997) a change in the distribution 

of force-generating states during the first seconds of 

activation probably accounts for the change from the high 

initial ATPase to that seen 0·4 s after photolytic release of 

ATP. 

In the isometric phase immediately prior to the period of 

applied shortening, the ATPase rate constant measured here 

(5·0 s¢) is 2—5 times faster than that measured by others, 

e.g. 1·27 s¢ in the presence of 3 mÒ Pé at 10 °C (Cooke et al. 

1988), 1·8 s¢ at 15 °C (Glyn & Sleep, 1985) and 2·1 s¢ at 

15 °C (Potma & Stienen, 1996). As discussed by He et al. 

(1997), this discrepancy may arise from the different time 

scales in the experiments or from methodological limitations 

of the linked assay system, and is unlikely to be caused by 






the slow shortening which we observed at this time. Such 

shortening probably also occurred in the work cited. 

The ATPase rate constant during shortening near Vmax is 

3—4 times higher than that immediately prior to the period 

of applied shortening (5·0 vs. 18·5 s¢), similar to the 2·7fold 

increase in ATPase caused by shortening seen by 

Potma & Stienen (1996) in rabbit psoas fibres at 15 °C using 

the NADH-linked assay, although these authors obtained 

absolute values for the ATPase rate constants in isometric 

and shortening muscle fibres which were approximately 

3_fold lower than the values found here. 

Curvature of the force—velocity relationship 

The curvature of the force—velocity relationship is well 

described by the value for aÏPï, although combinations of 

thevaluesfor(f1 + g1)orforgµ also describe it (Simmons & 

Jewell, 1974). The value for aÏPï of 0·42 is higher 

(force—velocity relationship is less curved), and Vmax is lower 

than that found by others under similar conditions. For 

example Cooke et al. (1988) obtained 0·23 and 1·6 ML s¢ for 

aÏPï andVmax, respectively, at 10 °C and Sweeney et al. 

(1988) obtained Vmax of 2·1 ML s¢ at 12 °C for muscle fibres 

of the same type. 

Binding of NPE-caged ATP to muscle fibres was found to 

reduce the maximal shortening velocity of rabbit fibres at 

20 °C for ATP concentrations of 1 mÒ or less (Thirlwell et 

al. 1995). The 3·5 mÒ NPE-caged ATP present in the fibres 

following the laser flash is likely to cause our measurement 

of maximal shortening velocity to be lower than if it was 

carried out in the absence of NPE-caged ATP. It is also the 

most likely explanation for the high value for aÏPï found 

herecomparedwiththatintheliterature.Usingthesame 

preparation at 10 °C and the same technique, He et al. 

(1998a) obtained a value for aÏPï of 0·12, lower than the 

value obtained here because in He et al. (1998a) few data 

points were obtained at high shortening velocities, resulting 

in a larger value for Vmax obtained by extrapolation 

(1·45 ML s¢), and because the initial sarcomere length was 

3·0 ìm, where resting tension contributes to the restoring 

force during shortening. 

Adifferencebetweenourworkandthatofothersisthat 

here the presence of MDCC-PBP results in a low 

concentration of Pé during the measurements (< 1 ìÒ). 

However, Cooke et al. (1988) showed that in the 

concentration range 3—20 mÒ,PédidnotalteraÏPïorVmax, 

althoughaneffectofPéonaÏPï andVmax is possible at 

Pé


853 

in rat fast muscle fibres (9·6 W l¢; Reggiani et al. 1997) or 

in human type IIB fibres (3·5 W l¢; Bottinelli et al. 1996). 

Potma & Stienen (1996) measured •20 W l¢ at a 

shortening velocity of 1 ML s¢ and 15 °C, although these 

authors did not show that this is maximal because no data 

were obtained for higher shortening velocities. The high 

power output obtained here results from the relatively linear 

force—velocity relationship: at intermediate shortening 

velocities, force is 2—3 times higher than in other studies. 

Maximal power output is temperature and species 

dependent so that the variations in power output 

measurements found in the literature are not surprising. For 

example, Ranatunga (1998) found that at 35 °C, power 

output of fast muscle fibres of the rat was 250 W l¢, 

dropping to less than 13 W l¢ at 10 °C, with a QÔÑ in the 

5—7 range below 20 °C. 

The efficiency of contraction obtained here reached 0·36 

(interpolation in Fig. 9). As power output is more 

temperature sensitive than the ATPase (Ranatunga, 1998), 

it is expected that the efficiency will increase with 

increasing temperature. In this calculation, the energy 

input includes the ATP hydrolysed to maintain the 

isometric state. The relationship between efficiency and 

speed of contraction is very similar to that obtained in 

intact frog muscle shortening at 0 °C (Fig. 4.38A in Woledge 

et al. 1985), even though the ATP cleavage in frog muscle 

includes that required for pumping calcium into the 

sarcoplasmic reticulum. Potma & Stienen (1996) obtained a 

value of 0·25, but these authors did not investigate 

shortening at velocities higher than 1 ML s¢. Reggiani et al. 

(1997) reported a value of 0·28. The experimental conditions 

differ mainly in the animal used (rabbit vs. rat) and in the 

concentration of Pé in the solution. In our work the Pé 

concentration was very low (< 1 ìÒ) because of its binding 

to MDCC-PBP, whereas in the work of Reggiani et al. and 

of Potma & Stienen, it would have been in the millimolar 

range. Power output and ATPase activity during shortening 

have been shown to be modulated by free Pé concentration 

(Potma & Stienen, 1996). These authors found that in rabbit 

psoas muscle fibres at 15 °C, the power output and ATP 

turnover rate decreased at low shortening velocities when 

30 mÒ Pé was added to the solutions. The high force at 

shortening velocities where power output is maximal is 

accompanied by a high ATPase rate so that the ratio of 

power output to energy consumed remains close to that 

found elsewhere. The slightly higher efficiency (0·4) reported 

by He et al. (1998a) is a consequence of the passive, 

restoring force encountered for muscle fibres shortening 

from an initial sarcomere length of 3·0 ìm. 

Step size, duty ratio and myosin head interaction 

distance with actin 

The maximum ATPase rate of 18·5 s¢ at 12 °C is comparable 

to that obtained by Ma & Taylor (1994) in shortening 

myofibrils of rabbit psoas muscle at 20 °C (22 s¢), but faster 

than their value at 10 °C (6·5 s¢). The direct measurement 

of the ATPase in shortening muscle fibres obtained here can 




be used to estimate the distance travelled by myosin heads 

for each ATP hydrolysed. At Vmax, assuming that all 

myosin heads in the overlap region are active, namely 

participating equally in the hydrolysis, the distance 

travelled per ATP for each sarcomere, d, isgivenbyd = VÏk 

where V is the shortening velocity (in nm s¢) and k is the 

maximum myosin head cycling rate (18·5 s¢). For 

Vmax = 1·21 ML s¢ at 12°C and a sarcomere length of 

2·7 ìm, each half-sarcomere shortens at 1633 nm s¢, giving 

a myosin head travel distance of 88·3 nm per ATP 

(1633Ï18·5). For a step size of 9 nm (mid-range of Goldman 

& A. F. Huxley, 1994), myosin heads may only remain 

attached to actin for 10 % of their cycle time (9Ï88·3) (cf. 

duty cycle ratio of 0·2; Ma & Taylor, 1994). This number is 

in agreement with stiffness measurements (Ford et al. 1985), 

X-ray diffraction data (Yagi & Takemori, 1995) and kinetic 

measurements (Brenner, 1988; Ma & Taylor, 1994), which 

suggest that, during shortening, the fraction of attached 

myosin heads at any one time is low. The ATPase rate is 

seen to increase continuously with shortening velocity 

(Fig. 8), even though the number of attached myosin heads 

is decreasing. If shortening reduces the number of 

participating myosin heads, the ATPase activity of the 

active fraction is proportionally greater. It is more likely 

that all myosin heads participate in shortening, and that 

the rate limiting step in the ATPase during shortening is 

the hydrolysis step which occurs while the myosin heads are 

detached from the thin filament. In the isometric state, the 

rate limiting step is the release of hydrolysis products (ADP 

or Pé), with rate constants which may depend on the strain 

experienced by the myosin heads (Homsher et al. 1997). 

The calculations made here are based on the results of 

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Acknowledgements 

We are grateful to Dr David R. Trentham, Professor Carlo 

Reggiani and Professor Sir Andrew F. Huxley for their help with 

the manuscript. 

Corresponding author 

M. A. Ferenczi: National Institute for Medical Research, The 

Ridgeway, Mill Hill, London NW7 1AA, UK. 

Email: m-ferenc@nimr.mrc.ac.uk

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