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

J. Physiol. 517.3 Efficiency of muscle contraction
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.
Downloaded from J Physiol (
jp.physoc.org)
by guest on March 5, 2013
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.