High mechanical efficiency of the cross-bridge powerstroke in skeletal muscle
Department of Physiology, School of Medicine, Teikyo University, Itabashi-ku, Tokyo 173-8605, Japan
* Author for correspondence (e-mail: sugi{at}med.teikyo-u.ac.jp)
Accepted 13 January 2003
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Summary |
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Key words: mechanical efficiency, cross-bridge, skeletal muscle, caged Ca2+, isotonic shortening, muscle work, ATP utilization, rabbit
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Introduction |
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The present work was undertaken to estimate the maximum mechanical
efficiency of the cross-bridge powerstroke in demembranated muscle fibres
containing ATP molecules almost equal in number to the cross-bridges
(Sugi et al., 1998). The
results obtained suggest that the maximum mechanical efficiency of the
cross-bridge powerstroke may be close to unity.
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Materials and methods |
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Experimental procedures and data analysis
In relaxing solution, the sarcomere length of the fibres was adjusted to
2.4 µm, at which the overlap between the thick and thin filaments was just
maximum (Page and Huxley,
1963). As the extent of fibre shortening was <15% of the
initial fibre length L0, the number of cross-bridges
interacting with the thin filament was always maximum during fibre shortening.
The fibres were kept in prephotolysis solution for 2 min, followed by
photolysis solution containing DM-nitrophen for 4050 s, and were then
exposed to air to prevent diffusion of ATP from the photolysis solution that
was to be subjected to laser flash irradiation. The ATP concentration of the
photolysis solution was determined to be 220 µmol l1. A
thin layer of photolysis solution at the fibre surface was removed by gently
blotting the fibre with a piece of filter paper. Very small rigor force
(
1% of Po) was always developed in the fibres
immediately before flash activation. This indicates that the number of ATP
molecules is slightly below, but not above, that of the cross-bridges, since
ATP molecules are slowly hydrolysed by the cross-bridges in the relaxed fibres
during the time between the moment of exposure of the fibre in air and the
moment of laser flash irradiation (23 s). The temperature of the space
where the fibres were activated was estimated to be 4°C
(Sugi et al., 1998
).
Length and force changes of the fibres after flash activation were stored in a digital memory for analysis. To indirectly estimate the amount of ATP (or more exactly M-ADP-Pi, where the ATP is hydrolyzed but the products have not yet been released from the cross-bridge) utilized at 1 s after flash activation (Pu), the fibres were subjected to a quick decrease in fibre length (quick release, 12% of L0, complete in 12 ms) at 1 s after flash activation to drop the force to zero, and then the fibre length was clamped to allow the fibres to develop isometric force. The amount of isometric force developed (Pr, relative to the maximum isometric force Po) was taken as a measure of the amount of M-ADP-Pi remaining in the fibre at 1 s after activation. The value of Pu was obtained as Pu=PoPr. After a flash-induced mechanical response, the fibres were made to relax in relaxing solution. The flash activation of the fibres could be repeated 510 times at 10 min intervals. Data were discarded when the decrease in rate of development of isometric force preceding fibre shortening was recognized.
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Results |
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During isometric contraction, in-phase stiffness, i.e. the magnitude of
force changes in response to sinusoidal length changes, increased
approximately in parallel with isometric force, while quadrature stiffness,
i.e. the 90° out-of-phase stiffness component, reached a maximum at
approximately 0.3 s after activation, and stayed almost unchanged for the
first 34 s. This indicates that there were no appreciable changes in
the number of force-generating cross-bridges during isometric force
development preceding fibre shortening, since quadrature stiffness is taken as
a measurement of the fraction of active cross-bridges
(Goldman et al., 1984).
Furthermore, under conditions identical to the present experiments, no
appreciable increase of internal resistance against fibre shortening takes
place at least for the first 12 s after activation
(Sugi et al., 1998
;
Fig. 3). It may therefore be
safe to conclude that, at least for 12 s after activation, the
cross-bridges may not readily form rigor links after releasing Pi and ADP,
irrespective of whether the fibre is shortening or kept isometric.
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Dependence of the amount of work and the amount of ATP utilized on
the isotonic load
Fig. 3 shows a typical
experiment in which the fibres were activated to contract isometrically or
isotonically under five different afterloads for 1 s, and then subjected to a
quick release to drop the force to zero, whereon the fibre length was clamped
and the fibres developed isometric force. The amount of isometric force
developed after a quick release (Pr), i.e. a measure of
the amount of ATP remaining in the fibre at 1 s after activation, was maximum
when P=Po (isometric contraction) and minimum
when P=0 (unloaded shortening). Similar results were obtained from 7
different preparations examined. The amount of ATP utilized at 1 s after flash
activation
(Pu=PoPr)
was therefore maximum during unloaded shortening (P=0), and minimum
during isometric contraction (P=Po).
On the other hand, the possibility that cross-bridges forming rigor links
with the thin filaments may produce rigor force to contribute to the isometric
force development after a quick release can largely be precluded by the
extremely slow development of rigor force in glycerinated rabbit psoas fibres
(Kobayashi et al., 1998). On
application of rigor solution, the ATP concentration at the center of the
fibre with radius of 2030 µm would be reduced to zero within 1 s, if
an appropriate diffusion constant of ATP within the fibre
(1.2x106 cm2 s1;
Kushmerick and Podolsky, 1969
)
is taken into consideration. Nevertheless, detectable rigor force development
is observed only at 710 s after application of rigor solution,
indicating a very slow development of rigor force after removal of ATP.
On this basis, the estimation of Pu value may not be influenced by rigor forces, except during isotonic shortening under small loads (<0.4 Po), after which the isometric force development reaches a maximum at more than 7 s after flash activation (Fig. 3). This implies that the value of Pu during isotonic shortening under small loads may be somewhat underestimated, though its extent is very small.
Fig. 4 shows the dependence of the amount of work done (W, expressed relative to the maximum value, Wmax) and the amount of ATP utilized for the whole mechanical response (Pu, expressed relative to Po) on the isotonic load (P). The data points were obtained from 8 different data sets. The value of Pu at P=0 was approximately 3 times larger than that at P=Po. The value of W was maximum (1.80±0.06x108 J, mean ± S.E.M., N=8) at approximately 0.4 Po. The W versus P relationship was bell-shaped, since W is necessarily zero at P=0 and P=Po.
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Dependence of the mechanical efficiency of individual cross-bridges
on the isotonic load
The amount of ATP utilized for the whole mechanical response
(Pu) is the sum of the amount of ATP utilized for the
preceding isometric force development (Pi) and that
utilized for the subsequent isotonic shortening (Ps) (see
Fig. 7). The value of
Pi as a function of isotonic load were obtained by
applying a quick release to isometrically contracting fibres at various times
after activation and measuring the amount of force developed after each quick
release (Fig. 5). Thus, the
value of Ps could be obtained by subtracting the value of
Pi for a given isometric force equal to the isotonic load
from Pu for the whole mechanical response. The value of
Ps obtained increased roughly linearly with the distance
of fibre shortening, irrespective of the isotonic load
(Fig. 6). The mechanical
efficiency of individual cross-bridges (E), averaged over the period
of work production, can be estimated as
E=W/(PuPi)=W/Ps,
using the results shown in Figs
4 and
5. The dependence of E
(expressed relative to the maximum value, Emax) on the
isotonic load is shown schematically in
Fig. 7 together with W,
Pu, Pi and Ps. The
E versus P relationship was bell-shaped, with a broad peak at
0.50.6 Po.
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Estimation of the absolute value of mechanical efficiency of
individual cross-bridges
Although the mechanical efficiency of individual cross-bridges is obtained
as relative values in the present study, we made a conservative estimation of
its absolute value as follows. The average fibre cross-sectional area of 8
preparations, from which the data shown in
Fig. 4 were obtained, was
6.1±0.1x105 cm2, while the fibre
length was 2.53 mm. To avoid underestimation of fibre volume
leading to overestimation of the efficiency, we use the maximum fibre length
of 3 mm to obtain mean fibre volume of 1.8x105
cm3. Assuming a cross-bridge concentration of 200 µmol
l1 (higher than the widely used values of 145 or 150 µmol
l1), the amount of M-ADP-Pi immediately before flash
activation is estimated to be 3.6x106 µmol
(200x1.8x105x103)=3.6x1012
mol. In Fig. 7, the value of
E is maximum at P=0.53 Po, and the
corresponding value of Ps is 0.13 Po,
where Po corresponds to the initial amount of M-ADP-Pi of
3.6x1012 mol. The number of ATP molecules utilized for
work production is calculated to be 2.8x1011
(3.6x1012x0.13x6x1023).
Assuming the energy released by ATP hydrolysis of 50 kJ mol1
(Bagshaw, 1994
;
Oiwa et al., 1991
), the energy
available from one ATP molecule is 8.3x1020 J
(50x103/6x1023). The energy released from
ATP molecules during work production is 2.3x108 J
(2.8x1011x8.3x1020). In
Fig. 7, the amount of work done
at 0.53 Po is 1.6x108 J. The
maximum mechanical efficiency of individual cross-bridges is therefore
estimated to be
(1.6x108)/(2.3x108)=0.7. Since
the above estimation is conservative, the actual maximum mechanical efficiency
of an individual cross-bridge is suggested to be 0.80.9, which is close
to unity.
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Discussion |
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At the beginning of fibre shortening, the power output rose rapidly to a peak, and then decreased with time (Fig. 2). The distance of fibre shortening at the peak of power output was <10 nm per half sarcomere. This can be taken as evidence that, at the beginning of fibre shortening, the cross-bridges start their powerstroke almost synchronously. In the present study, the period of fibre shortening was restricted to be <1 s (Fig. 3). Since the maximum rate of ATP utilization was 0.80 s1 per cross-bridge during unloaded shortening (Fig. 4), the average duration of ATP hydrolysis cycle was 1.3 s, and this value increased up to approximately 5 s with increasing load towards Po. This implies that, under large loads, a considerable fraction of cross-bridges, starting their powerstroke at the beginning of fibre shortening, would continue their ATP hydrolysis cycle over the whole period of work production. The mechanical efficiency obtained in the present study may therefore be regarded as largely reflecting that of individual cross-bridges, especially with large loads.
For the reasons stated above, the present results may constitute evidence
that the maximum mechanical efficiency of individual cross-bridges may be very
high, probably close to unity (0.80.9). In this connection, it is of
interest to note that it has also been suggested that the mechanical
efficiency of the ATP-dependent rotary motion of F0-F1 ATPase at the
mitochondrial membrane is close to unity
(Kinosita et al., 2000).
Relationship with previous studies
Due to the limited amount of ATP in the fibre and the low temperature at
which the present experiments were done, the maximum power output of the
fibres in the present study (0.6 W l1) was more than one
order of magnitude smaller than the value obtained from rabbit psoas fibres
(28 W l1 at 12°C) (He
et al., 1997) even when the high Q10 value (>5)
(He et al., 2000
) is taken into
consideration. The maximum mean rate of ATP utilization for the first 1 s
after activation (0.80 s1 per cross-bridge,
Fig. 4) was also markedly
smaller than the value of 18.5 s1 per cross-bridge (at
12°C) (He et al., 1997
).
Meanwhile the amount of ATP utilized for the first 1 s after activation
(Pu) increased with decreasing load P, reaching a
maximum at P=0 without any sign of leveling off
(Fig. 4). This may be
consistent with the result that a roughly proportional relationship exists
between the rate of ATP utilization and the fibre shortening velocity
(Reggiani et al., 1997
;
He et al., 2000
;
Potma and Stienen, 1996
), but
not with the biphasic relationship between the rate of energy liberation (heat
+ work) and the shortening velocity in whole muscle
(Hill, 1964
;
Linari and Woledge, 1995
). The
approximately linear dependence of the amount of ATP utilized for work
production on the distance of shortening
(Fig. 6) has already been
reported by Sun et al. (2001
),
suggesting that, irrespective of whether the amounts of ATP available for the
cross-bridges are limited or not, the amount of ATP hydrolyzed is primarily
determined by the distance of fibre shortening.
The maximum mechanical efficiency of Ca2+-activated skeletal
muscle fibres has been reported to range from 0.2 to 0.46
(He et al., 1997;
Reggiani et al., 1997
;
Sun et al., 2001
), indicating
that the net maximum mechanical efficiency of cross-bridges during their
asynchronous activity is much smaller than the maximum mechanical efficiency
of individual cross-bridges obtained in the present study. In this connection,
it is of interest that, in demembranated cardiac myocytes, the maximum
Ca2+-activated isometric force increases by one third when the ATP
concentration is reduced to 200 µmol l1
(Fabiato and Fabiato, 1975
).
This might result from an increased degree of synchronization of
force-generating cross-bridge activity, when the ATP concentration is reduced
to be nearly equal to that of cross-bridges.
The present experiments are closely related to those of Oiwa et al.
(1991), who measured the
amount of work done by ATP-induced sliding of a myosin-coated microneedle
along actin cables in giant algal cells. In response to a limited amount of
iontophoretically applied ATP, myosin molecules on the needle moved along
actin cables by bending the needle for a distance. By application of ATP under
various baseline forces generated by the bent needle, they obtained a
bell-shaped work versus baseline force relationship similar to the
present E versus P relationship
(Fig. 7), both exhibiting a
peak at approximately 0.5 Po. This seems to indicate that,
irrespective of whether the cross-bridges are regularly arranged in the fibres
or randomly oriented on the needle, they sense the amount of load and
determine their future work output when they are allowed to produce work. The
mechanism underlying the load-dependent mechanical efficiency of individual
cross-bridges remains to be investigated, although it is suggested that their
nucleotide affinity changes depending on the strain in the cross-bridge
structure (Geeves and Holmes,
1999
).
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