Initial mechanical efficiency of isolated cardiac muscle
1 Department of Physiology, Monash University, Clayton, Victoria 3800,
Australia
2 School of Physiotherapy and Exercise Science, Griffith University, Gold
Coast, Queensland 9726, Australia
* Author for correspondence (e-mail: c.barclay{at}griffith.edu.au)
Accepted 7 May 2003
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Summary |
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Key words: muscle energetics, heat production, efficiency, cardiac muscle
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Introduction |
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The efficiency of mechanical work generation by cross-bridges in cardiac
muscle is poorly established because it is difficult to experimentally
separate the initial and recovery energy costs. The kinetics of recovery
metabolism in cardiac muscle are so rapid that even the energy used within the
time course of a single twitch includes a significant recovery metabolism
component (Gibbs et al., 1967;
Mast and Elzinga, 1990
).
Peterson and Alpert (1991
)
subtracted the presumed recovery heat component from the energy output
recorded during isotonic shortening of rabbit papillary muscles and concluded
that the maximum eI in rabbit papillary muscles was 65%.
This value is high compared with an estimate based on reported values of
eN. eN of isolated cardiac muscle is
typically
15% (Gibbs et al.,
1967
; Syme, 1994
;
Mellors et al., 2001
;
Mellors and Barclay, 2001
).
The magnitude of the net metabolic cost of a series of contractions is
typically twice that of initial metabolism (e.g.
Mast et al., 1990
) so
eI should be
2-fold greater than
eN; that is, about 30%.
Both the approaches described above for determining eI
contain elements of uncertainty. For example, Peterson and Alpert
(1991) implicitly assumed that
the energy output associated with shortening was synchronous with shortening,
but, at least in isometric contractions, a substantial fraction of the initial
energy output associated with a single twitch appears late in the contraction,
during force relaxation (Mast and Elzinga,
1990
). To estimate eI from
eN, it must be assumed that the ratio of energy output
from recovery processes (R) to energy output from initial processes
(I) is the same in isometric contractions and contractions with
shortening because the R:I ratio in cardiac muscle has only
been measured using isometric contractions
(Mast et al., 1990
). Although
it seems reasonable to assume that the R:I ratio is
independent of contraction type, the only published comparison of the
R:I ratio in isometric and working contractions, which was
made using mouse skeletal muscle (Woledge
and Yin, 1989
), revealed that the ratio was greater in shortening
contractions (1.25) than in isometric contractions (1.0). It seems unlikely
that such an effect could underlie the combination of
eI=65% and eN=15% in cardiac muscle,
because this would require the R:I ratio in working
contractions to be an improbable 2.5. This emphasises the uncertainty attached
to the high eI value reported by Peterson and Alpert
(1991
).
It is important to establish whether initial efficiency is over 60% or just
30% because, although the latter can be easily accommodated within a
cross-bridge model using known mechanical properties of cardiac cross-bridges,
the former cannot. For example, an eI of 30% is consistent
with each cross-bridge converting 20% of the free energy from hydrolysis
of one ATP molecule into work (for details of this calculation, see
Discussion). This is quantitatively consistent with a cardiac cross-bridge
model in which each cross-bridge cycle is associated with splitting of one ATP
and in which the mean cross-bridge force and power stroke are approximately 2
pN and 10 nm, respectively. These values for cross-bridge force output and
displacement correspond to those measured in experiments using isolated
contractile proteins from cardiac muscle
(Van Buren et al., 1995
;
Sugiura et al., 1998
). If
these cross-bridge forces and displacements are correct but
eI is >60% then there must be approximately two
cross-bridge cycles performed using the energy from each ATP molecule.
Alternatively, if there is a one-to-one coupling between ATP-splitting cycles
and cross-bridge cycles, then an eI of 60% could only come
about if the product of cross-bridge force and power stroke were twice that
calculated from in vitro measurements from cardiac cross-bridges
(Sugiura et al., 1998
).
The purpose of the present study was to determine both the net and initial
mechanical efficiencies of cardiac muscle during steady contractile activity.
To do this, the enthalpy produced by rat papillary muscles during and after a
series of contractions was partitioned into initial and recovery components
using a mathematical analysis described previously
(Mast et al., 1990). This
overcomes the problem of assuming that work output and the associated energy
output are synchronous because all the energy produced by the muscles during
and after the series of contractions was measured. The analytical method also
calculated the R:I ratio using the energetic data recorded
during the protocol in which the muscles were performing work, thus avoiding
the need to extrapolate from reported values obtained using isometric
contraction protocols. Furthermore, a contraction protocol designed to
simulate in vivo strain patterns was used
(Mellors and Barclay, 2001
).
Most previous studies of cardiac efficiency using isolated preparations have
used less realistic protocols (e.g. Gibbs
et al., 1967
; Peterson and
Alpert, 1991
).
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Materials and methods |
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Papillary muscles were dissected from the left ventricle of hearts removed from adult, male rats (Rattus norvegicus L.). Rats were first rendered unconscious by inhalation of chloroform and then killed by cervical dislocation. All animal handling procedures complied with the requirements of the Monash University Animal Ethics Committee. Muscles were bathed in oxygenated (95% O2/5% CO2) KrebsHenseleit solution of the following composition: 118 mmol l-1 NaCl; 4.75 mmol l-1 KCl; 1.18 mmol l-1 KH2PO4; 1.18 mmol l-1 MgSO4; 24.8 mmol l-1 NaHCO3; 1.6 mmol l-1 CaCl2; 10 mmol l-1 glucose. During dissection, 30 mmol l-1 butanedione monoxime (BDM) was added to the solution to optimise the recovery of mechanical function after dissection. Following dissection of the muscle, further dissection was performed to give a thin preparation of uniform cross-section. The preparation characteristics (mean ± S.E.M., N=13) were: mass, 2.63±0.3 mg; length, 4.53±0.3 mm; cross-sectional area, 0.55±0.04 mm2; radius (assuming circular cross-section), 0.41±0.02 mm. During experiments, solution temperature was maintained at 30°C.
Small, platinum loops were tied to either end of the preparation and placed
over hooks on two tungsten connecting rods, one attached to a strain gauge
force transducer (SensoNor 801, Horten, Norway) and the other to the lever arm
of an ergometer (Cambridge 300H, Cambridge Instruments, MA, USA). The
preparation lay along a thermopile that was 4 mm long, contained 16
antimonybismuth thermocouples and had an output of 0.81 mV
deg.-1 (Barclay et al.,
1995; Mellors et al.,
2001
). The muscles were stimulated using rectangular electrical
pulses delivered to the muscle via fine platinum wires that contacted
the platinum loops attached to either end of the muscle.
Measurements of energy output
Enthalpy output was used as an index of muscle energy use. Contracting
muscles produce energy as both mechanical work and heat; enthalpy output is
the sum of the work and heat produced. Work output was calculated from records
of muscle force output and change in muscle length. Heat output, excluding
basal heat production, was calculated from the changes in muscle temperature,
measured using the thermopile, during and after a series of contractions.
Temperature records were corrected for heat lost from the muscle during
recording and then multiplied by muscle heat capacity to determine the heat
output. Rate of heat loss and effective heat capacity (i.e. the combined heat
capacity of the muscle, any adhering solution and the thermopile under the
muscle) were determined from the time course of cooling of the preparation
after the muscle had been heated using the Peltier effect
(Kretzschmar and Wilkie,
1972).
Contraction protocol
At the start of each experiment, the stimulus strength required to elicit
maximum twitch force and the length at which twitch force was maximal
(Lmax) were determined. During the remainder of the
experiment, a contraction protocol that was designed to closely match the
in vivo strain dynamics of papillary muscles was used
(Mellors and Barclay, 2001).
It consisted of 40 twitches delivered at a frequency of 2.2 Hz. During each
contraction cycle (total duration 455 ms), muscle length was held constant for
the first 45 ms after the stimulus was applied, then was allowed to decrease
at a constant velocity for
160 ms through an amplitude of
10%
Lmax, and finally was stretched back to
Lmax at constant velocity for the remainder of the cycle
(Fig. 1A). The timing of these
length changes allowed force relaxation to be complete just prior to the start
of the stretching phase of each cycle. The net efficiency measured using this
protocol (Mellors and Barclay,
2001
) is the same as the maximum net efficiency measured using
either isotonic contractions or contractions with sinusoidal length changes
(Mellors et al., 2001
).
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Analysis of initial and recovery energy output
Cumulative work output (Fig.
2A) was calculated by summing the net work produced in each
contraction. Net work was calculated by determining the area enclosed by a
plot of force output as a function of change in muscle length and was thus the
difference between the work done during shortening and the work done on the
(relaxed) muscle to stretch it back to Lmax. This method
excludes contributions to the work performed during shortening by both
parallel and series elastic elements
(Mellors et al., 2001).
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Enthalpy output was partitioned into initial and recovery components using
the procedure described by Mast et al.
(1990). This method uses the
rate of enthalpy output and, in the present study, this was
calculated by numerical differentiation of the cumulative enthalpy output
(Fig. 2B). Although this
creates a noisy signal, the analysis is sufficiently robust that the noise had
little quantitative effect on the energy partitioning. Full details of the
energy partitioning procedure and its underlying assumptions have been
presented by Mast et al.
(1990
). Note that these
authors demonstrated that this procedure gives the same result for
partitioning energy output whether applied to data obtained during an
energetic steady state or to data obtained during the transition from rest to
a steady state, the case used in the present study.
The partitioning method (Mast et al.,
1990) determines the amount of recovery heat produced per unit of
initial heat produced (R:I ratio). It requires calculation
of the time constant (
) of the decline in rate of heat output after the
contractions have ended. This was done by fitting, using the
LevenbergMarquardt method, a single exponential function through 50 s
of rate of heat output data recorded after the final contraction
(Fig. 2B). Using
, the
R:I ratio and the time course of changes in rate of enthalpy
output, the time course of changes in rate of recovery heat output can be
calculated. An iterative procedure was used to find the value of the
R:I ratio that provided the closest match between the
calculated time course of recovery heat output and the measured,
post-contraction decline in heat rate (i.e. when it can be assumed that all
the heat produced is recovery heat; Fig.
2B). This R:I ratio was then used to divide the
heat rate data during the contraction series into initial and recovery
components. The calculated rates of initial energy output and recovery energy
output were then integrated (Fig.
2C), and the cumulative total of each variable was used to
calculate the initial and net mechanical efficiencies.
Calculation of mechanical efficiency
Efficiency was defined as the ratio of work output to metabolic energy
cost, expressed as a percentage. Net mechanical efficiency
(eN) was defined as the ratio of the net mechanical work
output during the series of contractions (WN) to the
total, suprabasal enthalpy produced during and after the series of
contractions. Enthalpy output was the sum of the total heat output
(QT) and the net work performed (WN):
![]() | (1) |
![]() | (2) |
Preparation oxygenation
The adequacy of oxygenation was assessed by calculating the change in
partial pressure of O2 (PO) through the
cross-section of a cylindrical muscle. The analysis, which has been described
in detail previously (Loiselle,
1985a; Baxi et al.,
2000
), was based on Hill's analysis of diffusion into a cylinder
(Hill, 1928
) but incorporated
a realistic relationship between the rate of mitochondrial oxygen consumption
and PO (Loiselle,
1985a
). The analysis assumes that muscles are uniform cylinders,
that metabolic rate is constant and that diffusion of O2 into the
ends of the cylinder is negligible. Steady-state rate of O2
consumption was calculated from the rate of enthalpy output measured during
the last three steady-state contraction cycles, when the muscles were close to
an energetic steady state (i.e. muscle temperature was the same at the start
of successive cycles; Paul,
1983
). An energetic equivalent of 20 mJ µl-1
O2 was used to convert enthalpy measurements into equivalent
O2 consumption.
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Results |
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The denominator of the definition of eN incorporated all the suprabasal enthalpy output associated with generating work. Mechanical work was produced only during the contraction series, but the associated enthalpy output was produced both during, and for 4050 s after, the contraction series (Fig. 2A). The mean net mechanical efficiency was 13.3±0.7% (mean ± S.E.M.; N=13 muscles).
Each enthalpy output record was partitioned into initial and recovery components. The calculated initial enthalpy was produced, like the work, only during the contraction series (Fig. 2C). At the start of the contraction series, the rate of recovery enthalpy output increased slowly compared with the immediate onset of initial enthalpy output. The rate of recovery heat output became constant only near the end of the contraction series (Fig. 2B). Once the contraction series was complete, the rate of recovery enthalpy output decreased exponentially with a mean time constant of 10.9±1.1 s(Fig. 2B).
Within each steady-state cycle, the calculated initial enthalpy was produced largely while the muscle was shortening, and little was produced during the lengthening phase of the cycle (Fig. 3). Across all the muscles tested, 95.0±2.4% of the initial enthalpy had been produced by the end of the shortening phase during the last 10 cycles. The rate of recovery heat output was constant during the steady-state cycles (Fig. 3).
|
The mean value of the ratio of recovery enthalpy output to initial enthalpy output that provided the best match to the recorded data was 1.16±0.03. That is, the total amount of recovery heat produced was slightly greater, on average, than the total initial enthalpy produced. The net enthalpy output is the sum of the initial and recovery components and was thus 1+1.16=2.16-fold greater than the cumulative total of the initial enthalpy produced. This difference was reflected in the initial mechanical efficiency; the mean value of eI was 28.1±1.2% (N=13).
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Discussion |
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Comparison of results with those from previous studies
The R:I ratio determined in the present study (mean
value, 1.16) was similar to both that reported previously for rabbit papillary
muscles (1.10; Mast et al.,
1990) and the theoretical value (1.13;
Woledge et al., 1985
, p. 219).
Mast et al. (1990
) used
isometric contractions, whereas in the present study working contractions were
used. A comparison of R:I ratio for isometric and working
contractions of mouse soleus muscle (a slow-twitch muscle) found the ratio to
be significantly greater during a working contraction (1.25) than during
isometric contractions (1.0; Woledge and
Yin, 1989
). Although the present study did not explicitly examine
this phenomenon, comparison with the work of Mast et al.
(1990
) provides no evidence to
support the idea that, in cardiac muscle, the type of contraction performed
has a substantial effect on the R:I ratio.
The rate of decline in recovery metabolism of papillary muscles in the
present study (time constant, 11 s) is consistent with values reported
previously for cardiac muscle. For example, Van Beek et al.
(1999
) measured time constants
between 6 s and 12 s for changes in rate of O2 consumption of
isolated rabbit hearts (28°C) subjected to abrupt changes in work
load.
To account for the difference between eI calculated in
the present study and that reported by Peterson and Alpert
(1991), the work output in the
earlier study was substantially greater than that in the present study and/or
the initial energy output was substantially less. Peterson and Alpert
(1991
) calculated the work
done by the muscle during the shortening phase of the isotonic contraction
(active isotonic force output x distance shortened). We have previously
shown that, as long as an appropriate correction is made for work performed by
parallel elastic elements, the work output during an isotonic contraction is
equal to the net work as calculated in the present study
(Mellors et al., 2001
).
Although Peterson and Alpert
(1991
) did not correct for
parallel elastic work, their estimate of work output was conservative because
they used the passive force at Lmax as the active force
baseline and thus they most likely underestimated contractile element work
output.
The most likely possibility is that Peterson and Alpert
(1991) underestimated the
initial heat production associated with shortening. They measured only the
heat produced between the start of contraction and the end of shortening. The
basis of this method was the assumption that all the energy associated with
the shortening is produced within the time course of shortening. It is
possible that this assumption does not hold for cardiac muscle. For instance,
during an isometric twitch, over half the initial enthalpy output arising from
cross-bridge cycling appears during force relaxation
(Mast and Elzinga, 1990
).
Thus, measuring the enthalpy output only during shortening probably led
Peterson and Alpert (1991
) to
underestimate initial energy consumption. In the present study, shortening
continued until force relaxation was complete, and the majority of the initial
enthalpy was produced within this time
(Fig. 3).
Oxygenation of papillary muscles
Supply of O2 to isolated preparations is by diffusion from the
surrounding solution. Hill
(1928) introduced the idea
that the centre of a muscle may become anoxic if diffusive O2
supply cannot match metabolic demands. An analysis of the adequacy of
O2 supply was performed to check: (1) whether anoxia was likely to
have occurred in the present study and (2) whether the radius of the
preparations had any effect on efficiency.
The analysis of O2 diffusion into papillary muscles
(Fig. 4A) indicated that during
steady-state activity the PO in the centre of even the
largest muscles used would be in excess of the levels required to impair
mitochondrial oxidative phosphorylation (1 kPa; for a review, see
Loiselle, 1982). For 11 of the
13 preparations used, the estimated PO in the centre of
the muscles was 10 kPa. Note that the analysis was made assuming the muscles
were in a steady state whereas during experiments muscles progressed from rest
to close to a steady state, so the calculated central PO
values would tend to underestimate the actual PO. The
results of the analysis are consistent with the idea that anoxia was unlikely
to have occurred in the preparations used in this study.
|
As a further check, and one that does not depend on assumptions concerning O2 diffusion through muscle, rates of metabolism or muscle geometry, an analysis was performed to see whether there was any relationship between the radius of the preparations and net efficiency (Fig. 4B). There was no significant correlation between these variables (r2=0.2, P>0.05), indicating that muscle size did not affect net efficiency. Therefore, the results of both the analysis of a model for oxygen diffusion into isolated muscles and the analysis relating muscle size to measured efficiency support the idea that anoxia had no effect on efficiency.
Cross-bridge thermodynamic efficiency
It is possible, knowing eI, to estimate the
thermodynamic efficiency of cross-bridge energy conversion
(CB); that is, the fraction of the energy produced by
hydrolysis of one ATP molecule that is converted into work during one
cross-bridge ATP-splitting event. If eI is 28%, the
enthalpy of PCr splitting is 35 kJ mol-1
(Woledge and Reilly, 1988
),
the free energy change of ATP hydrolysis in cardiac cells is 60 kJ
mol-1 (Kammermeir et al.,
1982
) and it is assumed that 80% of the initial energy cost can be
attributed to cross-bridge cycling (reported values range from 70% to 85%;
Gibbs et al., 1988
;
Alpert et al., 1989
;
Schramm et al., 1994
), then
the cross-bridge thermodynamic efficiency is (28/0.8)x35/60)
20%. The
fraction of energy output assumed to be related to cross-bridge activity has
only a small influence on this value: if cross-bridge cycling accounted for
70% of the energy use then
CB would be 23%, and if
cross-bridge cycling accounted for 85% of initial energy use then
CB would be 19%. If one ATP were used in each cross-bridge
cycle, providing 100x10-21 J of free energy, then an
CB of 20% would correspond to 20x10-21 J
work per cross-bridge cycle.
The maximum work that could potentially be performed per cross-bridge cycle
can be determined from the cross-bridge force-extension relationship (or
T2 curve; Huxley and Simmons,
1971) determined from quick-release experiments. Colomo et al.
(1994
) determined T2
curves for frog atrial cells (10°C). Their data indicated that the maximum
work per cross-bridge cycle would be
8.5 P0 nm, where
P0 is the maximum isometric cross-bridge force. If, as
estimated above, maximum work per cross-bridge is 20x10-21 J,
and this corresponds to the maximum cross-bridge work estimated from the
T2 curve for amphibian atrial cells, then maximum cross-bridge
force would be 20x10-21 J/8.5x10-9
m=2.4x10-12 N. This force output is consistent with that
determined for myosin from cardiac muscle
(Sugiura et al., 1998
).
The data presented by Colomo et al.
(1994) are also consistent with
cross-bridges having a working stroke (i.e. the filament movement generated by
one cross-bridge in one attachment cycle) of
10 nm. However, other
experimental evidence has been interpreted as indicating that the cross-bridge
stroke in cardiac muscle may be as great as 2030 nm (see
De Winkel et al., 1995
and
references therein). For instance, De Winkel et al.
(1995
) calculated cross-bridge
working stroke from the dynamic stiffness of skinned rat trabelculae
(22°C) and concluded that it was at least 20 nm. It has been suggested
(Gibbs and Barclay, 1995
) that
these values are consistent with high efficiency values, such as those
reported by Peterson and Alpert
(1991
). If, however,
CB is only 20%, then such large working strokes would imply
that maximum cross-bridge force output must be <1 pN, which is much smaller
than values determined using isolated contractile proteins
(Van Buren et al., 1995
;
Sugiura et al., 1998
). Thus,
large cross-bridge working strokes seem unlikely but it is important to
clarify the amplitude of the working stroke of cardiac cross-bridges in intact
muscle.
Efficiency of oxidative recovery
The magnitude of the difference in estimates of eI
between the present study and that of Peterson and Alpert
(1991) also has significant
implications for the thermodynamics of oxidative recovery processes. It is
well established that eN is <20% in cardiac muscle of
both mammals (Gibbs et al.,
1967
; Mellors et al.,
2001
; Mellors and Barclay,
2001
) and amphibians (Syme,
1994
). eN is approximately the product of the
initial thermodynamic efficiency (
I, the ratio of work output
to initial free energy change, including both that associated with
cross-bridge cycling and ion pumping) and the efficiency with which
mitochondria convert the free energy from metabolic substrate into free energy
in ATP. This is because the free energy change and the enthalpy change for the
recovery processes have almost the same value (for a detailed discussion, see
Gibbs and Barclay, 1995
).
I is the product of the initial mechanical efficiency and the
ratio of
HPCr and
GATP
(=35/60
0.6). If eI were 60%
(Peterson and Alpert, 1991
)
then
I would be 36%. eN is 13% (present
study), so the efficiency of mitochondrial energy conversion would be
13/36
35%. However, the efficiency of the recovery processes appears likely
to be much higher than this, probably between 70% and 80%
(Gibbs and Barclay, 1995
;
Lou et al., 2000
). This
further supports the idea that it would be difficult to reconcile an
eI as high as 60% with the well-established values for
eN.
The data from the present study can be used to estimate the efficiency of
the recovery processes. If eI is 28% then
I
16.8% and the efficiency of the recovery processes would
be (13.3/16.8)x100=80%. This is similar to the value of 84% calculated
from measurements of the O2 consumed and heat produced by skeletal
muscle fibres from the dogfish (Scyliorhinus canicula;
Lou et al., 2000
).
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Conclusions |
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List of symbols |
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This work was supported by the National Health and Medical Research Council of Australia.
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References |
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