Energy-saving mechanisms in muscle: the minimization strategy
1 Department of Radiology, Box 357115, University of Washington Medical
Center, Seattle, WA 98195-7115, USA
2 Department of Physiology and Biophysics, University of Washington Medical
Center, Seattle, WA 98195-7115, USA
3 Department of Bioengineering, University of Washington Medical Center,
Seattle, WA 98195-7115, USA
4 Physiology and Functional Morphology Group, Department of Biological
Sciences, Northern Arizona University, Flagstaff, AZ 86011-5640,
USA
* Author for correspondence at address 1 (e-mail: kconley{at}u.washington.edu )
Accepted 13 May 2002
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Summary |
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Key words: sound production, flight, muscle, energetics
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Introduction |
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Energy-saving mechanisms |
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Light appendages/low work
Sound-producers and fliers use very light limbs that require little
mechanical work and correspondingly low muscle energy expenditure. The
rattlesnake tailshaker/rattle system offers a good example of how energy
minimization is achieved by reducing mechanical and muscle work. The hollow
and thin-walled structure of the rattle of rattlesnakes appears to be ideally
designed to minimize rattling work. In addition, several specializations of
muscle function ensure that contractile costs are very low for rattling; as a
result, the cost of tailshaking is among the lowest per contraction of any
vertebrate muscle (Conley and Lindstedt,
1996). These specializations can best be illustrated by analyzing
why the cost of rattling does not change with temperature and contraction
frequency.
Minimizing work
Tailshaking by the rattlesnake has a constant contractile cost of rattling
per twitch despite the fact that the mechanical work of rattling is expected
to increase at higher rattling frequencies. Brad Moon and Jo Hopp in my
laboratory resolved this paradox by considering the rattle movement during
tailshaking as an inverted pendulum (Moon
et al., 2002). The work (W) required per swing of the
pendulum increases as the frequency (f) of the swings (or rattles)
increases at a constant swing arc (
):
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To answer the question of how cost can remain constant despite a rise in
mechanical work requires an analysis of how the tailshaker muscle uses energy
in the generation of force. Rearrangement of the relationship between work and
force over distance in equation 2 shows that, to achieve a greater rattle
mechanical work, the muscle must increase peak force production (F):
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Minimizing contractile costs |
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The second reason that high-frequency contractions necessitate reduced
contractile cost is the need to balance ATP supply to demand. Since the cell
has a finite volume for structures involved in the ATP balance, any increase
in the volume of the structures supplying ATP comes at the expense of the
structures using ATP. Three cellular structures are involved in the ATP
balance and vie for space in the cell: mitochondria (ATP supply), sarcoplasmic
reticulum (Ca2+-ATPase) and contractile elements (myosin ATPase).
The consequence of maximizing ATP supply to sustain high-frequency
contractions is increased mitochondrial volume density and a decreased
fraction of the muscle available for ATP use
(Conley and Lindstedt, 1998;
Lindstedt et al., 1998
). Thus,
the simple fact of increasing the volume of the cell devoted to ATP supply
means less volume available for the structures using ATP.
This trade-off is illustrated for the rattlesnake body and tailshaker
muscles in Fig. 1
(Schaeffer et al., 1996).
Nearly 85% of the body muscle is made up of contractile elements (i.e. actin
and myosin), with a small volume fraction dedicated to mitochondria and
sarcoplasmic reticulum. In contrast, the tailshaker muscle has a large
increase in the volume of mitochondria and a greater sarcoplasmic reticulum
content for rapid Ca2+ cycling. Since the cell volume is a zero-sum
game, the higher proportion of mitochondria and sarcoplasmic reticulum comes
at the expense of actin and myosin content, which drops from 85 to 30% of cell
volume. This shift means that only one-third of the muscle cell is actually
made up of contractile elements in the tailshaker muscle! This lack of
contractile area is directly reflected in a reduction in the ability to
generate force by the muscle. For example, frog muscle with 83% of cell volume
as actin and myosin (Mobley and Eisenberg,
1975
) generates maximal muscle stress at an isometric tension of
200 kN m-2 (Bagshaw,
1993
), but this falls in tailshaker muscle with 30% of cell volume
as actin and myosin to approximately 63 kN m-2
(Martin and Bagby, 1973
). A
similar difference in maximal twitch tension between the body musculature and
the sound-producing muscles has been reported in two species of gray tree frog
(Marsh, 1999
).
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The reduction in actin and myosin content in sound-producing muscle is not as great in insect flight muscle, which must generate sufficient lift for flight. Fig. 2 compares the cellular composition of insect muscle from two types of flight muscle and a muscle involved in sound production. One characteristic that distinguishes flight from sound-producing muscle is the higher proportion of actin and myosin (>40%), presumably to meet the force production needs of flying. Another characteristic that distinguishes the two types of flight muscle is the proportion of sarcoplasmic reticulum. Asynchronous muscle (e.g. bee flight muscle at 220 Hz) relies on a stretch activation mechanism to trigger contraction rather than a direct link between a nerve impulse and a twitch. As a result, the proportion of the cell volume devoted to Ca2+ pumping for muscle relaxation drops from more than 30% in synchronous muscle (Fig. 2A) to a few per cent (Fig. 2B). This fall in sarcoplasmic reticulum content affects ATP balance in two ways: by nearly eliminating Ca2+ cycling costs but also by providing space for additional mitochondrial volume, which permits ATP supply to increase. For lower-frequency flight muscle and muscle involved in sound production, an ATP balance can be achieved with a high proportion of sarcoplasmic reticulum, permitting direct coupling between nerve activation and contraction.
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Reduced cross-bridge cycling |
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Fewer attached cross-bridges
A small proportion of attached cross-bridges with each twitch has been
reported recently for toadfish muscle generating its characteristic `whistle'
(at 200 Hz). Only 10% of the available cross-bridges attach with each twitch
compared with nearly 70% in the trunk muscles of this fish and typical of
locomotory muscles in general (Rome et
al., 1999). The impact of the low proportion of attached
cross-bridges and low contractile content is a very low maximal force per
cross-sectional area (see below).
Low strain
A final factor related to cross-bridge cycling is the muscle length change.
The total length change of the muscle with each twitch is termed the strain.
Larger strains are accomplished by more cross-bridge cycles and, presumably,
higher costs with each twitch. The few muscles studied from flying species
show a clear relationship between strain and frequency. Birds flying at a
flapping frequency of few hertz have strains as high as 32% of muscle length
(Biewener et al., 1998), while
strain drops to a few per cent (as low as 2%) in insect flight muscle
(Gilmour and Ellington, 1993
).
Fig. 3 shows that, as frequency
increases and the period of each contraction decreases, strain falls and
appears to reach a minimal value (i.e. 2%) above a sustained contraction
frequency of 100 Hz. This figure clearly demonstrates that muscle strain is
not constant, as has been assumed in simple models of muscle function (see
Pennycuick and Rezende,
1984
).
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Does the 2% strain represent a true minimal value? Such a minimum would be
defined by the cycle of a single cross-bridge. Since a cross-bridge cycle
covers approximately 20 nm in intact frog muscle
(Bagshaw, 1993) and sarcomere
length is 2.3 µm in tailshaker muscle (K.E.C. and S.L.L., unpublished
observation), then a 1% length change per half-sarcomere and 2% overall per
twitch defines a single cross-bridge cycle in intact muscle (shorter
cross-bridge length changes are reported for isolated myosin in in
vitro motility assays unconstrained by the three-dimensional structure of
the intact muscle; Molloy et al.,
1995
). The similarity between the minimal measured strain and the
distance for a cross-bridge cycle suggests that high-frequency contractions
may be at the limit of contractile function, with each twitch representing a
single cycle of the cross-bridges (see below).
Minimizing contractile costs
Fig. 4 shows that the
consequence of the minimization of contractile function is a decrease in ATP
cost per twitch as frequency increases in insect flight and sound-producing
muscles. The highest cost per twitch occurs in synchronous fliers that
contract at low frequency, but cost rapidly drops off with frequency to reach
a plateau above 80 Hz in the asynchronous fliers. Above 100 Hz, there is no
change in cost with frequency, but there is a striking difference in the cost
per contraction for asynchronous fliers (approximately 0.3 µmol
g-1 twitch-1) compared with sound producers (<0.05
µmol g-1 twitch-1). This minimal cost per contraction
suggests that the sound-producing muscles may represent muscles that have
adapted to function at the contractile limit. Let us use the anatomical and
functional properties of these muscles to evaluate the basis of these costs
and to test whether this minimal cost represents the functional limit of
contraction in muscle.
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Muscle at the contractile limit |
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Model of muscle contractile energetics
Power output per unit volume of muscle (P*) can be
predicted from a simple model based on muscle stress (), strain
(
) and twitch frequency (f) modified from Ellington
(1991
) and Pennycuick and
Rezende (1984
):
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This model can be expressed in terms of energy input per twitch
(ATP/twitch) based on the factors responsible for muscle stress and strain.
Two factors responsible for muscle stress are the cross-bridge content ([CB])
and the fraction of attached cross-bridges (fCB). For muscle
strain, the underlying factor is the number of cross-bridge cycles
(NCB) in each twitch. Finally, the contractile cost
relates to the number of cross-bridges cycling in each twitch assuming 1 ATP
per cross-bridge cycle, (ATP/CB)=1:
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This equation allows us to evaluate contractile cost on the basis of the
number and function of the cross-bridges in a muscle. The asynchronous muscle
of flying bees is a good place to start since we can ignore Ca2+
cycling costs because the stretch activation mechanism requires little
Ca2+ cycling. In addition, information on the content and cycling
of cross-bridges is available for flying bees
(Casey and Ellington, 1989)
using frog muscle as a standard (Bagshaw,
1993
).
Calculating contractile cost from muscle properties
The first property needed for this calculation is [CB] in bee muscle, which
can be calculated by adjusting the [CB] of frog muscle (240 µmol
l-1 myosin heads) for the difference in actin and myosin content of
these muscles. Correcting for the lower actin and myosin content in bee (57 %)
compared with frog (83 %) muscle reduces [CB] to 160 µmol l-1
for the bee muscle. The second property is the fraction of cross-bridges that
attach in a twitch (fCB). The conventional estimate is that 70 % of
the cross-bridges are attached in an isometric contraction
(fCB=0.7) (Bagshaw,
1993; Rome et al.,
1999
). This assumption of an isometric contraction may be correct
given the low strain (2 %) reported for the flight muscle of these bees
(Gilmour and Ellington, 1993
)
and suggests that the cross-bridges undergo a single cycle per twitch
(NCB=1). Using these values in equation 4 yields a
contractile cost of 116 µmol l-1 ATP twitch-1
(chemical concentration is expressed per total muscle water with the
assumption that 1 ml=1 g) or 0.116 µmol ATP g-1
twitch-1. This value is remarkably close to the mean measured value
of 0.12 µmol g-1 twitch-1 reported for these bees
(assuming ATP:O2=6). This agreement between a simple model of ATP
use by the flight muscle and measured energy use supports our assumptions of
cross-bridge attachment (70 % of cross-bridges attach per twitch) and
cross-bridge cycling (one cross-bridge cycle per twitch). The implication of
one cross-bridge cycle per twitch is that fliers have pushed cross-bridge
cycling to one limit of contractile function. Have sound-producers approached
another limit by reducing the proportion of attached cross-bridges in each
twitch from 70 % to only 10 % (Rome et
al., 1999
)?
Sound production and the limits of contractile function
The lowest reported contractile cost is for tailshaking by the rattlesnake
(Conley and Lindstedt, 1996).
We can evaluate the basis of this minimal contractile cost using the
anatomical and energetic information available for the tailshaker muscle
(Fig. 1) (Schaeffer et al., 1996
). The
30 % actin and myosin content in tailshaker muscle translates to 85 µmol
l-1 cross-bridges. If only 10 % of the cross-bridges attach
(fCB=0.1) and go through one cycle (NCB=1) with
each twitch, then 8.5 µmol cross-bridge l-1 cycle with each
twitch for a cost of 0.0085 µmol ATP g-1 twitch-1.
For synchronous muscle, we also need to take into account that 2
Ca2+ are required to activate each cross-bridge. The minimum cost
of recycling Ca2+ is given by the stoichiometry of the sarcoplasmic
reticulum Ca2+ ATPase: 1 ATP per 2 Ca2+. Thus, each
cross-bridge cycle requires 1 ATP for the myosin head and 1 ATP to recycle
Ca2+. This equal partitioning of costs between Ca2+ and
cross-bridge cycling (50 %/50 %) is close to the 35-45 % for `activation
costs' (and 55-65 % for cross-bridge cycling) recently reported for toadfish
muscle (Rome and Klimov,
2000
). Thus, Ca2+ cycling requires an additional 0.0085
µmol ATP g-1 twitch-1 for a total cost of 0.017
µmol ATP g-1 twitch-1, which is, again, remarkably
close to the measured contractile cost per twitch of 15 µmol ATP
twitch-1 or 0.015 µmol ATP g-1 twitch-1
(Conley and Lindstedt, 1996
).
These calculations indicate that the minimal contractile cost during rattling
reflects the tailshaker muscle operating at the limits of contractile
function: one cross-bridge cycle per twitch and attachment of only 10 % of
available cross-bridges. Thus, the tailshaker muscle and sound-producers in
general have minimized contractile cost by pushing muscle to the lower limits
of contractile function.
Contractile cost versus muscle properties
This simple calculation approach allows us to evaluate the relative
importance of the factors underlying muscle stress and strain in determining
contractile cost. We can use equation 4 to estimate the maximum contractile
cost for comparison with the minimal cost in the sound-producers. The upper
end of [CB] (240 µmol l-1) and cross-bridge attachment
(fCB=0.7) are represented by frog muscle. The highest strain shown
in Fig. 3 is 32 %, which
results in NCB=16 (NCB=1 for 2 %
strain). The resulting cross-bridge cost of 2688 µmol l-1 or 2.6
µmol ATP g-1 twitch-1 plus an additional 30 % for
Ca2+ cycling (typical `activation cost' in vertebrate muscle;
Rall, 1985) yields 3.5 µmol
ATP g-1 twitch-1. This upper limit of costs is very
close to the highest value shown in Fig.
4 (i.e. 3.8 µmol ATP g-1 twitch-1). Thus,
the range of anatomical and functional properties found among muscles results
in the full range of measured contractile costs.
We can now use equation 4 to estimate the relative importance of each
muscle property in determining cost. Surprisingly, the smallest relative
change in cost comes from the range in [CB], which varies threefold between
frog (240 µmol l-1) and sound-producers (85 µmol
l-1). A larger contribution comes from cross-bridge attachment,
which changes sevenfold from the minimal 10 % cross-bridge attachment in
sound-producing muscle (fCB=0.1) to the value of 70 % thought to be
typical of most vertebrate and insect flight muscle (fCB=0.7).
Finally, the largest contribution comes from muscle strain (or the number of
cross-bridge cycles), which varies 16-fold from the minimal value in
sound-producers and fliers (2 %) to the highest value in a flying bird (32 %;
Biewener et al., 1998). The
contribution of muscle strain to cost is apparent in the similarity in the
shape of the data plots in Figs
3 and
4, in which the large decline
in strain with frequency is directly reflected in a sharp drop in contractile
cost. Similarly, the role of cross-bridge attachment is reflected in the
difference in cost above a frequency of 100 Hz in
Fig. 4: the nearly 10-fold
difference in cost between asynchronous fliers (fCB=0.7) and
sound-producers (fCB=0.1) is close to the sevenfold difference in
cross-bridge attachment.
These results demonstrate a remarkable correspondence between the measured
contractile costs of muscle and those predicted on the basis of a simple model
of cross-bridge content and function. Of course, each assumption of this
simple model can be challenged, such as the proportion of cross-bridges
attached, a single cross-bridge cycle per twitch, etc. However, what is
remarkable is how well this simple model predicts the range of contractile
costs, even with these assumptions. This predictive power illustrates two
points. First, it appears that the model quantitatively accounts for the major
ATP-using processes in active muscle. Thus, the contribution of
energy-recovery mechanisms, such as elastic storage, is probably close to the
estimate (approximately 10 %; Dickinson and
Lighton, 1995) for insect flight muscle contracting at high
frequency (>100 Hz). Second, the minimal contractile cost measured for
sound-producing muscle reflects muscle working close to the functional limit
of the cross-bridges. Thus, the constraints imposed on muscle to achieve high
frequency rapid contractile kinetics and high sustained ATP demand
result in a reduction in cross-bridge content and function that
minimizes ATP use per contraction. The result is a reduction in muscle
function to the lower limits of contraction, with the consequence of achieving
a minimal cost per contraction in sound-producers such as the rattlesnake.
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Concluding remarks |
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Acknowledgments |
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References |
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