Contractile properties of mouse single muscle fibers, a comparison with amphibian muscle fibers
Department of Physiological Sciences, Biomedical Centre, F11, University of Lund, S-221 84 Lund, Sweden
e-mail: paul.edman{at}farm.lu.se
Accepted 7 March 2005
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Summary |
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Key words: muscle fiber, muscle contraction, mammalian muscle, force-velocity relationship, length-tension relationship
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Introduction |
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The present investigation has been performed on isolated mouse muscle
fibers using techniques that previously have been employed in studies of
amphibian fibers. Interest has been focussed on the shape of the
force-velocity relationship, as previous studies of frog muscle fibers have
shown that the force-velocity relation in these muscles is not a simple
hyperbolic function, as originally thought
(Hill, 1938), but contains two
distinct portions on either side of a breakpoint in the high-force range
(Edman, 1988
). This observation
suggests that the kinetics of cross-bridge function is changed as the load on
the muscle exceeds a critical value (Edman
et al., 1997
). With the techniques used it has furthermore been
possible to length clamp a limited region of an isolated mammalian muscle
fiber, in this way making it feasible to delineate the relationship between
force and sarcomere length in the preparation used.
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Materials and methods |
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The flexor digitorum brevis muscle (FDB) of the mouse is classified as a
`fast' skeletal muscle. A recent study
(González et al., 2003)
based on immunostaining techniques has demonstrated that fibers expressing the
fast-type myosin heavy chain (MHC) isoforms IIX and IIA were predominant in
FDB, amounting to 83-87% of the fiber population. No staining for the
fast-type MHC IIB was observed. An additional 13-17% of the fibres expressed
the slow-type MHC I. A similar isomyosin composition of the FDB of the mouse
has been observed by Reggiani and co-workers (C. Reggiani, personal
communication), based on gel electrophoretical separation. However, in the
latter study, myosin isoform IIB was constantly found to be present in
approximately 10% of the fibre population.
Solutions
The bathing solution had the following composition (mmol l-1):
NaCl, 137; KCl, 5; MgCl2, 1; NaH2PO4, 1;
NaHCO3, 16; Glucose, 11; CaCl2, 2; pH 7.4. The bathing
solution was equilibrated with a mixture of 95% O2 and 5%
CO2 before entering the muscle chamber, the latter being
thermostatically controlled by circulating a water-glycerol solution from a
Colora Ultrathermostat (Colora Messtechnik GMBH, Lorch, Germany) through
jackets surrounding the muscle chamber. The bathing fluid was perfused through
the muscle chamber (volume, approximately 2.5 ml) at a speed of approximately
2 ml min-1. The bath temperature was constant to within 0.2°C
during any given experiment, but varied between 21 and 27°C among the
different experiments. Fiber length and fiber width were determined as
described by Edman and Reggiani
(1984). Contrary to the
relatively thick frog muscle fibers, whose cross-section is markedly irregular
in shape from one end to the other (see
Blinks, 1965
), the thinner
mouse fibers were found to have a more uniform, rounded shape. The
cross-section of the mouse muscle fibers was therefore calculated from the
measured fiber diameter (d) assuming a circular cross-section, i.e.
as
(d/2)2.
Determination of sarcomere length
Because the thin, single muscle fibers gave a very weak laser diffraction
pattern, the sarcomere length was measured at rest at 800x magnification
within a marked segment of the fiber. This was achieved at a given length of
the segment by means of a light microscope that was fitted with a 40x
water-immersion objective and an ocular micrometer. Rows of about 20
sarcomeres were measured and a mean value of the sarcomere length was formed.
By knowing the sarcomere length at rest, the overall sarcomere spacing within
the segment could be determined at any time during activity by monitoring the
length of the marked segment (see below). Unless otherwise stated, the
experiments were performed at a resting sarcomere length of 2.6-2.7 µm,
i.e. just above slack fiber length.
Force transducer
The principal unit of the force transducer was a semiconductor strain-gauge
element (AE 801, Aksjeselskapet Mikroelektronikk, Horten, Norway). A thin
extension (approximately 5 mm in length) made of wood was glued by epoxy resin
to the silicon bar outside the domain of the strain-gauge elements. The tip of
the extended arm was provided with a hook of stainless-steel wire (diameter,
0.1 mm) for attachment of the muscle fiber (see above). The resonant frequency
was approximately 2 kHz when the transducer arm was submerged in the bathing
solution.
Stimulation
Rectangular pulses of 0.2 ms duration were passed between a pair of
platinum plate electrodes that were placed symmetrically, approximately 4 mm
apart, on either side of the muscle fiber. The stimulus strength was set to
approximately 15% above the mechanical threshold. A train of pulses of
appropriate frequency (60-80 Hz) was used to produce a fused tetanus of 0.5-1
s duration.
Measurements of length changes
An electromagnetic puller of the type described previously
(Edman and Reggiani, 1984) was
used for performing controlled length changes of the muscle fibers. The
technique used for recording changes in length of a marked segment of the
fiber was the same as that described by Edman and Lou
(1990
). Two opaque markers cut
from letterpress (approximately 75 µmx75 µm; mass approximately
0.1 µg) were attached to the upper surface of the fiber with the non-glue
side of the letterpress material facing downwards, the distance between the
markers being 0.3-0.35 mm. A laser beam, expanded to cover the marked segment,
illuminated the fiber from below, and a magnified image of the segment was
projected onto a photodiode array (Fairchild CCD 133, Milpitas, CA, USA). The
distance between the two markers was read throughout a contraction with a time
resolution of 40 µs. An analogue circuit converted the output from the
photodiode array to a signal proportional to the percentage change of the
segment length. The accuracy of the measurement was better than 0.2% of the
segment's length.
The marker recording technique was used in certain experiments for actively controlling the length of the segment during the stimulation period (`segment length clamp'). This was achieved by adjusting the overall length of the fiber appropriately using the segment-length signal for feedback control of the electromagnetic puller. Using this approach, it was possible to make the segment shorten at a given speed to a predetermined sarcomere length, to be held stationary at this length for the remainder of the activity period. This was accomplished by altering the reference level of the feedback system by means of a voltage ramp. A small initial transient of the length signal, covering approximately 5 ms, frequently occurred affecting the onset of tension rise during the corresponding time.
Load-clamp recording
Load clamping for isotonic shortening was carried out by rapidly changing
the mode of operation of the electromagnetic puller from fiber-length control
to force control. The switch-over to force control occurred during the plateau
of a 1-s tetanus (approximately 400-500 ms after the onset of stimulation),
and the force-control mode was thereafter maintained throughout the tetanus
period. With the experimental device used it was possible to achieve a period
of stable tension over a wide force range, even quite close to zero force
level. In the present series of experiments, the load was varied between
P0 (isometric force) and 5% P0
(five experiments), and between P0 and 8%
P0 (one experiment).
Recording and measurement of data
The signals of the force and displacement transducers, and the
segment-length signal were fed into an acquisition and analysis program
(Labview, National Instruments, Austin, TX, USA) and stored on disks. For the
analysis of the force-velocity relationship, the slope of the digital length
records was measured within the relatively straight portion of the record that
occurred after the initial transient had been passed during the force-clamp
manoeuvre. The slope was measured over a time interval of approximately 20 ms
using a computer program based on the least-squares method.
The force-velocity relation was biphasic with two distinct curvatures on
either side of a breakpoint near 80% of the measured isometric force, similar
to the situation in extra- and intrafusal fibers of frog muscle
(Edman, 1988;
Edman et al., 2002
). The
biphasic equation previously described
(Edman, 1988
) was used to fit
the experimental data:
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where V is the velocity of shortening, P the load on the
muscle fiber and P0 the measured isometric force. The
first term of the equation expresses the force-velocity relation below 0.8
P0, and represents a rectangular hyperbola in the form
described by Hill (1938).
P0* is the isometric force predicted from this
hyperbola, and a and b are constants with dimensions of force and velocity,
respectively. The second term within parenthesis [referred to as the
`correction term' (Edman,
1988
)] reduced V at high loads to fit the distinct
upward-concave curvature at loads greater than approximately 0.8
P0. The constant k1 in the correction term has
the dimension of 1/force, whereas k2 is dimensionless.
k1 determines the steepness of the high-force curvature and
k2 the relative force at which the correction term reaches its half
value. The two constants are useful parameters when comparing data from
different studies.
Statistics
All statistics are given as means ±
S.E.M. Student's t-test was used for
determination of statistical significance.
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Results |
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The maximum tetanic force determined in 10 different mouse fibers was
368±57 kN m-2 (21-27°C). For comparison, a mean tetanic
force of 416±16 kN m-2 (N=20) was recorded in the
frog single muscle fibers at optimal length at 20-22°C (K. A. P. Edman and
T. Radzyukevich, unpublished). The tetanic force produced by the mouse fibers
was thus not significantly different from that generated by Rana
temporaria muscle fibers at 21°C. It is of interest to note that
substantially lower mean values of the isometric tetanic force (291 and 258 kN
m-2) have been recorded in the high temperature range (20-24°C)
by Cecchi et al. (1978) and
Piazzesi et al. (2003
), in
studies of single fibers from Rana esculenta.
The possibility was considered that the slow onset of tetanic force might
be due to a larger series compliance within the mammalian fiber during
activity, as this would delay the attainment of steady force. In order to test
this point, experiments were performed in which a short (0.3 mm) segment,
located midway between the tendons, was held at constant length during
stimulation (see Materials and methods). As illustrated in
Fig. 1B, the rate of rise of
force during length-clamp recording (following the initial transient at the
onset of activation; see Materials and methods) was quite similar to that
recorded under standard conditions, suggesting that the slow attainment of
maximum force reflects a lower rate of activation of the mammalian fibers.
Force-velocity relationship
Load-clamp recordings at different loads performed in a mouse single muscle
fiber are illustrated in Fig.
2. As can be seen, constant force could be attained within 15-25
ms of switching from length- to force-control of the electromagnetic puller.
The slope of the length records was determined by regression analysis within a
time interval of approximately 20 ms after the initial transient had been
passed during the load-clamp manoeuvre (see Materials and methods).
Fig. 3 illustrates a typical
force-velocity analysis with data points ranging from P0
(isometric force) to 3% P0. The force-velocity
relationship of the mouse muscle fibers exhibited the same characteristic
biphasic shape as has been previously demonstrated in frog muscle fibers
(Edman, 1988). The
force-velocity relationship can thus be seen to have two distinct curvatures
located on either side of a breakpoint near 80% of the isometric force. The
two phases of the force-velocity relationship, and the location of the
breakpoint, are most clearly illustrated in the semilogarithmic plot shown in
Fig. 3B. The data displayed in
the standard forcevelocity diagram (Fig.
3A) can be fitted well by the biphasic equation (see Eqn 1) that
has previously been employed to characterize the force-velocity relationship
in frog muscle fibers (Edman,
1988
). In this equation, the constant k1 expresses the
degree of curvature at high loads, whereas k2 indicates the
position of the high-force curvature along the force axis (see Materials and
methods).
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Numerical values of the various parameters in Eqn 1 derived from six different experiments are summarised in Table 1. The data are in general agreement with those obtained in frog muscle fibers. The extension of the curve derived at low and intermediate loads can be seen to intersect the abscissa at a point, P0*, that was considerably (mean, 1.4x) higher than the measured isometric force P0, indicating that the power output of the fiber decreased dramatically as the load exceeded the breakpoint of the force-velocity relation.
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Vmax, the speed of shortening at zero load estimated
from the force-velocity curve, was 4.0±0.3 L s-1
(N=6, 23.1-23.8°C). A higher value of the maximum speed of
shortening (7.89± 0.35 L s-1, 22-24°C) of
intact fibers from the same muscle species (mouse, NMRI) has been reported by
Westerblad et al. (1998),
using the slack-test method (Edman,
1979
). This difference in results is not readily understood but
could mean that the measurements in the two studies refer to different
portions of the multi-headed muscle. It should be pointed out that hyperbolic
extrapolation of force-velocity data derived at finite loads may provide a
somewhat lower value of the maximum shortening velocity than that derived by a
slack-test analysis (for details, see
Edman, 1979
;
Josephson and Edman, 1988
).
However, as the present study included load-clamp measurements quite close to
zero load, it is reasonable to conclude that the value of
Vmax derived in the present study does represent a valid
estimate of the maximum speed of shortening in the fibers used (see
Josephson and Edman, 1988
).
Considerably higher speeds of shortening than those produced by the mouse
fibers were recorded in frog single muscle fibers at the same temperature
(19.3-22.7°C) in this laboratory (K. A. P. Edman and T. Radzyukevich,
unpublished). The speed of unloaded shortening (slack tests) of the frog
fibers was found to be 8.2±1.9 L s-1
(N=19), i.e. twice the value derived in the present study of mouse
muscle fibers.
Length-tension relationship
A series of experiments was performed in which the tetanic force of a
marked, length-clamped segment (approximately 0.3 mm in length) of a single
mouse muscle fiber was recorded at different sarcomere lengths. The sarcomere
length was determined by measuring the space taken up by rows of 20 sarcomeres
using a microscope at 800x magnification as described in Materials and
methods. This measurement was carried out with the fiber adjusted to just
above slack length. Before starting the sarcomere length measurement, the
fiber was stretched passively 2-3 times to an extreme length. The sarcomere
spacing during activity was calculated from the measured sarcomere length at
rest and the overall change in length of the marked segment. The force
measurements during length-clamp recording were performed in repeated
sequences in both directions along the descending limb of the length-tension
relation. Force measurements below slack length were performed during standard
isometric recording (fixed fiber ends), as tension creep was insignificant
during the tetanus under these conditions (see below).
Fig. 4A illustrates length-clamp recordings during tetanic stimulation at sarcomere lengths within the plateau region and the descending limb of the length-tension relation, and Fig. 4B shows standard isometric tetani recorded on the ascending limb of the length-tension relation. In both cases, the force records can be seen to exhibit a minimum of tension creep, and they may therefore be considered to represent the actual capacity of the fiber to produce force at the various sarcomere lengths.
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Fig. 5 illustrates the
variation in force, with sarcomere length based on data compiled from three
mouse fibers (one for the ascending limb and three for the descending limb),
the data points being normalised to the force recorded at 2.45 µm sarcomere
length in the respective fiber. The straight line is the linear regression of
force upon sarcomere length calculated for values between 2.35 µm and 4.0
µm (correlation coefficient: 0.96). The line intersects the abscissa at
3.88 µm and reaches maximum force (1.0) at 2.40 µm. The latter value
thus represents the calculated right end of the plateau of the length-tension
relation, i.e. the point where, theoretically, the thin filaments have reached
the inert, or bare, zone in the middle of the thick filaments. Based on this
assumption, the regression line in Fig.
5 suggests that the average length of the actin filaments is 1.10
µm. For this calculation, it is assumed that the bare zone of the thick
filament is 0.16 µm (Craig and Offer,
1976; ter Keurs et al.,
1984
) and the width of the Z disk is 0.05 µm
(Page and Huxley, 1963
). On
the same assumptions, the intersection of the regression line with the
abscissa at 3.88 µm sarcomere length is compatible with an average thick
filament length of 1.63 µm. The values of the thick and thin filament
lengths so derived agree exceedingly well with recent electron microscopical
measurements of the two filaments in rabbit psoas muscle
(Sosa et al., 1994
).
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Tetanic force stays fairly constant between 2.1 and 2.4 µm sarcomere length and can be seen to decrease steeply by reducing the sarcomere length below 2.0 µm; at 1.5 µm sarcomere spacing, the measured force was merely 45% of the plateau value.
The asterisks plotted along the ascending limb of the length-tension
relation (Fig. 5) are estimated
values of force based on the model previously described in a corresponding
study of frog muscle fibres (Edman and
Reggiani, 1987). The following assumptions were used: (1) active
force is produced in proportion to the amount of single overlap
(OS, inset, Fig.
5) between adjacent thick and thin filaments; (2) the decrease in
tension below optimum length is attributed to the occurrence of double
filament overlap (OD, inset,
Fig. 5) that leads to a
decrease in the number of active cross-bridges or, alternatively, to a force
opposing filament sliding; and (3) an additional counteracting force is
thought to arise as the ends of the thick filaments are compressed as a result
of collision with the Z disks at lengths below 1.68 µm sarcomere length.
The expected force along the ascending limb of the length-tension relation was
thus derived from the following expression:
![]() | (2) |
where KS, KD and KC are proportionality coefficients with dimensions of force per micrometer filament overlap per half sarcomere. For these calculations, the above numerical values of the filament lengths, the widths of the Z disk and the bare zone have been used, and the calculated force (F) is expressed in units of the force calculated at optimum sarcomere length, i.e. at 2.40 µm sarcomere length, where OS (=0.735 µm) is maximum (see above). The numerical value of KS used for calculating the force was therefore the reciprocal of 0.735.
Fig. 5 (asterisks) shows the predicted force at selected sarcomere lengths calculated according to the above model, assuming that the three proportionality coefficients have the same numerical value, 1/0.735. As can be seen, the predicted force values accord remarkably well with the actual measurements of force below optimal length.
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Discussion |
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Time course of mechanical activation
The onset of tension rise during tetanic stimulation was found to be less
steep in the mouse fibers than in frog muscle fibers, the time required to
reach 90% of maximum force being approximately four times longer in the
mammalian fibers when measured at equal temperatures (20-25°C). The
possibility was ruled out that the relatively slow rise of the tetanic force
during standard isometric recording (fixed fiber ends) was due to larger
series compliance in the mammalian preparation, which would delay the
attainment of maximum force. This was achieved by recording force while a
short (approximately 0.3 mm) segment was held at constant length during
tetanic stimulation, in this way eliminating any influence on the force
measurement by compliant structures outside the domain of the fiber segment.
The length-clamp recording confirmed the relatively slow development of force
observed during standard recording, indicating that this is a characteristic
feature of the mammalian fiber at sarcomere level.
Force-velocity relationship
The results show that the force-velocity relationship of the mouse muscle
fibers has the same biphasic shape as has been previously demonstrated in frog
muscle (Edman, 1988;
Edman et al., 1997
), i.e.
there are two distinct curvatures, both with an upwards concave shape, on
either side of a breakpoint near 80% of the isometric force. The
force-velocity data could be fitted well with the biphasic equation that has
previously been applied to frog muscle fibers, using quite similar numerical
values of the parameters defining the two curvatures of the force-velocity
relationship.
The present results strengthen the view that the biphasic shape of the force-velocity relation is a genuine property of the contractile system in striated muscle, and its relevance in muscle function is twofold. (1) By this arrangement the muscle is capable of producing a relatively high-power output at intermediate loads, the region most often used during muscle work. (2) At the same time, because of the sharp decrease in velocity at loads exceeding 80% of P0, the muscle has acquired a mechanism designed to stabilize the myofilament system at high loads.
As has been previously demonstrated in frog muscle fibers
(Edman, 1988), there is a
smooth continuation of the force-velocity relation as the load exceeds
P0, and the muscle fiber is being stretched, resulting in
a flat sigmoidal force-velocity relationship with inflexion at
P0. This feature of the force-velocity relationship
implies that there is a fairly wide region around P0 (cf.
fig. 7 in Edman, 1988
) where
the force may be allowed to vary substantially with little change in speed of
shortening or lengthening. This provides an expedient mechanism of stabilizing
the myofilament system, in that stronger and weaker regions in series will
stay nearly isometric in the high-load range, i.e. any tendency towards
redistribution of sarcomere length between weaker and stronger segments will
be minimized.
The molecular mechanism underlying the high-force curvature of the
force-velocity relationship dealt with in the present paper is still
incompletely understood, but all the evidence would seem to suggest that the
biphasic shape of the force-velocity curve is an inherent feature of the
sliding filament process. Supporting this view, the high-force deviation of
the force-velocity relation appears in skinned muscle fibers, as well as in
intact preparations, and is unrelated to the state of activation of the
contractile system (Lou and Sun,
1993; Edman et al.,
1997
). Several attempts have been made to simulate the
characteristic change of the force-velocity relation in the high-force range
(0.8 P0-P0) based on different
cross-bridge models (Mitsui and Chiba,
1996
; Edman et al.,
1997
; Nielsen,
2003
). The cross-bridge model presented by Edman et al.
(1997
) was found to simulate
the experimental force-velocity and stiffness-velocity relationships
exceedingly well. An important aspect of this model is the assumption of a
Gaussean position-dependence of the attachment rate constant along the thin
filament, in this way creating a region early during the power stroke where
the cross-bridge attachment is slow. This feature of the model leads to a
marked decrease in the number of pulling cross-bridges during shortening in
the high-force range, and to a lower force output per bridge. Together, these
changes account for the upwards-concave region of the force-velocity relation
at high loads (0.8 P0-P0) according to
the model.
The length-tension relationship
The length-tension relationship in mammalian muscle has previously been
delineated in studies of skinned fibers
(Stephenson and Williams,
1982) and intact muscle fiber bundles
(ter Keurs et al., 1984
) from
rat skeletal muscle. The present study is a first attempt to determine this
relationship in intact single fibers from a mammalian muscle. With the
technique used, it was possible to measure tetanic force without appreciable
tension creep from a short marked segment along the fiber by holding the
selected segment at constant length throughout the stimulation period by
feedback control. The results show that the tetanic force stays quite constant
within a range of sarcomere lengths, from approximately 2.1 to 2.4 µm, from
which point the force starts to decline linearly with further extension of the
sarcomeres. A considerably wider plateau region (extending from approximately
2.1 to 2.7 µm sarcomere length) was derived by Stephenson and Williams
(1982
) and ter Keurs et al.
(1984
). This difference in
results is explainable by assuming that there was a wider dispersion of
sarcomere length in the earlier experiments.
The slope of the descending limb of the length-tension relation provides
relevant information on the effective lengths of the myofilaments. As
described in the Results, the linear regression of the data points along the
descending limb is consistent with an average thin-filament length of 1.10
µm and an average thick filament length of 1.63 µm, both values
according well with recent electron microscope measurements in mammalian
muscles (Sosa et al.,
1994).
The above values of the thick and thin filaments also accord with the slope of the ascending limb of the length-tension relation, if it is assumed that active force is reduced in proportion to the length of double filament overlap (OD) and the amount of compression of the thick filaments (OC) when colliding with the Z disk. The good agreement between the calculated and experimental data shown in Fig. 5 is based on the assumption that the proportionality coefficients KD and KC have the same numerical value as that of KS (see Results). This is in line with the idea that the thin filaments intruding from the opposite half of the sarcomere prevent any interaction between the thick and thin filaments within the region of double filament overlap.
The present observation differs from the results obtained in a similar
study on frog muscle fibers (Edman and
Reggiani, 1987) in that the proportionality coefficient
KD required a value 1.7x larger than that of
KS in order to fit the frog muscle data. The ascending
limb of the length-tension relation in frog muscle fibers is thus steeper than
predicted on the basis of filament overlap as discussed above. The relatively
steep decline of tension below optimal length in frog muscle fibers is also
apparent in the earlier studies by Gordon et al.
(1966
) and Edman
(1966
) (see fig. 9 in
Edman and Reggiani, 1987
).
The mechanism underlying the greater steepness of the ascending limb in
frog muscle fibers is still unclear. A possibility worth considering would be
that the relatively wide frog muscle fibers become incompletely activated
during tetanic stimulation at short lengths because of decremental inward
spread of activation as the fiber diameter expands with shortening
(Taylor and Rüdel, 1970;
however, see Gonzalez-Serratos,
1975
). This would reduce the force output below the expected
values along the ascending limb in the frog fibers. Failure of the inward
spread of activation is, however, unlikely to affect the mechanical output of
the much thinner mammalian fibers used in the present study.
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Acknowledgments |
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References |
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