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First published online March 27, 2009
Journal of Experimental Biology 212, 1115-1119 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.020982
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Non-linear myofilament elasticity in frog intact muscle fibres
Department of Experimental Medical Science, Biomedical Centre, University of Lund, S-221 84 Lund, Sweden
e-mail: paul.edman{at}med.lu.se
Accepted 9 February 2009
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: muscle fibre, striated muscle, myofilament elasticity, muscle mechanics, stiffness measurement
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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; Wakabayashi et al.,
1994). In line with these findings, it has been demonstrated in
both intact (Julian and Morgan,
1981; Bagni et al.,
1990) and skinned (Higuchi et
al., 1995) muscle fibres that the instantaneous stiffness of the
fibre during activity is steadily increased as the sarcomere length is reduced
within the plateau region of the length–tension relation, i.e. under
conditions where the number of active cross-bridges can be presumed to remain
constant while the free portions of the thick and thin filaments are
reduced.
There is still a lack of information concerning the nature of the filament
elasticity. Thus, it is still unknown whether the filament elasticity is
Hookean or not, i.e. whether the strain of the filaments is proportional to
the applied stress or whether there is a non-linear elasticity like that
present in the tendons (Cleworth and Edman,
1972; Edman and Josephson,
2007). In a true Hookean spring, the stiffness, i.e. the force
response to a given length change, remains the same at different loads applied
to the spring. The simplest assumption, and so far the standpoint generally
taken when account has been made of filament compliance in mechanical
measurements (e.g. Piazzesi et al.,
2007), is postulating that the myofilaments behave as a Hookean
spring. Departure from this hypothesis is bound to complicate any modelling of
muscle contraction as pointed out by Colombini and colleagues
(Colombini et al., 2007).
The present study was undertaken to further elucidate the nature of the
elasticity that acts in series with the myosin motors. The instantaneous
stiffness was recorded by applying a high-frequency length oscillation to
isolated muscle fibres, using an approach by which the compound stiffness
signal from the fibre could be read out online
(Edman and Lou, 1990). The
stiffness was measured after the fibre was released to shorten against a
pre-set load starting at two selected sarcomere lengths (2.20 and 2.60 µm).
By keeping the load constant during the shortening phase at the two sarcomere
lengths, both the cross-bridge stiffness, i.e. the stiffness emanating from
the active cross-bridges, and the external series elasticity can be presumed
to stay constant. Any difference in stiffness recorded between the two
sarcomere lengths can therefore be presumed to reflect a change in filament
compliance in consequence of altered filament overlap. Evidence will be
presented to show that over a wide range of loads the filament elasticity has
the characteristics of a non-Hookean spring.
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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For an experiment, the muscle fibre was mounted between a force transducer
and an arm extending from the moving coil of a fast electromagnetic puller
(motor No. 1), which was the motor used to achieve low-amplitude length
oscillations for stiffness measurements. The force transducer was mounted on
the arm extending from a second electromagnetic puller (motor No. 2) that
served to produce larger fibre movements during load-clamp recordings. The
slip of tendon attached to the force transducer was held by a small aluminium
clip, which was positioned on the transducer hook in such a way that any
lateral, vertical or twisting movements of the fibre during stimulation were
minimized (Edman and Reggiani,
1984). For attaching the fibre to motor No.1 (the puller producing
sinusoidal length changes), the tendon slip at this end was firmly attached to
the puller arm by a strip of Parafilm (Pechiney Plastic Packaging Company,
Chicago, IL, USA). This was wound on the outside of the tendon around the
puller arm, leaving a minimum of free tendon outside the end of the puller
arm. The Parafilm strip was held in place by attaching its ends to a small
hook on the puller arm. Details of the muscle dissection, instrumentation and
methods used for measuring fibre length, fibre cross-sectional area and
sarcomere length (laser diffraction) are given in Edman and Reggiani
(Edman and Reggiani, 1984).
The bathing solution had the following composition (mmol l–1): NaCl, 115.5; KCl, 2.0; CaCl2, 1.8; Na2HPO4+NaH2PO4 (total concentration), 2.0; pH 7.0. The temperature of the bathing solution was constant to within 0.2°C in a given experiment but ranged from 2.0 to 2.5°C for experiments on different fibres. During the experiment, a glass coverslip (0.1 mm thickness) was placed on top of the muscle chamber in contact with the bathing fluid. In addition to providing a plane upper surface for the laser diffraction measurements, the presence of the coverslip ensured that the bath temperature remained constant along the length of the preparation (to within ±0.1°C) during the experiment. The latter point was tested using a thermistor probe that was moved underneath the cover slip by means of a micromanipulator.
Force transducer
Tension was recorded by means of a semiconductor strain-gauge element (AE
801, Aksjeselskapet Mikroelektronikk, Horten, Norway). The transducer element
had been modified to increase the frequency response of the transducer as
described by Edman and Lou (Edman and Lou,
1990). The resonant frequency of the force transducer was
approximately 19 kHz when the transducer was submerged in the bathing
solution.
Stimulation
The fibre was stimulated by passing 0.2 ms current pulses between two
platinum plate electrodes placed symmetrically on either side of the
preparation approximately 2 mm from it. The stimulus strength was about 15%
above threshold. A train of pulses of appropriate frequency (16–22 Hz)
was used to produce a fused tetanus of 1 s duration; the tetanic bursts of
stimuli being separated by 2 min intervals. A 20–30 min period of
regularly paced, tetanic stimulation preceded data collection in each
experiment.
Measurement of fibre stiffness
A detailed description of the methods and apparatus used to measure fibre
stiffness is given by Edman and Lou (Edman
and Lou, 1990). In the present experiments, the fibres were
mounted between two electromagnetic pullers (motors Nos 1 and 2) as described
above. Motor No. 2, which had the force transducer mounted on its shaft, was
used to clamp force to a pre-set level. For stiffness measurements, motor No.
1 produced a sinusoidal length oscillation of constant amplitude throughout
the tetanus period. The frequency of the oscillation employed in these
experiments was 2–4 kHz, and the peak-to-peak amplitude was 10–11
mm corresponding to approximately 1.7 nm per half-sarcomere with the fibre
lengths used. This means that the fibre underwent alternating stretches and
releases of <1 nm per half-sarcomere in amplitude about the unperturbed
length of the fibre. The stiffness measurement was thus performed within the
straight portion of stress–strain relationship of the sarcomere
elasticity located above and below the isometric force (e.g.
Ford et al., 1977;
Månsson, 1989). The
stretch and release movements produced during the stiffness measurement were
completed in 0.125–0.250 ms and may thus be considered fast enough to
provide a useful index of the instantaneous stiffness of active muscle
(Huxley and Simmons, 1971;
Ford et al., 1977).
The oscillation was initiated just before the onset of stimulation and
continued throughout the plateau phase of the tetanus. A stiffness signal was
formed by passing the signal from the force transducer through a narrow
band-pass filter (Q value 5.5), the optimum frequency of which was
set to the actual frequency of the length oscillation used. By rectifying the
filtered signal, a direct read-out of the fibre stiffness could be obtained
during the course of contraction [for further details, see
fig. 1 of Edman and Lou
(Edman and Lou, 1990)]. The
bandwidth of the rectified signal was DC-1.3 kHz. The force signal was
recorded without the superimposed force oscillation by using a notch filter,
which produced maximum attenuation at the frequency used for the length
oscillation.
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Eight experiments were performed in which force and stiffness were recorded
as shown in Fig. 1 with
measurements at 2.20 and 2.60 µm sarcomere length. This range of sarcomere
lengths was selected to avoid interference in the measurements from passive
elasticity in the fibres (see Edman,
1979). Two or three different force-clamp levels were studied in
the same fibre at the two lengths. By performing the stiffness measurements at
the same force level at the two sarcomere lengths, it was ensured that elastic
elements acting in series with the myofilaments (such as tendons and fibre
attachments) were equally extended. Furthermore, by using identical load-clamp
levels at the two sarcomere lengths, an equal number of myosin motors can be
presumed to be involved in force production at the two lengths.
Fig. 2 illustrates example
records of force and stiffness from two fibres at 2.20µm and 2.60µm
sarcomere lengths. The rising phase and plateau of the tetanus, including the
load-clamp phase, are shown superimposed at the two lengths. Determinants of
the force rise time and tetanus amplitude have been described in detail
previously (Edman and Josephson,
2007; Edman and Reggiani,
1987) and are not considered in the present study. The clamp
tension differs in A and B but can be seen to be the same at the two sarcomere
lengths in the respective fibre. By contrast, in both fibres, the stiffness
recorded during the load-clamp phase is clearly lower at 2.60µm than at
2.20µm sarcomere length. This change in stiffness is most likely to be
attributable to the fact that the free (non-overlapping) portion of the thick
and thin filaments is greater at the longer sarcomere length. Assuming that
the thick and thin filaments have a length of 1.55 and 1.94µm,
respectively, and the width of the Z disk is 0.05µm (see
Edman and Reggiani, 1987), the
portion of the thick and thin filaments outside the overlap region can be
estimated to be 0.81µm at 2.20µm sarcomere length and 1.61µm at
2.60µm sarcomere length.
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For the subsequent analysis of the filament compliance, it was of relevance to establish how the fibre stiffness recorded at 2.60µm sarcomere length (S2.60) related to that measured at 2.20µm (S2.20) as the force during the load-clamp manoeuvre was varied. Fig. 3 summarizes the results from eight individual muscle fibres in which the S2.60/S2.20 ratio was measured at different loads ranging between 40 and 70% of the tetanic force at optimum length. The results show that within the range of loads investigated, the S2.60/S2.20 ratio was quite constant, the individual data points varying between 0.83 and 0.97. The regression of the S2.60/S2.20 ratio upon force results in a nearly horizontal line with the S2.60/S2.20 ratio ranging from 0.89 to 0.91.
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 | (1) |
The use of active force as an index of cross-bridge stiffness presupposes
that there is a fairly constant ratio of `weak' to `strong' cross-bridges at
the different clamp levels, shortening velocities and sarcomere lengths
investigated (see Discussion). The validity of this assumption cannot be fully
established at the present time. However, the findings by Ford and colleagues
(Ford et al., 1981;
Ford et al., 1985) that the
instantaneous sarcomere stiffness varies almost in proportion to the measured
force, at different sarcomere lengths and at different speeds of shortening,
support the view that the ratio of `weak' to `strong' cross-bridges is indeed
maintained quite constant under the test situations studied in the present
investigation.
The myofilament stiffness was calculated from Eqn 1 for various values of force according to the regression line in Fig. 3. The results of this calculation are shown in Fig. 4 in which the filament stiffness is expressed as a multiple of the maximum cross-bridge stiffness (see above). Stiffness values, referring to both 2.20 µm (open symbols) and 2.60 µm (closed symbols) sarcomere lengths, are plotted for comparison in Fig. 4. The myofilament stiffness can be seen to increase progressively as the load on the fibre was raised from 40 to 70% of the maximum tetanic force. At full overlap, i.e. at 2.20 µm sarcomere length, and at 40% of maximum load on the fibre, the calculated myofilament stiffness was approximately 2.5 times the maximum cross-bridge stiffness. The myofilament stiffness more than doubled as the load was increased to 70% of maximum tetanic force. The myofilament elasticity thus exhibits the characteristics of a non-Hookean spring.
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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;
Wakabayashi et al., 1994). The
existence of filament compliance has later been corroborated in several
studies on various isolated muscle preparations (see earlier), even by
measurements on isolated actin filaments
(Kojima et al., 1994).
Subsequent studies on skinned skeletal muscle fibres have further elucidated
the existence of myofilament compliance and its contribution to the kinetic
properties of the muscle fibre during activity
(Martyn et al., 2002).
In the present study, an approach has been used to evaluate the spring-like
properties of the myofilaments in an intact muscle fibre. The stiffness
measurements (for details, see Materials and methods) were performed during
load-clamp recordings at two selected sarcomere lengths, 2.20 and 2.60 µm,
i.e. over a range where the resting tension is negligible
(Edman, 1979). An important
point in these measurements is the fact that the same load was held by the
fibre during the load-clamp phase at the two lengths. This ensures that
passive elastic elements acting in series with the myofilament system, such as
tendons and attachments to the transducer arm, remained constant during the
stiffness measurements at the two sarcomere lengths. Furthermore, by using the
same clamp-force at the two sarcomere lengths, the number of myosin motors
involved in force production can be presumed to be the same in the two
situations. The load held by the fibre during the stiffness measurement was
limited to be within the range 40–70% of maximum tetanic force for the
following reasons: (1) the force employed during the load-clamp test was not
allowed to exceed the isometric tetanic force at 2.60 µm sarcomere length
in order to avoid stretching the muscle fibre; (2) previous measurements
(performed in the same experimental setup as that used in the present study)
have demonstrated that the error in the fibre stiffness measurement due to
tendon compliance is negligible at force levels greater than 40% of maximum
tetanic force (Edman et al.,
1997).
With the approach used, the stiffness measurement was specifically focused on the free, non-overlapping portions of the thick and thin filaments without distinction between the two filaments. Excluded from the measurements are the anchoring sites of the filaments at the M line and Z disk, as the measurements would only include those portions of the filaments that become free of overlap when the sarcomeres are extended from 2.20 to 2.60 µm.
It is worth pointing out that the stiffness measurement presented in the
current study refers to the myofilaments in situ in the fibre, i.e.
in an environment where the actin and myosin filaments are surrounded by, and
interwoven with, a number of auxiliary filaments, such as titin and desmin
that make up the cytoskeleton (e.g.
Maruyama et al., 1977;
Wang and Ramirez-Mitchell,
1983; Wang et al.,
2001; Erickson,
1997; Granzier et al.,
1997; Linke et al.,
1998; Granzier et al.,
2002; Kreplak et al.,
2008). These cytoskeletal structures may be regarded as an
integral part of the `myofilament elasticity' measured in intact whole muscle
or isolated muscle fibres irrespective of the measuring technique used. The
contribution to the measured filament stiffness coming from the cytoskeletal
structures is still difficult to assess and requires further studies to be
settled. Interaction between the titin and actin filaments may occur (see
Granzier et al., 1997;
Yamasaki et al., 2001) and
this could affect the tensile properties of the actin filament. It is of
interest to mention in this connection that the intact muscle fibre behaves as
a constant volume (see Edman,
1999). The fibre diameter thus varies as an inverse square root
function of the sarcomere length. This means that elastic structures that are
oriented transversely, like desmin, may in fact also respond to longitudinal
length changes of the fibre.
It is now generally believed (see
Gordon et al., 2000) that the
myosin cross-bridge cycle is initiated in a weakly bound state that translates
into a strongly bound state that is associated with force production. Bridges
in the weakly bound state are thought to contribute to fibre stiffness but not
to active force. In the above calculations, it was implicitly assumed that the
ratio of `weak' to `strong' cross-bridges remains the same during loaded
shortening at the sarcomere lengths and clamp levels tested. This assumption
is based on the findings by Ford and colleagues
(Ford et al., 1981;
Ford et al., 1985), who
demonstrated that the measured sarcomere stiffness varies almost in proportion
to the developed force, both during active shortening at various loads and
velocities of shortening and during isometric contraction at various degrees
of filament overlap. These observations support the view that the ratio of
`weak' to `strong' cross-bridges is maintained fairly constant at the
different force levels and sarcomere lengths studied.
Earlier studies suggest that the stiffness of the thick and thin filaments
is similar in magnitude to that residing in the myosin cross-bridges during
maximal activity (Huxley et al.,
1994; Wakabayashi et al.,
1994). The present results indicate that the myofilament stiffness
at full overlap (2.20 µm sarcomere length) markedly exceeds the
cross-bridge stiffness and, furthermore, that it increases in magnitude with
increasing tension on the muscle fibre. The calculated myofilament stiffness
was thus found to more than double as the load on the fibre was raised from 40
to 70% of maximum isometric force. This result is in fair agreement with
previous stiffness measurements reported by Higuchi and colleagues
(Higuchi et al., 1995), who
estimated the thin filament compliance by imposing small cyclical length
changes on skinned muscle fibres in rigor at sarcomere lengths where the
overlap between the thick and thin filaments is complete. Their results
suggest, in accordance with the present data, that the thin filament stiffness
is nearly doubled as the load on the fibre is increased from 50 to 150 kN
m–2, i.e. over a force range similar to that covered in the
present experiments. Non-linearity of myosin compliance has similarly been
suggested in two recent X-ray diffraction studies, in which muscle force was
varied by the muscle relaxant BDM
(Griffith et al., 2006) and by
recording the myosin reflections at various speeds of active shortening
(Huxley et al., 2006).
In conclusion, with the approach used in the present study, it has been possible to evaluate the stiffness of the free portions of the thick and thin filaments, relative to the cross-bridge stiffness, in intact single muscle fibres. The data indicate that the filament stiffness calculated at optimum filament overlap (2.20µm sarcomere length) exceeds that residing in the cross-bridges at full activation. The myofilament elasticity has the characteristics of a non-Hookean spring; the stiffness of the filaments increases 2.5-fold as the tension held by the fibre is raised from 40 to 70% of maximum tetanic force.
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Footnotes |
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