The structural basis of the increase in isometric force production with temperature in frog skeletal muscle
1 Laboratorio di Fisiologia, DBAG, Università di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy and Istituto Nazionale di Fisica della Materia, OGG, Grenoble, France
2 Randall Division of Cell and Molecular Biophysics, School of Biomedical Sciences, King's College London, London SE1 1UL, UK
3 European Synchrotron Radiation Facility, F-38043 Grenoble Cedex, France
Abstract
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X-ray diffraction patterns were recorded from isolated single fibres of frog skeletal muscle during isometric contraction at temperatures between 0 and 17°C. Isometric force was 43 ± 2% (mean ±S.E.M., n= 10) higher at 17°C than 0°C. The intensity of the first actin layer line increased by 57 ± 18% (n= 5), and the ratio of the intensities of the equatorial 1,1 and 1,0 reflections by 20 ± 7% (n= 10), signalling radial or azimuthal motions of the myosin head domains. The M3 X-ray reflection from the axial repeat of the heads along the filaments was 27 ± 4% more intense at 17°C, suggesting that the heads became more perpendicular to the filaments. The ratio of the intensities of the higher and lower angle peaks of the M3 reflection (RM3) was 0.93 ± 0.02 (n= 5) at 0°C and 0.77 ± 0.02 at 17°C. These peaks are due to interference between the two halves of each myosin filament, and the RM3 decrease shows that heads move towards the midpoint of the myosin filament at the higher temperature. Calculations based on a crystallographic model of the heads indicated that the observed RM3 change corresponds to tilting of their light-chain domains by 9 deg, producing an axial displacement of 1.4 nm, which is equal to that required to strain the actin and myosin filaments under the increased force. We conclude that the higher force generated by skeletal muscle at higher temperature can be accounted for by axial tilting of the myosin heads.
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Introduction
The force generated by skeletal muscle during isometric contraction is greater at higher temperature. In amphibian muscles, this effect occurs within the physiological temperature range (Ford et al. 1977; Bershitsky et al. 1997; Piazzesi et al. 2003). The increased force is not accompanied by an increased stiffness of the muscle sarcomeres (ibid.), so it is not caused by an increase in the number of myosin cross-bridges interacting with actin filaments. Each individual myosin cross-bridge must therefore generate a larger force at higher temperature, and the phenomenon provides an opportunity to investigate the structural basis of isometric force generation in the actin–myosin cross-bridges in their native sarcomeric arrangement.
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We used X-ray diffraction from isolated intact fibres of frog skeletal muscle to characterize the structural changes associated with the enhanced force production at higher temperature. We measured the intensities of the axial X-ray reflections from the periodic repeat of the myosin heads along the filaments, the actin-based layer line reflections corresponding to the helical periodicities of the actin filament, and the equatorial reflections related to the mass distribution in the plane perpendicular to the filaments during active isometric contraction in the temperature range 0 to 17°C. We also used a new X-ray interference technique (Linari et al. 2000; Reconditi et al. 2004) to give a precise measure of the axial motions of the myosin heads towards the centre of the sarcomere when isometric force is modulated by temperature.
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Preliminary results have been presented in abstract form (Reconditi et al. 2002).
Methods
Muscle fibre preparation and mounting
Frogs (Rana temporaria) were cooled to 2–4°C and killed by decapitation followed by destruction of the brain and spinal cord, in conformation with EU Directive 86/609/EEC and the UK (Scientific Procedures) Act 1995. Single fibres were dissected from the lateral head of the tibialis anterior muscle. The fibre tendons were clamped in aluminium foil clips and mounted between a pair of hooks in Ringer solution at sarcomere length 2.1 μm. One of the hooks was attached to a capacitance force transducer (Huxley & Lombardi, 1980), and the other was fixed. The temperature of the bathing Ringer solution was controlled by feedback to a thermoelectric module. Fibres were stimulated via electrodes mounted on mica windows, on either side of the fibre and 600 μm apart.
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Experimental protocol
Fibres were mounted at beamline ID02 of the European Synchrotron Radiation Facility (ESRF), Grenoble, France (Narayanan et al. 2001).
Two dimensional X-ray patterns were collected during isometric tetani at 0, 4, 10 and 17°C. Isometric force was not reliably maintained during tetanic stimulation at temperatures higher than about 17°C in the fibres used here. One or two cycles of four series of tetani (one series at each temperature) were typically recorded from each fibre. The order of the measurements at the four temperatures within a cycle was randomised. Isometric force developed faster at higher temperature, and tetanus duration was reduced accordingly. X-ray patterns were collected at the plateau of isometric tetani, from 350–370, 300–320, 250–270, or 130–150 ms after the first stimulus at 0, 4, 10 and 17°C, respectively. In a few experiments, noted below, the tetanus duration was increased and X-ray data were collected from later periods of the tetanus: 850–870, 700–720, 500–520 and 300–320 ms, respectively. Stimulus frequency and intertetanus interval were set in preliminary experiments to the minimum values required for force fusion and constant plateau force (T0), respectively (see Table 1 of Piazzesi et al. 2003). Because the time required for changing temperature was longer than the inter-tetanus interval in some cases, T0 could be higher in the first tetanus than in subsequent tetani of a series, and the first tetanus at a new temperature was not used for X-ray data collection. Each experiment was terminated when the fibre showed the first sign of radiation damage, a sudden failure of fibre activation or relaxation, typically occurring after about 50 tetani. Data are presented from ten fibres with cross-sectional area 22100 ± 5200 μm2 (S.D.)
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X-ray data collection
The X-ray beam at ID02 had full-width at half-maximum (FWHM) ca 150 μm vertically and 300 μm horizontally, with a total flux of up to 5 x 1013 photons s–1 at wavelength 0.1 nm. Data are presented from some experiments in which the fibre was mounted vertically, and some in which it was mounted horizontally. The camera length was either 3 m or 10 m, depending on the region of the diffraction diagram under study. The diffraction data were recorded with a FReLoN CCD detector with image intensifier, and corrected for dark current and spatial distortion as described by Narayanan et al. (2001). The 2048 x 2048 pixels of the CCD were binned by factors of 16 in the radial direction and 2 in the axial direction before the read-out after each tetanus. The axial point-spread function of the detector had FWHM 250 μm. A fast shutter limited X-ray exposure of the fibre to periods of data acquisition. The fibre was translated along its axis by 100–200 μm between contractions to spread the effects of radiation damage.
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In order to make precise measurements of the temperature dependence of the spacings of the axial X-ray reflections in resting muscle, whole sartorius muscles of Rana temporaria were mounted vertically at ID02 between mica windows in a temperature-controlled chamber. X-ray data were collected with a camera length of 2 m.
X-ray data analysis
X-ray diffraction patterns were analysed with Fit2D (A. Hammersley, ESRF) and Peakfit (SPSS Science). Images were centred and aligned using the M3 meridional and (1,1) equatorial reflections. The distribution of diffracted intensity along the meridional axis of the X-ray pattern (parallel to the fibre axis) was calculated by integrating from 0.025 nm–1 on either side of the meridian. The background intensity distribution was fitted using a convex hull algorithm and subtracted. The fine structure of each axial reflection was analysed by multi-gaussian fitting to obtain the intensity and the position of each component peak under the constraint that they had equal axial width. Axial periodicities were calibrated using the M3 reflection in an isometric tetanus at 4°C, with periodicity of 14.573 nm (Linari et al. 2000). Integration limits for other reflections were as follows: 1st actin layer line (A1L): 1/21–1/4.8 nm–1 radially; sixth (A6L) and seventh (A7L) actin layer lines: 1/91–1/6.5 nm–1 radially; equatorial (1,0) and (1,1) reflections: 1/100 nm–1 on each side of the equator. The A6L and A7L layer lines were also analysed using narrower integration limits, 1/29–1/17 nm–1 (Bordas et al. 1999), with similar results. These narrower integration limits were also used for analysis of A6L and A7L in resting muscles, in order to avoid the contribution of the M7 meridional reflection. Backgrounds were subtracted using a convex hull algorithm for the A1L, (1,0), and (1,1) reflections; a constant background was subtracted for the A6L and A7L reflections.
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Results
Intensities of axial X-ray reflections
The intensities of the axial X-ray reflections are sensitive to the distribution of mass along the myosin and actin filaments. The M3 X-ray reflection, corresponding to the 14.5 nm axial periodicity of myosin heads, is relatively intense during isometric contraction because the actin-attached myosin heads are orientated roughly perpendicular to the filament axis (Huxley et al. 1982; Irving et al. 2000). The intensity of the M3 reflection, IM3, was 11 ± 6% (mean ±S.E.M., n= 10) greater during active isometric contraction at 17°C than at 0°C (Fig. 1B, squares). The radial width of the M3 reflection was 16 ± 4% greater at the higher temperature, indicating a decrease in the axial alignment of neighbouring myosin filaments. After correction of the observed change in IM3 for this effect by multiplying by the width (Huxley et al. 1982), the increase in IM3 from 0 to 17°C was 27 ± 4% (Fig. 1B, circles). Isometric plateau force (T0) increased by 43 ± 2% in the same temperature range (Fig. 1A), from 210 ± 30 kPa (mean ±S.D.) at 0°C to 302 ± 44 kPa at 17°C. The increase in IM3 suggests that the myosin heads have tilted to become more perpendicular to the filament axis at the higher temperature.
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A, isometric force (T0). B, intensity of the M3 X-ray reflection (IM3), before (, continuous line) and after (, dashed line) correcting for the change in radial width. C, intensity of the M6 X-ray reflection (IM6). D, ratio (I11/I10) of the intensities of the equatorial (1,1) and (1,0) reflections. All data normalized by the corresponding values at 0°C. Mean ±S.E.M. for n= 10 (A and B) or n= 5 (C and D); the data in A and B are from the same 10 fibres.
There was no significant change in the intensity of the M6 reflection, IM6, with temperature (Fig. 1C). This reflection is much less sensitive to the conformation of the myosin heads, and seems to be associated with other components of the myosin filament (Huxley et al. 2003; Reconditi et al. 2004).
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Intensities of equatorial X-ray reflections
The equatorial X-ray reflections give information about the distribution of mass in the plane perpendicular to the myosin and actin filament axis. The intensity of the 1,1 reflection characteristically increases, and that of the 1,0 reflection decreases, when muscles are activated or put into rigor (Haselgrove & Huxley, 1973). This transition is conveniently monitored by the ratio I11/I10 of the intensities of the 1,1 and 1,0 reflections. In the present experiments I11/I10 was 20 ± 7% larger during isometric contraction at 17°C than at 0°C (Fig. 1D).
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Intensities of actin-based layer lines
The actin-based layer lines are related to the helical periodicities of the actin filament, and thus are sensitive to stereospecific attachment of myosin heads to actin. The first actin-based layer line (A1L), with an axial spacing of about 38 nm, comes from the long-pitch actin helix. This layer line is more intense in rigor muscle, in which all the myosin heads are strongly bound to actin and take up its helical periodicity, than in resting muscle, when the heads are detached from actin (Huxley & Brown, 1967). The intensity of this layer line, IA1L, is also greater during isometric contraction than at rest (Bordas et al. 1993; Piazzesi et al. 1999), indicating that active force generating heads take up the periodicity of the long-pitch actin helix. IA1L was 57 ± 18% (mean ±S.E.M.; n= 5) larger during isometric contraction at 17°C than at 0°C (Fig. 2B, circles), similar to the fractional increase in force in this group of fibres (Fig. 2A). These results suggest that the higher isometric force at higher temperature is associated with a mass distribution of the myosin heads that has greater helical order on the long-pitch actin helix.
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A, isometric force (T0). B, intensity (IA1L) of the first actin-based layer line reflection, with periodicity ca 38 nm (), intensity (IA6L) of the sixth actin-based layer line reflection, with periodicity ca 5.9 nm (), intensity (IA7L) of the seventh actin-based layer line reflection, with periodicity ca 5.1 nm (). All data normalized by the corresponding values at 0°C. Mean ±S.E.M., n= 5 fibres.
The helical structure of the actin filament also gives rise to layer line reflections with axial spacings of ca 5.9 and 5.1 nm, corresponding to the axial repeats of the two ‘genetic helices’ that connect every actin monomer in the filament (Huxley & Brown, 1967). These reflections will be referred to here as A6L and A7L, respectively, with corresponding intensities IA6L and IA7L. This nomenclature relates to a simplified model of the actin filament structure in which there are 13 actin monomers in six and seven turns of the two genetic helices. This relation does not hold exactly in the native filament, and the reciprocal spacings of the A6L and A7L reflections are not integer multiples of that of A1L (Huxley & Brown, 1967; Bordas et al. 1999). The intensities of the A6L and A7L reflections increase when muscles are activated (Matsubara et al. 1984; Bordas et al. 1999) or put into rigor (Huxley & Brown, 1967). However IA6L was only 5 ± 4% (mean ±S.E.M.; n= 5) greater during isometric contraction at 17°C than at 0°C (Fig. 2B, squares), and IA7L was 20 ± 13% larger at 17°C (Fig. 2B, triangles). Neither of these changes is statistically significant (P > 0.05).
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Axial spacings of the X-ray reflections
The axial spacings of the M3 and M6 reflections during isometric contraction, SM3 and SM6, respectively, showed small but reproducible increases with temperature. SM3 was 14.568 ± 0.002 nm (mean ±S.E.M., n= 10) at 0°C and 14.587 ± 0.002 nm at 17°C. The change in SM3 with temperature during active contraction was linearly related to the isometric force (Fig. 3A). Linear regression of these data (dashed line) corresponds to a myosin filament compliance of 0.35 ± 0.01%/T0,4, where T0,4 refers to the isometric force at 4°C. The SM6 data (Fig. 3B) were more noisy, but gave a mean compliance estimate of 0.27 ± 0.09%/T0,4, which is close to that, 0.26 ± 0.01%/T0,4, measured by imposing rapid force steps during active contraction at 4°C (Reconditi et al. 2004).
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A, spacing of the M3 reflection (SM3). B, spacing of the M6 reflection (SM6). C, spacing of the sixth actin-based layer line reflection (SA6L). D, spacing of the seventh actin-based layer line reflection (SA7L). E, axial periodicity of the actin monomers (SA) calculated as described in the text. The abscissa is the isometric force from the same set of fibres, normalized to 4°C. Data are means ±S.E.M., n= 10. Dashed lines are linear regression on the data.
To assess the possible contribution of thermal expansion of the myosin filament to these spacing changes, some control experiments were made to measure the temperature dependence of SM3 and SM6 in resting muscle fibres. Experiments on resting single muscle fibres suggested that the thermal expansion of the myosin filament is small; SM3 was only 0.03 ± 0.03% (mean ±S.E.M., n= 3) larger at 17°C than at 4°C. To improve the precision of these measurements, they were repeated using whole sartorius muscles, and in this preparation SM3 was 0.044 ± 0.008% (mean ±S.E.M., n= 3) larger at 17°C than at 6°C. The corresponding change in SM6 was –0.003 ± 0.015%. These results show that thermal expansion of the myosin filament could make only a minor contribution to the larger axial periodicity of the myosin filament during active contraction at higher temperature (Fig. 3), which is therefore likely to be predominantly due to myosin filament compliance.
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The axial spacings of the sixth and seventh actin-based layer lines, SA6L and SA7L, respectively, also increased with temperature (Fig. 3C and D). Linear regression of SA6L and SA7L against isometric force (dashed lines) gave slopes of 0.51 ± 0.12%/T0,4 (mean ±S.E.M., n= 5) and 0.94 ± 0.24%/T0,4, respectively. The change in axial periodicity SA of monomers along the actin filament was calculated from these data (Huxley et al. 1994; Wakabayashi et al. 1994; Bordas et al. 1999), and linear regression of SA against isometric force (Fig. 3E) has a slope of 0.74 ± 0.18%/T0,4.
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Control measurements of the temperature dependence of SA6L, SA7L and SA were made in resting muscle in order to assess the possible contribution of thermal expansion of the actin filaments. In resting sartorius muscles SA was 0.033 ± 0.027% (mean ±S.E.M., n= 3) larger at 17°C than at 6°C. The increase in active force in this temperature range is about 0.2 T0,4 (Fig. 1A) so, based on the relation between SA and active force (Fig. 3E), SA during isometric contraction is larger at the higher temperature by 0.2 x (0.74 ± 0.18) = 0.15 ± 0.04%/T0,4. This is much larger than the 0.033 ± 0.027% difference observed in resting conditions, suggesting that thermal expansion could be responsible for only a small fraction of the actin periodicity changes reported in Fig. 3.
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Interference fine structure of the M3 reflection
The M3 reflection from the 14.5 nm repeat of the myosin heads along the filament is split into two closely spaced peaks by interference between the two arrays of myosin heads in each myosin filament (Linari et al. 2000). This phenomenon allows the axial motions of the myosin heads towards the centre of the sarcomere, the M-line, to be measured with a precision of the order of 0.1 nm (Piazzesi et al. 2002; Reconditi et al. 2004). During isometric contraction at 0°C, the two peaks of the M3 reflection had almost equal intensities; the ratio of the intensity of the higher angle peak to that of the lower angle peak of the M3 reflection, RM3, was 0.93 ± 0.02 (mean ±S.E.M., n= 5). During isometric contraction at higher temperatures, RM3 was smaller (Fig. 4B), and at 17°C it was 0.77 ± 0.02. This decrease in RM3 shows that the interference distance between the two arrays of myosin heads in each filament has decreased, i.e. the centroids of the myosin heads have moved closer to the centre of the filament (Fig. 4C).
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A, isometric force, normalized to that at 0°C. B, relative intensity RM3 of the higher and lower angle peaks of the M3 reflection. Mean ±S.E.M. for n= 5 fibres. C, schematic diagram of myosin heads (red) attached to the actin filament (grey). At higher temperature the light-chain domain of the myosin head tilts, displacing its catalytic domain towards the midpoint of the myosin filament (blue), stretching the actin filament and decreasing the interference distance L.
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The measurements of RM3 in Fig. 4B were made soon after the establishment of the isometric tetanus plateau at each temperature (see Methods). In a few fibres we also measured RM3 later in the tetanus plateau, and found that RM3 decreased slightly while the plateau force was maintained. For example, 350–370 ms after the first stimulus at 0°C, RM3 was 0.93 ± 0.02 (Fig. 4B) and 500 ms later it was 0.87 ± 0.01 (n= 3). This small decrease in RM3 during a tetanus was present at each temperature studied, and may be related to progressive development of sarcomere inhomogeneity. The effect of temperature on RM3 was of similar magnitude in the series of measurements made early and later in the tetanus, consistent with the hypothesis that the lower RM3 at higher temperature is causally related to the higher steady force.
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Discussion
Temperature dependence of the X-ray pattern during isometric contraction
The higher isometric force generated by intact single fibres from skeletal muscle at higher temperatures is accompanied by the following changes in the X-ray pattern: (1) the intensity of the axial M3 reflection (IM3) increases (Fig. 1B), indicating that myosin heads tilt to become more perpendicular to the filament axis; (2) the ratio (I11/I10) of the intensities of the (1,1) and (1,0) equatorial reflections increases (Fig. 1D), signalling a change of mass distribution in the plane perpendicular to the filaments; (3) the intensity of the first actin layer line (IA1L) increases (Fig. 2B), showing that a greater fraction of the mass of the myosin heads has taken up the periodicity of the 38 nm long-pitch actin helix; (4) the axial periodicities of both the myosin (Fig. 3A and B) and actin (Fig. 3C–E) filaments increase; (5) the ratio of the intensity of the higher angle peak to that of the lower angle peak of the M3 reflection (RM3) decreases (Fig. 4B), showing that myosin heads have moved towards the centre of the sarcomere.
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Broadly similar changes in the intensities of the equatorial, axial M3 and first actin layer line reflections have been observed in demembranated fibres from frog muscle following a temperature jump from 6 to 16°C (Tsaturyan et al. 1999), but there has been no previous systematic study of the effect of temperature on the X-ray pattern from intact muscle fibres. Griffiths et al. (2002) reported that the intensity of the M3 reflection from bundles of fibres from frog muscle was 11–20%smaller during isometric contraction at 24°C than at 4°C, but that study used a one-dimensional detector and did not report or correct for changes in the width of the M3 reflection. The temperature dependence of the interference fine structure of the axial reflections has not been reported previously.
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Although the isometric force was 42% larger at 17°C than at 0°C, there is no change in the stiffness of the sarcomere under these conditions (Ford et al. 1977; Bershitsky et al. 1997; Piazzesi et al. 2003), so neither the force increase nor the associated changes in the X-ray pattern are due to a change in the number of myosin heads bound to actin. This suggests that some or all of the X-ray changes listed above are associated with conformational changes in the actin-attached myosin heads that are responsible for the higher isometric force at higher temperature.
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Comparison with changes in the X-ray pattern in response to rapid length steps
Many previous studies of the conformational changes in the myosin heads associated with active force generation have focused on the changes in the X-ray pattern following a rapid change of fibre length (Huxley et al. 1983; Irving et al. 1992, 2000; Lombardi et al. 1995; Dobbie et al. 1998; Piazzesi et al. 2002; Griffiths et al. 2002). When a step decrease in fibre length is imposed during isometric contraction, there is an elastic force decrease during the step (phase 1 of the force transient) followed by partial force recovery on the millisecond timescale (phase 2; Huxley & Simmons, 1971). Phase 1 is due to the compliance of the myosin heads and the actin and myosin filaments; phase 2 is associated with the working stroke in the actin-attached myosin heads (Huxley & Simmons, 1971; Piazzesi et al. 2002).
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Changes in the intensity and interference fine structure of the M3 reflection (IM3 and RM3) during phases 1 and 2 of the length step response have been measured in the preparation used here, at 4°C (Irving et al. 1992, 2000; Lombardi et al. 1995; Dobbie et al. 1998; Piazzesi et al. 2002). When a shortening step is imposed, the myosin heads tilt so that their catalytic domains move towards the M-line of the sarcomere, during both the elastic fall of force (phase 1) and the rapid force recovery accompanying the working stroke (phase 2). This motion initially increases the axial alignment of the catalytic and light-chain domains of the myosin heads, producing an increase in IM3, but as tilting continues the catalytic domain moves beyond the light chain domain, and IM3 starts to decrease once more (Irving et al. 2000). These length step experiments established the conformation of the myosin heads during isometric contraction at 4°C. The increase in IM3 during isometric contraction at higher temperatures in the present experiments (Fig. 1B) is consistent with a small tilt in the forward direction through the working stroke from this initial conformation, similar to that seen in the response to a small shortening step.
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The decrease in RM3 during isometric contraction at higher temperature (Fig. 4B) indicates axial motion of the myosin heads towards the M-line. Again, this direction of motion is the same as that inferred from the changes in RM3 following a shortening step (Piazzesi et al. 2002). These similarities in the tilting and axial motion of the myosin heads inferred from the changes in the M3 X-ray reflection in response to changes in either length or temperature suggest that they may be associated with a common mechanism of force generation.
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In contrast with the large changes in the intensity of the M3 reflection produced by imposing length steps during isometric contraction, no significant changes in the intensities of the equatorial 1,0 and 1,1 reflections (I11 and I10) have been detected in previous length-step experiments (Huxley et al. 1983; Irving et al. 1992). The intensity of the first actin layer line (IA1L) increases by only about 10% at the end of phase 2 after a shortening step of 6 nm per half-sarcomere in intact fibres from frog muscle (authors' unpublished data). A larger change in IA1L, a 25% decrease, occurs in response to a ca 5 nm per half-sarcomere stretch of bundles of demembranated rabbit psoas fibres treated with 1-ethyl-3-[3-dimethylamino)propyl]-carbodiimide to cross-link the actin and myosin filaments (Ferenczi et al. 2005). However, that perturbation produced a roughly 200% increase in isometric force, much larger than the force changes observed in the intact muscle fibres used in the present experiments. The ca 10% increase in IA1L following a shortening step in intact fibres from frog muscle is much smaller than that produced by increasing temperature in the same preparation (Fig. 2B), even though the force changes are similar in the two protocols. The change in I11/I10 following a shortening step is also much smaller than that associated with a temperature increase (Fig. 1D).
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I1,1/I1,0 and IA1L depend on the three-dimensional distribution of the myosin heads within the lattice of myosin and actin filaments, so they are sensitive to radial and azimuthal motions of the heads. Thus the higher force during isometric contraction at higher temperature is associated with radial and/or azimuthal motions of the myosin heads that are either absent or much smaller during the force recovery that follows a shortening step. If force generation is driven by the same structural transition in the myosin heads under all conditions, this comparison suggests that the radial and/or azimuthal motions of the myosin heads associated with isometric contraction at higher temperature are not related to force generation per se. It is also possible that distinct modes of force generation occur in response to changes of length and temperature (Bershitsky et al. 1997; Tsaturyan et al. 1999; Huxley, 2000; Bershitsky & Tsatsuyan, 2002), and Ferenczi et al. (2005) recently interpreted the increase in IA1L they observed following a stretch in demembranated cross-linked fibres from rabbit psoas muscle in terms of an azimuthal component of the motion of the myosin heads during the rapid force recovery following a length step. The present results do not distinguish between these possibilities, but the quantitative analysis of the temperature-dependent changes in the M3 reflection presented below suggests that the increased force at higher temperature can be explained in terms of the observed axial motions of the myosin heads. The observation that the working stroke elicited by a rapid shortening step is smaller at higher temperature, by just the amount required to account for the change in filament strain and isometric force, also suggests that length and temperature changes act through the same mechanism (Piazzesi et al. 2003).
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Temperature dependence of the myosin and actin filament periodicities
The axial periodicities of both the myosin and actin filaments were larger during active contraction at higher temperature (Fig. 3). Comparison with the smaller changes in filament periodicities associated with increasing the temperature of resting muscle showed that the periodicity changes in active conditions could not be explained by thermal expansion of the filaments; rather they are associated with the greater active force at higher temperature. The observed changes in periodicities of the myosin-based axial reflections were linearly related to force (Fig. 3A and B) and close to those expected from the instantaneous compliance of the myosin filament (0.26%/T0,4; Reconditi et al. 2004).
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The changes in the periodicities of the actin-based layer line reflections (Fig. 3C and D) were larger, corresponding to an apparent actin filament compliance of 0.74%/T0,4 (Fig. 3E). This is larger than the values estimated from the changes in actin filament periodicity following imposed length changes in two studies on whole muscles, 0.2–0.3%/T0,4 (Huxley et al. 1994; Wakabayashi et al. 1994), but similar to the value, 0.65%/T0, estimated in another study (Bordas et al. 1999). Both the latter value and that estimated from the data in Fig. 3E are much larger than the instantaneous actin filament compliance, 0.26%/T0,4, determined from either the modulation of SA6L during 3 kHz length oscillations (Dobbie et al. 1998) or the dependence of sarcomere stiffness on sarcomere length (Linari et al. 1998). Moreover an instantaneous actin filament compliance of 0.7%/T0,4 would be too large to be compatible with the instantaneous compliance of the half-sarcomere, 5.1 nm/T0,4 (Dobbie et al. 1998).
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Taken together, these results show that the observed changes in the periodicity of the actin filaments cannot all be explained by a simple elasticity. The recent observation of an increase in actin periodicity in the transition from relaxation to low-force rigor (Tsaturyan et al. 2005) provides further support for this conclusion. When myosin heads are bound to actin and length and force changes are applied on a time scale that is fast compared with myosin head detachment, the actin compliance is small, corresponding to an instantaneous compliance of 0.26%/T0,4 (Dobbie et al. 1998; Linari et al. 1998; Tsaturyan et al. 2005). When the force changes on a time scale that is slow compared with myosin head detachment and reattachment, the apparent compliance may be larger (Fig. 3; Bordas et al. 1999; Tsaturyan et al. 2005), although there are some discrepancies between the published results. It seems that additional changes in actin filament periodicity can occur under these conditions, although the mechanism and functional significance of these changes remain to be investigated.
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Thermal ratchet and tilting head models
In the influential model for the mechanism of muscle contraction proposed by Huxley (1957), force is generated by preferential attachment of myosin heads to actin sites further from the centre of the sarcomere, the M-line. Attachment is coupled to extension of an elastic element in series with the myosin head, driven by thermal energy. In ‘thermal ratchet’ models of this type the force is expected to be larger at higher temperature because the increased thermal energy drives a greater extension of the elastic element. The increased force would then be accompanied by an increase in the average distance of the myosin heads from the M-line, in contradiction with the observed changes in the interference fine structure of the M3 reflection (Fig. 4B). Thus this type of model is not consistent with the present results, at least in its simplest form.
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In the model of Huxley & Simmons (1971), force is generated in a rapid equilibrium between a series of actin-attached states. We consider here the simplest case, in which there are only two attached states, called A1 and A2. The transition from A1 to A2 displaces the actin-binding site of the myosin head towards the M-line of the sarcomere (Fig. 4C) and generates force, stretching the myosin and actin filaments (Piazzesi et al. 2002; Reconditi et al. 2004). If the free energy decrease between A1 and A2 were larger at higher temperature, this mechanism would lead to a larger fraction of heads in A2, a higher isometric force and filament strain and a smaller working stroke in response to an imposed shortening step, as observed (Piazzesi et al. 2003). The present results show directly that the average axial position of the myosin heads moves towards the M-line at higher temperature, as predicted by this type of model.
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Axial motions of myosin heads in a tilting lever arm model
The changes in the interference fine structure of the M3 reflection observed in the present experiments (Fig. 4B) can be used to quantify the axial motions of the myosin heads associated with higher isometric force production at higher temperature. The approach is similar to that applied previously to length-step (Piazzesi et al. 2002) and load-step (Reconditi et al. 2004) experiments, and in the comparison of active contraction and rigor (Reconditi et al. 2003). The catalytic domain of the myosin head is assumed to bind to actin in the conformation determined by cryo-electron microscopy of isolated actin filaments decorated with myosin head fragments in the absence of ATP (Rayment et al. 1993a,b). The light-chain domain is assumed to tilt to accommodate sliding between the myosin and actin filaments with the catalytic domain remaining attached to actin. During isometric contraction at 4°C, the long axes of the light-chain domains of the two heads of each myosin molecule, defined as the lines joining residues 707 and 843 of the myosin heavy chain, are at 60 and 70 deg to the filament axis, with residue 843 closer to the M-line (Irving et al. 2000; Piazzesi et al. 2002). Only one of the two heads of each myosin (that with its light-chain domain at 60 deg) is assumed to be bound to actin and to respond to filament sliding (Piazzesi et al. 2002). This model, together with the experimental values of the instantaneous compliance of the myosin and actin filaments (SM=SA= 0.26%/T0,4) reproduces the observed changes in RM3, SM3 and IM3 in the phase 1 and phase 2 responses to either a length step (Piazzesi et al. 2002) or a load step (Reconditi et al. 2004).
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In the present experiments the sarcomere length is constant, but the light-chain domains of the myosin heads tilt so that the end closer to actin moves towards the M-line at higher temperature (Fig. 4C), causing RM3 to decrease (Fig. 4B). The increased strain in the myosin filament due to the higher force at higher temperature makes a small contribution to the change in RM3, and this was included in the calculations using a distributed filament compliance algorithm (Linari et al. 1998).RM3 was 0.16 smaller during isometric contraction at 17°C than at 0°C (Fig. 4B), and this decrease can be reproduced by tilting the light-chain domains of the actin-attached heads by 9 deg so that the end closer to actin moves towards the M-line at the higher temperature. This type of myosin head motion was inferred previously from measurements of IM3 changes in response to sinusoidal length changes imposed during active contraction at different temperatures (Griffiths et al. 2002).
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According to the model, this 9 deg tilt of the light-chain domain would produce an increase in IM3 of 9% between 0 and 17°C, similar to the observed 11% increase (Fig. 1B, squares), but smaller than the 27% increase after correction for the change in the width of the reflection (Fig. 1B, circles). The origin of this discrepancy is unknown, but it might be caused by a decrease in the axial disorder of the myosin heads during active contraction at higher temperature. This would not be expected to produce a corresponding increase in the intensities of the higher-order myosin-based reflections (e.g. IM6, Fig. 1C), since those reflections are predominantly due to the filament backbone (Linari et al. 2000; Huxley et al. 2003; Reconditi et al. 2004).
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Tilting of the light-chain domains by 9 deg between isometric contraction at 0 and 17°C corresponds to an axial motion of the catalytic domains by 1.4 nm towards the M-line, measured with respect to the junction between the light-chain domain and the myosin filament. Scaling this motion by the observed force increase (Fig. 4A), and using units of the isometric force at 4°C (T0,4) for comparison with previous experiments, this corresponds to an axial motion of 3.8 nm per T0,4. The instantaneous compliance of each overlapping array of actin and myosin filaments, the half-sarcomere, is 5.1 nm per T0,4 (Dobbie et al. 1998). The internal compliance of the myosin heads accounts for 1.4 nm per T0,4 of this (Reconditi et al. 2004), so the combined contribution of the actin and myosin filaments to the half-sarcomere compliance is 3.7 nm per T0,4, essentially the same as the 3.8 nm per T0,4 axial motion of the myosin heads deduced from the present results.
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These model calculations show that the light-chain domains of the myosin heads tilt towards the M-line during isometric contraction at higher temperature by exactly the amount required to strain the actin and myosin filaments to bear the higher force. In other words, the tilting of the light-chain domains that we have observed by comparing steady isometric contractions produced by electrical stimulation at different temperatures is the same as the tilting that would have been produced during an instantaneous rise in temperature if myosin heads had stayed attached to the same actin monomer and tilted to strain the filaments to the steady force characteristic of the new temperature. The filament strain used in these calculations corresponds to the instantaneous compliance of the filaments, and we have already noted that in the case of the actin filament this is smaller than the observed difference in filament periodicity during isometric contraction at different temperatures (Fig. 3). The myosin head conformation during isometric contraction at different temperatures is therefore determined by the instantaneous stress and strain in the myosin heads and filaments, rather than by the absolute filament periodicities at each temperature. The molecular mechanism of this relationship remains to be elucidated, but the demonstration that a structural model developed to describe the axial motions of myosin heads following length and load steps (Piazzesi et al. 2002; Reconditi et al. 2003, 2004) can satisfactorily account for the axial motions accompanying the variation of isometric force with temperature suggests that a single mechanism of force generation may operate in all three protocols.
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2 Randall Division of Cell and Molecular Biophysics, School of Biomedical Sciences, King's College London, London SE1 1UL, UK
3 European Synchrotron Radiation Facility, F-38043 Grenoble Cedex, France
Abstract
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X-ray diffraction patterns were recorded from isolated single fibres of frog skeletal muscle during isometric contraction at temperatures between 0 and 17°C. Isometric force was 43 ± 2% (mean ±S.E.M., n= 10) higher at 17°C than 0°C. The intensity of the first actin layer line increased by 57 ± 18% (n= 5), and the ratio of the intensities of the equatorial 1,1 and 1,0 reflections by 20 ± 7% (n= 10), signalling radial or azimuthal motions of the myosin head domains. The M3 X-ray reflection from the axial repeat of the heads along the filaments was 27 ± 4% more intense at 17°C, suggesting that the heads became more perpendicular to the filaments. The ratio of the intensities of the higher and lower angle peaks of the M3 reflection (RM3) was 0.93 ± 0.02 (n= 5) at 0°C and 0.77 ± 0.02 at 17°C. These peaks are due to interference between the two halves of each myosin filament, and the RM3 decrease shows that heads move towards the midpoint of the myosin filament at the higher temperature. Calculations based on a crystallographic model of the heads indicated that the observed RM3 change corresponds to tilting of their light-chain domains by 9 deg, producing an axial displacement of 1.4 nm, which is equal to that required to strain the actin and myosin filaments under the increased force. We conclude that the higher force generated by skeletal muscle at higher temperature can be accounted for by axial tilting of the myosin heads.
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Introduction
The force generated by skeletal muscle during isometric contraction is greater at higher temperature. In amphibian muscles, this effect occurs within the physiological temperature range (Ford et al. 1977; Bershitsky et al. 1997; Piazzesi et al. 2003). The increased force is not accompanied by an increased stiffness of the muscle sarcomeres (ibid.), so it is not caused by an increase in the number of myosin cross-bridges interacting with actin filaments. Each individual myosin cross-bridge must therefore generate a larger force at higher temperature, and the phenomenon provides an opportunity to investigate the structural basis of isometric force generation in the actin–myosin cross-bridges in their native sarcomeric arrangement.
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We used X-ray diffraction from isolated intact fibres of frog skeletal muscle to characterize the structural changes associated with the enhanced force production at higher temperature. We measured the intensities of the axial X-ray reflections from the periodic repeat of the myosin heads along the filaments, the actin-based layer line reflections corresponding to the helical periodicities of the actin filament, and the equatorial reflections related to the mass distribution in the plane perpendicular to the filaments during active isometric contraction in the temperature range 0 to 17°C. We also used a new X-ray interference technique (Linari et al. 2000; Reconditi et al. 2004) to give a precise measure of the axial motions of the myosin heads towards the centre of the sarcomere when isometric force is modulated by temperature.
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Preliminary results have been presented in abstract form (Reconditi et al. 2002).
Methods
Muscle fibre preparation and mounting
Frogs (Rana temporaria) were cooled to 2–4°C and killed by decapitation followed by destruction of the brain and spinal cord, in conformation with EU Directive 86/609/EEC and the UK (Scientific Procedures) Act 1995. Single fibres were dissected from the lateral head of the tibialis anterior muscle. The fibre tendons were clamped in aluminium foil clips and mounted between a pair of hooks in Ringer solution at sarcomere length 2.1 μm. One of the hooks was attached to a capacitance force transducer (Huxley & Lombardi, 1980), and the other was fixed. The temperature of the bathing Ringer solution was controlled by feedback to a thermoelectric module. Fibres were stimulated via electrodes mounted on mica windows, on either side of the fibre and 600 μm apart.
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Experimental protocol
Fibres were mounted at beamline ID02 of the European Synchrotron Radiation Facility (ESRF), Grenoble, France (Narayanan et al. 2001).
Two dimensional X-ray patterns were collected during isometric tetani at 0, 4, 10 and 17°C. Isometric force was not reliably maintained during tetanic stimulation at temperatures higher than about 17°C in the fibres used here. One or two cycles of four series of tetani (one series at each temperature) were typically recorded from each fibre. The order of the measurements at the four temperatures within a cycle was randomised. Isometric force developed faster at higher temperature, and tetanus duration was reduced accordingly. X-ray patterns were collected at the plateau of isometric tetani, from 350–370, 300–320, 250–270, or 130–150 ms after the first stimulus at 0, 4, 10 and 17°C, respectively. In a few experiments, noted below, the tetanus duration was increased and X-ray data were collected from later periods of the tetanus: 850–870, 700–720, 500–520 and 300–320 ms, respectively. Stimulus frequency and intertetanus interval were set in preliminary experiments to the minimum values required for force fusion and constant plateau force (T0), respectively (see Table 1 of Piazzesi et al. 2003). Because the time required for changing temperature was longer than the inter-tetanus interval in some cases, T0 could be higher in the first tetanus than in subsequent tetani of a series, and the first tetanus at a new temperature was not used for X-ray data collection. Each experiment was terminated when the fibre showed the first sign of radiation damage, a sudden failure of fibre activation or relaxation, typically occurring after about 50 tetani. Data are presented from ten fibres with cross-sectional area 22100 ± 5200 μm2 (S.D.)
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X-ray data collection
The X-ray beam at ID02 had full-width at half-maximum (FWHM) ca 150 μm vertically and 300 μm horizontally, with a total flux of up to 5 x 1013 photons s–1 at wavelength 0.1 nm. Data are presented from some experiments in which the fibre was mounted vertically, and some in which it was mounted horizontally. The camera length was either 3 m or 10 m, depending on the region of the diffraction diagram under study. The diffraction data were recorded with a FReLoN CCD detector with image intensifier, and corrected for dark current and spatial distortion as described by Narayanan et al. (2001). The 2048 x 2048 pixels of the CCD were binned by factors of 16 in the radial direction and 2 in the axial direction before the read-out after each tetanus. The axial point-spread function of the detector had FWHM 250 μm. A fast shutter limited X-ray exposure of the fibre to periods of data acquisition. The fibre was translated along its axis by 100–200 μm between contractions to spread the effects of radiation damage.
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In order to make precise measurements of the temperature dependence of the spacings of the axial X-ray reflections in resting muscle, whole sartorius muscles of Rana temporaria were mounted vertically at ID02 between mica windows in a temperature-controlled chamber. X-ray data were collected with a camera length of 2 m.
X-ray data analysis
X-ray diffraction patterns were analysed with Fit2D (A. Hammersley, ESRF) and Peakfit (SPSS Science). Images were centred and aligned using the M3 meridional and (1,1) equatorial reflections. The distribution of diffracted intensity along the meridional axis of the X-ray pattern (parallel to the fibre axis) was calculated by integrating from 0.025 nm–1 on either side of the meridian. The background intensity distribution was fitted using a convex hull algorithm and subtracted. The fine structure of each axial reflection was analysed by multi-gaussian fitting to obtain the intensity and the position of each component peak under the constraint that they had equal axial width. Axial periodicities were calibrated using the M3 reflection in an isometric tetanus at 4°C, with periodicity of 14.573 nm (Linari et al. 2000). Integration limits for other reflections were as follows: 1st actin layer line (A1L): 1/21–1/4.8 nm–1 radially; sixth (A6L) and seventh (A7L) actin layer lines: 1/91–1/6.5 nm–1 radially; equatorial (1,0) and (1,1) reflections: 1/100 nm–1 on each side of the equator. The A6L and A7L layer lines were also analysed using narrower integration limits, 1/29–1/17 nm–1 (Bordas et al. 1999), with similar results. These narrower integration limits were also used for analysis of A6L and A7L in resting muscles, in order to avoid the contribution of the M7 meridional reflection. Backgrounds were subtracted using a convex hull algorithm for the A1L, (1,0), and (1,1) reflections; a constant background was subtracted for the A6L and A7L reflections.
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Results
Intensities of axial X-ray reflections
The intensities of the axial X-ray reflections are sensitive to the distribution of mass along the myosin and actin filaments. The M3 X-ray reflection, corresponding to the 14.5 nm axial periodicity of myosin heads, is relatively intense during isometric contraction because the actin-attached myosin heads are orientated roughly perpendicular to the filament axis (Huxley et al. 1982; Irving et al. 2000). The intensity of the M3 reflection, IM3, was 11 ± 6% (mean ±S.E.M., n= 10) greater during active isometric contraction at 17°C than at 0°C (Fig. 1B, squares). The radial width of the M3 reflection was 16 ± 4% greater at the higher temperature, indicating a decrease in the axial alignment of neighbouring myosin filaments. After correction of the observed change in IM3 for this effect by multiplying by the width (Huxley et al. 1982), the increase in IM3 from 0 to 17°C was 27 ± 4% (Fig. 1B, circles). Isometric plateau force (T0) increased by 43 ± 2% in the same temperature range (Fig. 1A), from 210 ± 30 kPa (mean ±S.D.) at 0°C to 302 ± 44 kPa at 17°C. The increase in IM3 suggests that the myosin heads have tilted to become more perpendicular to the filament axis at the higher temperature.
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A, isometric force (T0). B, intensity of the M3 X-ray reflection (IM3), before (, continuous line) and after (, dashed line) correcting for the change in radial width. C, intensity of the M6 X-ray reflection (IM6). D, ratio (I11/I10) of the intensities of the equatorial (1,1) and (1,0) reflections. All data normalized by the corresponding values at 0°C. Mean ±S.E.M. for n= 10 (A and B) or n= 5 (C and D); the data in A and B are from the same 10 fibres.
There was no significant change in the intensity of the M6 reflection, IM6, with temperature (Fig. 1C). This reflection is much less sensitive to the conformation of the myosin heads, and seems to be associated with other components of the myosin filament (Huxley et al. 2003; Reconditi et al. 2004).
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Intensities of equatorial X-ray reflections
The equatorial X-ray reflections give information about the distribution of mass in the plane perpendicular to the myosin and actin filament axis. The intensity of the 1,1 reflection characteristically increases, and that of the 1,0 reflection decreases, when muscles are activated or put into rigor (Haselgrove & Huxley, 1973). This transition is conveniently monitored by the ratio I11/I10 of the intensities of the 1,1 and 1,0 reflections. In the present experiments I11/I10 was 20 ± 7% larger during isometric contraction at 17°C than at 0°C (Fig. 1D).
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Intensities of actin-based layer lines
The actin-based layer lines are related to the helical periodicities of the actin filament, and thus are sensitive to stereospecific attachment of myosin heads to actin. The first actin-based layer line (A1L), with an axial spacing of about 38 nm, comes from the long-pitch actin helix. This layer line is more intense in rigor muscle, in which all the myosin heads are strongly bound to actin and take up its helical periodicity, than in resting muscle, when the heads are detached from actin (Huxley & Brown, 1967). The intensity of this layer line, IA1L, is also greater during isometric contraction than at rest (Bordas et al. 1993; Piazzesi et al. 1999), indicating that active force generating heads take up the periodicity of the long-pitch actin helix. IA1L was 57 ± 18% (mean ±S.E.M.; n= 5) larger during isometric contraction at 17°C than at 0°C (Fig. 2B, circles), similar to the fractional increase in force in this group of fibres (Fig. 2A). These results suggest that the higher isometric force at higher temperature is associated with a mass distribution of the myosin heads that has greater helical order on the long-pitch actin helix.
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A, isometric force (T0). B, intensity (IA1L) of the first actin-based layer line reflection, with periodicity ca 38 nm (), intensity (IA6L) of the sixth actin-based layer line reflection, with periodicity ca 5.9 nm (), intensity (IA7L) of the seventh actin-based layer line reflection, with periodicity ca 5.1 nm (). All data normalized by the corresponding values at 0°C. Mean ±S.E.M., n= 5 fibres.
The helical structure of the actin filament also gives rise to layer line reflections with axial spacings of ca 5.9 and 5.1 nm, corresponding to the axial repeats of the two ‘genetic helices’ that connect every actin monomer in the filament (Huxley & Brown, 1967). These reflections will be referred to here as A6L and A7L, respectively, with corresponding intensities IA6L and IA7L. This nomenclature relates to a simplified model of the actin filament structure in which there are 13 actin monomers in six and seven turns of the two genetic helices. This relation does not hold exactly in the native filament, and the reciprocal spacings of the A6L and A7L reflections are not integer multiples of that of A1L (Huxley & Brown, 1967; Bordas et al. 1999). The intensities of the A6L and A7L reflections increase when muscles are activated (Matsubara et al. 1984; Bordas et al. 1999) or put into rigor (Huxley & Brown, 1967). However IA6L was only 5 ± 4% (mean ±S.E.M.; n= 5) greater during isometric contraction at 17°C than at 0°C (Fig. 2B, squares), and IA7L was 20 ± 13% larger at 17°C (Fig. 2B, triangles). Neither of these changes is statistically significant (P > 0.05).
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Axial spacings of the X-ray reflections
The axial spacings of the M3 and M6 reflections during isometric contraction, SM3 and SM6, respectively, showed small but reproducible increases with temperature. SM3 was 14.568 ± 0.002 nm (mean ±S.E.M., n= 10) at 0°C and 14.587 ± 0.002 nm at 17°C. The change in SM3 with temperature during active contraction was linearly related to the isometric force (Fig. 3A). Linear regression of these data (dashed line) corresponds to a myosin filament compliance of 0.35 ± 0.01%/T0,4, where T0,4 refers to the isometric force at 4°C. The SM6 data (Fig. 3B) were more noisy, but gave a mean compliance estimate of 0.27 ± 0.09%/T0,4, which is close to that, 0.26 ± 0.01%/T0,4, measured by imposing rapid force steps during active contraction at 4°C (Reconditi et al. 2004).
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A, spacing of the M3 reflection (SM3). B, spacing of the M6 reflection (SM6). C, spacing of the sixth actin-based layer line reflection (SA6L). D, spacing of the seventh actin-based layer line reflection (SA7L). E, axial periodicity of the actin monomers (SA) calculated as described in the text. The abscissa is the isometric force from the same set of fibres, normalized to 4°C. Data are means ±S.E.M., n= 10. Dashed lines are linear regression on the data.
To assess the possible contribution of thermal expansion of the myosin filament to these spacing changes, some control experiments were made to measure the temperature dependence of SM3 and SM6 in resting muscle fibres. Experiments on resting single muscle fibres suggested that the thermal expansion of the myosin filament is small; SM3 was only 0.03 ± 0.03% (mean ±S.E.M., n= 3) larger at 17°C than at 4°C. To improve the precision of these measurements, they were repeated using whole sartorius muscles, and in this preparation SM3 was 0.044 ± 0.008% (mean ±S.E.M., n= 3) larger at 17°C than at 6°C. The corresponding change in SM6 was –0.003 ± 0.015%. These results show that thermal expansion of the myosin filament could make only a minor contribution to the larger axial periodicity of the myosin filament during active contraction at higher temperature (Fig. 3), which is therefore likely to be predominantly due to myosin filament compliance.
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The axial spacings of the sixth and seventh actin-based layer lines, SA6L and SA7L, respectively, also increased with temperature (Fig. 3C and D). Linear regression of SA6L and SA7L against isometric force (dashed lines) gave slopes of 0.51 ± 0.12%/T0,4 (mean ±S.E.M., n= 5) and 0.94 ± 0.24%/T0,4, respectively. The change in axial periodicity SA of monomers along the actin filament was calculated from these data (Huxley et al. 1994; Wakabayashi et al. 1994; Bordas et al. 1999), and linear regression of SA against isometric force (Fig. 3E) has a slope of 0.74 ± 0.18%/T0,4.
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Control measurements of the temperature dependence of SA6L, SA7L and SA were made in resting muscle in order to assess the possible contribution of thermal expansion of the actin filaments. In resting sartorius muscles SA was 0.033 ± 0.027% (mean ±S.E.M., n= 3) larger at 17°C than at 6°C. The increase in active force in this temperature range is about 0.2 T0,4 (Fig. 1A) so, based on the relation between SA and active force (Fig. 3E), SA during isometric contraction is larger at the higher temperature by 0.2 x (0.74 ± 0.18) = 0.15 ± 0.04%/T0,4. This is much larger than the 0.033 ± 0.027% difference observed in resting conditions, suggesting that thermal expansion could be responsible for only a small fraction of the actin periodicity changes reported in Fig. 3.
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Interference fine structure of the M3 reflection
The M3 reflection from the 14.5 nm repeat of the myosin heads along the filament is split into two closely spaced peaks by interference between the two arrays of myosin heads in each myosin filament (Linari et al. 2000). This phenomenon allows the axial motions of the myosin heads towards the centre of the sarcomere, the M-line, to be measured with a precision of the order of 0.1 nm (Piazzesi et al. 2002; Reconditi et al. 2004). During isometric contraction at 0°C, the two peaks of the M3 reflection had almost equal intensities; the ratio of the intensity of the higher angle peak to that of the lower angle peak of the M3 reflection, RM3, was 0.93 ± 0.02 (mean ±S.E.M., n= 5). During isometric contraction at higher temperatures, RM3 was smaller (Fig. 4B), and at 17°C it was 0.77 ± 0.02. This decrease in RM3 shows that the interference distance between the two arrays of myosin heads in each filament has decreased, i.e. the centroids of the myosin heads have moved closer to the centre of the filament (Fig. 4C).
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A, isometric force, normalized to that at 0°C. B, relative intensity RM3 of the higher and lower angle peaks of the M3 reflection. Mean ±S.E.M. for n= 5 fibres. C, schematic diagram of myosin heads (red) attached to the actin filament (grey). At higher temperature the light-chain domain of the myosin head tilts, displacing its catalytic domain towards the midpoint of the myosin filament (blue), stretching the actin filament and decreasing the interference distance L.
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The measurements of RM3 in Fig. 4B were made soon after the establishment of the isometric tetanus plateau at each temperature (see Methods). In a few fibres we also measured RM3 later in the tetanus plateau, and found that RM3 decreased slightly while the plateau force was maintained. For example, 350–370 ms after the first stimulus at 0°C, RM3 was 0.93 ± 0.02 (Fig. 4B) and 500 ms later it was 0.87 ± 0.01 (n= 3). This small decrease in RM3 during a tetanus was present at each temperature studied, and may be related to progressive development of sarcomere inhomogeneity. The effect of temperature on RM3 was of similar magnitude in the series of measurements made early and later in the tetanus, consistent with the hypothesis that the lower RM3 at higher temperature is causally related to the higher steady force.
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Discussion
Temperature dependence of the X-ray pattern during isometric contraction
The higher isometric force generated by intact single fibres from skeletal muscle at higher temperatures is accompanied by the following changes in the X-ray pattern: (1) the intensity of the axial M3 reflection (IM3) increases (Fig. 1B), indicating that myosin heads tilt to become more perpendicular to the filament axis; (2) the ratio (I11/I10) of the intensities of the (1,1) and (1,0) equatorial reflections increases (Fig. 1D), signalling a change of mass distribution in the plane perpendicular to the filaments; (3) the intensity of the first actin layer line (IA1L) increases (Fig. 2B), showing that a greater fraction of the mass of the myosin heads has taken up the periodicity of the 38 nm long-pitch actin helix; (4) the axial periodicities of both the myosin (Fig. 3A and B) and actin (Fig. 3C–E) filaments increase; (5) the ratio of the intensity of the higher angle peak to that of the lower angle peak of the M3 reflection (RM3) decreases (Fig. 4B), showing that myosin heads have moved towards the centre of the sarcomere.
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Broadly similar changes in the intensities of the equatorial, axial M3 and first actin layer line reflections have been observed in demembranated fibres from frog muscle following a temperature jump from 6 to 16°C (Tsaturyan et al. 1999), but there has been no previous systematic study of the effect of temperature on the X-ray pattern from intact muscle fibres. Griffiths et al. (2002) reported that the intensity of the M3 reflection from bundles of fibres from frog muscle was 11–20%smaller during isometric contraction at 24°C than at 4°C, but that study used a one-dimensional detector and did not report or correct for changes in the width of the M3 reflection. The temperature dependence of the interference fine structure of the axial reflections has not been reported previously.
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Although the isometric force was 42% larger at 17°C than at 0°C, there is no change in the stiffness of the sarcomere under these conditions (Ford et al. 1977; Bershitsky et al. 1997; Piazzesi et al. 2003), so neither the force increase nor the associated changes in the X-ray pattern are due to a change in the number of myosin heads bound to actin. This suggests that some or all of the X-ray changes listed above are associated with conformational changes in the actin-attached myosin heads that are responsible for the higher isometric force at higher temperature.
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Comparison with changes in the X-ray pattern in response to rapid length steps
Many previous studies of the conformational changes in the myosin heads associated with active force generation have focused on the changes in the X-ray pattern following a rapid change of fibre length (Huxley et al. 1983; Irving et al. 1992, 2000; Lombardi et al. 1995; Dobbie et al. 1998; Piazzesi et al. 2002; Griffiths et al. 2002). When a step decrease in fibre length is imposed during isometric contraction, there is an elastic force decrease during the step (phase 1 of the force transient) followed by partial force recovery on the millisecond timescale (phase 2; Huxley & Simmons, 1971). Phase 1 is due to the compliance of the myosin heads and the actin and myosin filaments; phase 2 is associated with the working stroke in the actin-attached myosin heads (Huxley & Simmons, 1971; Piazzesi et al. 2002).
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Changes in the intensity and interference fine structure of the M3 reflection (IM3 and RM3) during phases 1 and 2 of the length step response have been measured in the preparation used here, at 4°C (Irving et al. 1992, 2000; Lombardi et al. 1995; Dobbie et al. 1998; Piazzesi et al. 2002). When a shortening step is imposed, the myosin heads tilt so that their catalytic domains move towards the M-line of the sarcomere, during both the elastic fall of force (phase 1) and the rapid force recovery accompanying the working stroke (phase 2). This motion initially increases the axial alignment of the catalytic and light-chain domains of the myosin heads, producing an increase in IM3, but as tilting continues the catalytic domain moves beyond the light chain domain, and IM3 starts to decrease once more (Irving et al. 2000). These length step experiments established the conformation of the myosin heads during isometric contraction at 4°C. The increase in IM3 during isometric contraction at higher temperatures in the present experiments (Fig. 1B) is consistent with a small tilt in the forward direction through the working stroke from this initial conformation, similar to that seen in the response to a small shortening step.
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The decrease in RM3 during isometric contraction at higher temperature (Fig. 4B) indicates axial motion of the myosin heads towards the M-line. Again, this direction of motion is the same as that inferred from the changes in RM3 following a shortening step (Piazzesi et al. 2002). These similarities in the tilting and axial motion of the myosin heads inferred from the changes in the M3 X-ray reflection in response to changes in either length or temperature suggest that they may be associated with a common mechanism of force generation.
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In contrast with the large changes in the intensity of the M3 reflection produced by imposing length steps during isometric contraction, no significant changes in the intensities of the equatorial 1,0 and 1,1 reflections (I11 and I10) have been detected in previous length-step experiments (Huxley et al. 1983; Irving et al. 1992). The intensity of the first actin layer line (IA1L) increases by only about 10% at the end of phase 2 after a shortening step of 6 nm per half-sarcomere in intact fibres from frog muscle (authors' unpublished data). A larger change in IA1L, a 25% decrease, occurs in response to a ca 5 nm per half-sarcomere stretch of bundles of demembranated rabbit psoas fibres treated with 1-ethyl-3-[3-dimethylamino)propyl]-carbodiimide to cross-link the actin and myosin filaments (Ferenczi et al. 2005). However, that perturbation produced a roughly 200% increase in isometric force, much larger than the force changes observed in the intact muscle fibres used in the present experiments. The ca 10% increase in IA1L following a shortening step in intact fibres from frog muscle is much smaller than that produced by increasing temperature in the same preparation (Fig. 2B), even though the force changes are similar in the two protocols. The change in I11/I10 following a shortening step is also much smaller than that associated with a temperature increase (Fig. 1D).
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I1,1/I1,0 and IA1L depend on the three-dimensional distribution of the myosin heads within the lattice of myosin and actin filaments, so they are sensitive to radial and azimuthal motions of the heads. Thus the higher force during isometric contraction at higher temperature is associated with radial and/or azimuthal motions of the myosin heads that are either absent or much smaller during the force recovery that follows a shortening step. If force generation is driven by the same structural transition in the myosin heads under all conditions, this comparison suggests that the radial and/or azimuthal motions of the myosin heads associated with isometric contraction at higher temperature are not related to force generation per se. It is also possible that distinct modes of force generation occur in response to changes of length and temperature (Bershitsky et al. 1997; Tsaturyan et al. 1999; Huxley, 2000; Bershitsky & Tsatsuyan, 2002), and Ferenczi et al. (2005) recently interpreted the increase in IA1L they observed following a stretch in demembranated cross-linked fibres from rabbit psoas muscle in terms of an azimuthal component of the motion of the myosin heads during the rapid force recovery following a length step. The present results do not distinguish between these possibilities, but the quantitative analysis of the temperature-dependent changes in the M3 reflection presented below suggests that the increased force at higher temperature can be explained in terms of the observed axial motions of the myosin heads. The observation that the working stroke elicited by a rapid shortening step is smaller at higher temperature, by just the amount required to account for the change in filament strain and isometric force, also suggests that length and temperature changes act through the same mechanism (Piazzesi et al. 2003).
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Temperature dependence of the myosin and actin filament periodicities
The axial periodicities of both the myosin and actin filaments were larger during active contraction at higher temperature (Fig. 3). Comparison with the smaller changes in filament periodicities associated with increasing the temperature of resting muscle showed that the periodicity changes in active conditions could not be explained by thermal expansion of the filaments; rather they are associated with the greater active force at higher temperature. The observed changes in periodicities of the myosin-based axial reflections were linearly related to force (Fig. 3A and B) and close to those expected from the instantaneous compliance of the myosin filament (0.26%/T0,4; Reconditi et al. 2004).
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The changes in the periodicities of the actin-based layer line reflections (Fig. 3C and D) were larger, corresponding to an apparent actin filament compliance of 0.74%/T0,4 (Fig. 3E). This is larger than the values estimated from the changes in actin filament periodicity following imposed length changes in two studies on whole muscles, 0.2–0.3%/T0,4 (Huxley et al. 1994; Wakabayashi et al. 1994), but similar to the value, 0.65%/T0, estimated in another study (Bordas et al. 1999). Both the latter value and that estimated from the data in Fig. 3E are much larger than the instantaneous actin filament compliance, 0.26%/T0,4, determined from either the modulation of SA6L during 3 kHz length oscillations (Dobbie et al. 1998) or the dependence of sarcomere stiffness on sarcomere length (Linari et al. 1998). Moreover an instantaneous actin filament compliance of 0.7%/T0,4 would be too large to be compatible with the instantaneous compliance of the half-sarcomere, 5.1 nm/T0,4 (Dobbie et al. 1998).
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Taken together, these results show that the observed changes in the periodicity of the actin filaments cannot all be explained by a simple elasticity. The recent observation of an increase in actin periodicity in the transition from relaxation to low-force rigor (Tsaturyan et al. 2005) provides further support for this conclusion. When myosin heads are bound to actin and length and force changes are applied on a time scale that is fast compared with myosin head detachment, the actin compliance is small, corresponding to an instantaneous compliance of 0.26%/T0,4 (Dobbie et al. 1998; Linari et al. 1998; Tsaturyan et al. 2005). When the force changes on a time scale that is slow compared with myosin head detachment and reattachment, the apparent compliance may be larger (Fig. 3; Bordas et al. 1999; Tsaturyan et al. 2005), although there are some discrepancies between the published results. It seems that additional changes in actin filament periodicity can occur under these conditions, although the mechanism and functional significance of these changes remain to be investigated.
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Thermal ratchet and tilting head models
In the influential model for the mechanism of muscle contraction proposed by Huxley (1957), force is generated by preferential attachment of myosin heads to actin sites further from the centre of the sarcomere, the M-line. Attachment is coupled to extension of an elastic element in series with the myosin head, driven by thermal energy. In ‘thermal ratchet’ models of this type the force is expected to be larger at higher temperature because the increased thermal energy drives a greater extension of the elastic element. The increased force would then be accompanied by an increase in the average distance of the myosin heads from the M-line, in contradiction with the observed changes in the interference fine structure of the M3 reflection (Fig. 4B). Thus this type of model is not consistent with the present results, at least in its simplest form.
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In the model of Huxley & Simmons (1971), force is generated in a rapid equilibrium between a series of actin-attached states. We consider here the simplest case, in which there are only two attached states, called A1 and A2. The transition from A1 to A2 displaces the actin-binding site of the myosin head towards the M-line of the sarcomere (Fig. 4C) and generates force, stretching the myosin and actin filaments (Piazzesi et al. 2002; Reconditi et al. 2004). If the free energy decrease between A1 and A2 were larger at higher temperature, this mechanism would lead to a larger fraction of heads in A2, a higher isometric force and filament strain and a smaller working stroke in response to an imposed shortening step, as observed (Piazzesi et al. 2003). The present results show directly that the average axial position of the myosin heads moves towards the M-line at higher temperature, as predicted by this type of model.
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Axial motions of myosin heads in a tilting lever arm model
The changes in the interference fine structure of the M3 reflection observed in the present experiments (Fig. 4B) can be used to quantify the axial motions of the myosin heads associated with higher isometric force production at higher temperature. The approach is similar to that applied previously to length-step (Piazzesi et al. 2002) and load-step (Reconditi et al. 2004) experiments, and in the comparison of active contraction and rigor (Reconditi et al. 2003). The catalytic domain of the myosin head is assumed to bind to actin in the conformation determined by cryo-electron microscopy of isolated actin filaments decorated with myosin head fragments in the absence of ATP (Rayment et al. 1993a,b). The light-chain domain is assumed to tilt to accommodate sliding between the myosin and actin filaments with the catalytic domain remaining attached to actin. During isometric contraction at 4°C, the long axes of the light-chain domains of the two heads of each myosin molecule, defined as the lines joining residues 707 and 843 of the myosin heavy chain, are at 60 and 70 deg to the filament axis, with residue 843 closer to the M-line (Irving et al. 2000; Piazzesi et al. 2002). Only one of the two heads of each myosin (that with its light-chain domain at 60 deg) is assumed to be bound to actin and to respond to filament sliding (Piazzesi et al. 2002). This model, together with the experimental values of the instantaneous compliance of the myosin and actin filaments (SM=SA= 0.26%/T0,4) reproduces the observed changes in RM3, SM3 and IM3 in the phase 1 and phase 2 responses to either a length step (Piazzesi et al. 2002) or a load step (Reconditi et al. 2004).
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In the present experiments the sarcomere length is constant, but the light-chain domains of the myosin heads tilt so that the end closer to actin moves towards the M-line at higher temperature (Fig. 4C), causing RM3 to decrease (Fig. 4B). The increased strain in the myosin filament due to the higher force at higher temperature makes a small contribution to the change in RM3, and this was included in the calculations using a distributed filament compliance algorithm (Linari et al. 1998).RM3 was 0.16 smaller during isometric contraction at 17°C than at 0°C (Fig. 4B), and this decrease can be reproduced by tilting the light-chain domains of the actin-attached heads by 9 deg so that the end closer to actin moves towards the M-line at the higher temperature. This type of myosin head motion was inferred previously from measurements of IM3 changes in response to sinusoidal length changes imposed during active contraction at different temperatures (Griffiths et al. 2002).
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According to the model, this 9 deg tilt of the light-chain domain would produce an increase in IM3 of 9% between 0 and 17°C, similar to the observed 11% increase (Fig. 1B, squares), but smaller than the 27% increase after correction for the change in the width of the reflection (Fig. 1B, circles). The origin of this discrepancy is unknown, but it might be caused by a decrease in the axial disorder of the myosin heads during active contraction at higher temperature. This would not be expected to produce a corresponding increase in the intensities of the higher-order myosin-based reflections (e.g. IM6, Fig. 1C), since those reflections are predominantly due to the filament backbone (Linari et al. 2000; Huxley et al. 2003; Reconditi et al. 2004).
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Tilting of the light-chain domains by 9 deg between isometric contraction at 0 and 17°C corresponds to an axial motion of the catalytic domains by 1.4 nm towards the M-line, measured with respect to the junction between the light-chain domain and the myosin filament. Scaling this motion by the observed force increase (Fig. 4A), and using units of the isometric force at 4°C (T0,4) for comparison with previous experiments, this corresponds to an axial motion of 3.8 nm per T0,4. The instantaneous compliance of each overlapping array of actin and myosin filaments, the half-sarcomere, is 5.1 nm per T0,4 (Dobbie et al. 1998). The internal compliance of the myosin heads accounts for 1.4 nm per T0,4 of this (Reconditi et al. 2004), so the combined contribution of the actin and myosin filaments to the half-sarcomere compliance is 3.7 nm per T0,4, essentially the same as the 3.8 nm per T0,4 axial motion of the myosin heads deduced from the present results.
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These model calculations show that the light-chain domains of the myosin heads tilt towards the M-line during isometric contraction at higher temperature by exactly the amount required to strain the actin and myosin filaments to bear the higher force. In other words, the tilting of the light-chain domains that we have observed by comparing steady isometric contractions produced by electrical stimulation at different temperatures is the same as the tilting that would have been produced during an instantaneous rise in temperature if myosin heads had stayed attached to the same actin monomer and tilted to strain the filaments to the steady force characteristic of the new temperature. The filament strain used in these calculations corresponds to the instantaneous compliance of the filaments, and we have already noted that in the case of the actin filament this is smaller than the observed difference in filament periodicity during isometric contraction at different temperatures (Fig. 3). The myosin head conformation during isometric contraction at different temperatures is therefore determined by the instantaneous stress and strain in the myosin heads and filaments, rather than by the absolute filament periodicities at each temperature. The molecular mechanism of this relationship remains to be elucidated, but the demonstration that a structural model developed to describe the axial motions of myosin heads following length and load steps (Piazzesi et al. 2002; Reconditi et al. 2003, 2004) can satisfactorily account for the axial motions accompanying the variation of isometric force with temperature suggests that a single mechanism of force generation may operate in all three protocols.
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