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Biophys J, December 1999, p. 3197-3207, Vol. 77, No. 6
and
*LLS-IFAE, Universitat Aut-noma de Barcelona, E-08193
Bellaterra, Barcelona, Spain; #Department of Physics and
Astronomy, University of Leicester, Leicester LE1 7RH, United Kingdom;
§Department of Physics, Oliver Lodge Laboratory,
University of Liverpool, Liverpool L69 3BX, United Kingdom;
¶Open University Research Unit, Boars Hill, Oxford
OX1 5HR, United Kingdom; Daresbury Laboratory,
Warrington WA4 4AD, United Kingdom; and **ESRF, 220, F-38043 Grenoble
Cedex, France
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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When isometrically contracting muscles are subjected to a quick release followed by a shortening ramp of appropriate speed (Vo), tension decays from its value at the isometric plateau (Po) to <0.05 Po with the same time course as the quick part of the release; thereafter, tension remains at a negligible level for the duration of the shortening ramp. X-ray diffraction data obtained under these conditions provide evidence that 1) at Vo very few heads form an actomyosin complex, while the number of heads doing so at Po is significant; 2) relative to rest the actin filament at Vo is ~0.12% shorter and more twisted, while it is ~0.3% longer and less twisted at Po; and 3) the myosin heads attaching to actin during force development do so against a thin filament compliance of at least 0.646 ± 0.046% nm per Po.
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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The most generally accepted model of muscle
contraction (H. E. Huxley, 1969
; A. F. Huxley, 1974) proposes
that the globular heads (S1 portion) of the myosin molecules attach to
specific sites on the actin filaments, and tension is generated by a
tilting motion of the attached heads in the direction of the muscle
axis. The tilting of the attached heads results from a shape change induced by hydrolysis of ATP. In this model practically all the sarcomere elasticity is attributed to myosin cross-bridges (Huxley and
Simmons, 1971; Ford et al., 1977, 1981).
By using x-ray diffraction techniques Huxley et al. (1994) and
Wakabayashi et al. (1994) investigated the contribution of the
filaments to the total sarcomere elasticity. Both groups found that in
the transition from rest to isometric tetanic tension (Po)
the length of the actin filaments increased by 0.2-0.3%. Both groups
also detected a 0.2-0.3% increase in the length of the myosin
filaments in experiments where a contracting muscle was stretched
slowly from Po. Wakabayashi et al. reported results that
point to the existence of changes in the helical symmetry of the actin
filaments. However, Huxley et al. (1994) stated that their own
observations did not support that conclusion. Also, Huxley et al.
(1996, 1998) recorded a small decrease relative to the rest state in
the spacing of the 2.7-nm axial repeat during the early activation
phase of contraction and also during contraction against a negligible
load (Vo); however, they argued that the small decrease
might be simply due to a disordering artifact. We have attempted to
clarify the situation by recording high-resolution x-ray diffraction
diagrams from muscles at rest, Po and Vo, and time-resolved x-ray diffraction data during the transition from rest to
Po, and during a quick release from Po followed
by unloaded shortening so that tension is kept at <0.05
Po.
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MATERIALS AND METHODS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Muscles and length control
Sartorius muscles were dissected from small specimens of
Rana pipiens and mounted in Perspex cells containing
oxygenated Ringer's solution and maintained at 7-8°C throughout the
experiment. The muscles were mounted, stimulated, and their length and
speed of shortening controlled as described previously
(Martin-Fernandez et al., 1994).
Experimental protocols
Data collection at the European Synchrotron Radiation Facility (ESRF), Grenoble, France
Diffraction patterns were collected using x-rays with a wavelength of 0.1 nm delivered by an undulator (ID2) and conditioned by x-ray optics described elsewhere (Boesecke et al., 1995). The system
delivered a flux of ~8 × 1012 photons/s with a
stored beam of 100 mA. The beam size at the sample and focal spot
positions is described by a two-dimensional Gaussian with full-width
half-maxima of 0.32 and 0.86 mm in the vertical and horizontal
directions, respectively.
The high x-ray flux density deteriorated the x-ray pattern for exposure
times >1s, and a visible destruction of the muscle occurred for
exposures >5 s. Therefore, the total exposure per muscle was limited
to 
500 ms. A 7-m camera was used to achieve high angular resolution
in a spacing range extending from ~500.0 to 4.2 nm, and a 3-m camera
to extend the data to a resolution of ~2.0 nm.
The diffraction patterns were collected using image plates
(Fuji). The muscles were exposed to the x-rays and the data
recorded during selected times in the contractile cycle by
synchronizing the opening and closing of a fast shutter. This shutter
had opening and closing times of ~1 ms.
To record diffraction diagrams at Po, the muscles were
stimulated from rest with a pulse train of 1-s duration. After the tension plateau was reached (~200 ms after the onset of stimulation) the pattern was recorded during a total exposure time of 500 ms. Patterns collected during this period of time are referred to as
patterns at Po.
For data collection immediately after a quick release and during the
early stages of isotonic shortening, muscles were released 200 ms after
the onset of stimulation. The function generator controlling the length
of the muscles was programmed so that for the initial 1 ms, the speed
of the release was ~700 mm/s and in the subsequent 50 ms the speed of
shortening was reduced to ~60 mm/s. By this maneuver tension dropped
to <0.05 Po in ~3 ms, and thereafter was kept at that
level for the subsequent 50 ms. The total extent of shortening was 4 mm, i.e., ~10% of the initial muscle length of ~40 mm. The
exposure was synchronized so that the shutter opened for 20 ms
immediately after the tension had dropped to <0.05 Po. To
accumulate statistics, up to 25 cycles of this procedure were repeated
for any given muscle. Patterns collected during this time interval are
referred to as the patterns at Vo.
Data collection at the Synchrotron Radiation Source (SRS) at Daresbury Laboratory, UK
Essentially identical protocols were used, but the data were collected in a time-resolved mode. An x-ray wavelength of 0.135 nm from the wiggler station 16.1, a camera length of ~6 m, and a two-dimensional proportional gas chamber detector were used (Bliss et al., 1995). The evacuated pipe between specimen and two-dimensional
area detector was tilted upward, and the detector was displaced by
~20 cm from the position of the direct beam. The unacceptable scatter
produced by the direct beam hitting the beam pipe wall was avoided by
placing a baffle/beam stop inside the beam pipe so that the direct beam
was trapped. With this arrangement it was possible to record
two-dimensional x-ray diffraction diagrams over a range of spacings
from the fifth myosin layer line (at ~8.68 nm spacing) to the first
meridional actin reflection at ~2.7 nm spacing, while also recording
the 5.9- and 5.1-nm actin layer lines with adequate reciprocal radial
resolution despite the horizontally elongated shape of the x-ray focal
spot. Nevertheless, we could collect data (albeit within a restricted
range) with better time resolution than that possible at the ESRF
because of the time-framing capabilities of the proportional gas
chamber. We limited the time resolution to 10 ms. This is because the
detector used for these experiments had a total count rate limitation
of ~6 · 105 counts/s, and the total intensity in
the 2.7 nm layer line is only ~
of the total
diffracted/scattered intensity. Therefore, we had to limit the time
resolution to obtain adequate statistics within the granted beam time.
Because the detector was displaced upward, only one side of the pattern
could be recorded. Thus, the calibration of the spacings depended
critically on the use of the meridional reflections on the 6M and 9M as
internal markers. These reflections have splittings due to interference
effects (unpublished data): the combination of focal spot size at the
SRS and detector resolution did not allow full resolution of the
splittings. Because of this the absolute spacing calibration was not
sufficiently accurate for our purposes, and as a result the absolute
spacing values from these data are much less reliable than those from
the data collected at the ESRF. In fact, regarding spacing changes, the
main goal of these experiments was to confirm the trends in the
relative spacing changes provided by the ESRF data. In these
experiments 20 muscles were used and each produced 30 contraction cycles.
Spatial calibration of the image plate scanner and area detector
Neither the image plate scanner (Molecular Dynamics) nor the
two-dimensional proportional gas chamber have sufficiently accurate spatial linearity to collect diffraction data with the precision required for our determination of absolute values of spacings. However,
both devices are capable of yielding very accurate values for the
percentage changes if one has prior knowledge of, say, the rest value
of a given reflection. To overcome this limitation a very precise grid
of 0.2-mm-diameter holes spaced at intervals of 2 mm was constructed.
This grid was placed in front of the detector and the scatter from a
plastic tape was measured. The resulting pattern was used to calibrate
and correct for spatial distortions by interpolation and remapping of
the detector pixels. This procedure involved linear intensity
interpolation between any two adjacent pixels, both in the reciprocal
radial (R) and axial directions (z), to 10 times
the number of original pixels. This resulted in a remapping of the
detector output with an accuracy of ~
of a pixel.
Therefore, it is straightforward to work out the correct position of
any pixel by referring to the remapping grid pattern and reassigning
the corresponding pixel intensity. The correction functions are
time-independent as long as the same settings of the image plate
scanner and of the detector electronics are systematically used
throughout the experimental session(s). Absolute spacings in the muscle
patterns were determined by assigning a spacing of 14.34 nm to the
strong peak on the meridian of the third myosin layer line (3M) at rest.
Data reduction and evaluation
The analysis of the diffraction data was carried out using the
programs OTOKO and BSL (Koch and Bendall, 1981; Mant and Bordas, unpublished results). To find the dependence of the spacings and intensities of diffraction diagrams from averaged diffraction patterns
(Figs. 1-7) we chose suitable data sets which were then corrected for
detector nonlinearity and aligned if necessary by rotation and/or
translation. The position of the strong meridional reflections on the
3M and on the equator were used for the alignment procedure. The
resulting patterns were then summed. This was followed by averaging the
data in the four diffraction quadrants. The positions and intensities
along the layer lines were then extracted by applying peak stripping
procedures using the Levenberg-Marquardt method (Press et al., 1992).
Polynomials were used to fit the backgrounds and Gaussian functions to
fit the diffraction maxima. Whenever there were two overlapping
reflections the Gaussians were constrained to have the same axial width.
One-dimensional traces obtained by radial integration in the region
containing the [1,1,0] equatorial reflection (i.e., 0.035 nm
1 < R < 0.06 nm1)
were produced for each individual muscle pattern. These were used to
determine the axial spacings of the 37.0, 5.9, and 5.1 nm layer lines
with the Levenberg-Marquardt method. The results were used for the
statistical analysis of the data given in Tables 1 and 2.
This particular region of radial integration was chosen because it is
where the intensity increase during isometric contraction is largest;
for R < 0.035 nm1 there are tails from
meridional reflections of nonhelical origin; and for
R-values > 0.06 nm1 the arching of the
layer lines unacceptably distorts the value of the spacings. The traces
obtained in this fashion will be referred to as the [1,1,0]-row
lines.
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The spacings of the 2.7-nm meridional reflection for each individual
data set were derived in the same fashion from traces obtained by
radial integration in the region where 
0.025 nm1 < R < 0.025 nm1. This region was chosen
as the best compromise between statistics and distortion induced by
arching and layer line broadening.
The ESRF data was collected from different muscles in the various conditions of contraction. Intensity normalization was carried out by scaling the diffraction patterns to the total exposure by means of recording the flux falling on the specimen with an ion chamber. In addition, and to compensate for muscle variability, the intensities of the averaged diffraction patterns were checked out against the intensities of the SRS data. The latter was collected as a time sequence using the same muscles and, therefore, the accuracy in the relative intensities is only limited by counting statistics. The radial intensity distribution of the 5.9- and 5.1-nm actin layer lines and that in the meridian of the third myosin layer line were used to refine the intensity calibration of the ESRF data.
Relevant relationships between parameters of the actin helix
Given the helical symmetry of the actin filament the following
relationships hold:
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Manipulation of the formulas above yields
![<FR><NU>&Dgr;n</NU><DE>n</DE></FR>=<FR><NU>&Dgr;P</NU><DE>P</DE></FR><UP>−</UP><FR><NU>&Dgr;p</NU><DE>p</DE></FR> <UP>and</UP> <FR><NU>&Dgr;n</NU><DE>n</DE></FR>=<FR><NU>2P<SUB>5.9</SUB>P<SUB>5.1</SUB></NU><DE>[P<SUP>2</SUP><SUB>5.9</SUB><UP>−</UP>P<SUP>2</SUP><SUB>5.1</SUB>]</DE></FR> <FENCE><FR><NU>&Dgr;P<SUB>5.1</SUB></NU><DE>P<SUB>5.1</SUB></DE></FR><UP>−</UP><FR><NU>&Dgr;P<SUB>5.9</SUB></NU><DE>P<SUB>5.9</SUB></DE></FR></FENCE>.](/content/vol77/issue6/fulltext/3197/img006.gif)
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n/n < 0) or untwists (i.e., n/n > 0) depending
on whether
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Data collected at the ESRF under steady-state conditions
The analysis described below (see Figs. 1-7) was performed on the average of the individual patterns used for the statistical analysis, also presented below (see Tables 1 and 2).
[1,1,0]-row lines
The [1,1,0]-row line traces at rest and Vo (Fig. 1, A and B) show the well-known myosin layer lines indexing with a repeat of ~43.0 nm and the 5.9- and 5.1-nm actin layer lines. Even though the absolute intensities of the myosin layer lines are lower at Vo than at rest, their relative intensities are much the same. Note also that the 5.9- and 5.1-nm actin layer lines have very similar intensities.
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). The myosin layer lines are weaker than at rest and most of them weaker than at Vo (with the exception of the 3M and
6M, which are comparable). The first myosin layer line (1M-LL) overlaps with the 1A-LL. This overlapping of myosin- and actin-based layer lines
is a recurrent feature throughout the Po trace. Finally, the 5.9- and 5.1-nm actin layer lines are noticeably stronger than at
rest or Vo.
The 1A-LL and the 1M-LL
Background-subtracted x-ray patterns in the region between the first and the third myosin layer line at rest (left) and at Vo (right) are compared in Fig. 2 A. A similar comparison between the patterns at Vo (left) and Po (right) is shown in Fig. 2 B.
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1 and 42.5-43.2 nm
elsewhere (Fig. 2 C, left). The spacing of the 1M-LL for
R > 0.013 nm1 shows an oscillatory
behavior which is due to the slight arching of the diffraction spots.
The 1A-LL at rest has a spacing of ~38.5 nm for R < 0.03 nm1 and 36.0-36.5 nm for larger
R-values. From the values of the spacings one can conclude
that 1) near the meridian the 1M-LL intensity is dominated by the
C-protein periodicity (Rome et al., 1973a), while for R > 0.013 nm1 it is dominated by the first myosin layer
line; and 2) the 1A-LL is dominated by the troponin periodicity (Rome
et al., 1973b) at R < 0.03 nm1 and by
the actin periodicity elsewhere.
The 1M-LL and 1A-LL periodicities at Po as a function of
R are shown in Fig. 2 C, right. The 1M-LL has a
spacing of ~44.5 nm for R < 0.012 nm1
and a value of ~43.5 nm at higher R-values, while the
1A-LL has a spacing of ~38.5 nm for R < 0.035 nm1 and ~37.0 nm at higher R-values. This
shows that, similarly to the situation at rest and Vo, the
1M-LL is dominated by the C-protein periodicity at low
R-values and by the myosin periodicity elsewhere, while at
low R-values the 1A-LL is dominated by the troponin
periodicity and by the actin periodicity at higher R-values.
The main point of interest here is that the spacing of the 1A-LL at
Po is ~37.0 nm, while it is 36.0-36.5 nm at rest and
Vo (Fig. 2 C). In other words, the spacing of
the 1A-LL at Po is 3.2-1.8% longer than at rest or
Vo.
Intensities of the 1A-LL and 1M-LL. Fig.
3 A shows a comparison of the
radial intensities of the 1M-LL and 1A-LL at rest (left) and
at Vo (right). A similar comparison between the
radial intensities at Vo (left) and at
Po (right) is shown in Fig. 3 B.
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1 for both the rest and Vo traces. The most
prominent difference is that the 1A-LL at rest shows some
crystallographic sampling (specially visible in the troponin peak at
~0.026 nm1), which is barely detectable at
Vo.
The 1M-LL and the 1A-LL at Po (Fig. 3 B, right)
show well-defined diffraction maxima at a radial position of ~0.026
nm1. These are due to partly sampled C-protein and
troponin peaks. For values of R > 0.03 nm1, the 1M-LL shows a continuous, unsampled, practically
featureless, intensity distribution, while the 1A-LL has a prominent,
possibly partly sampled, maximum which peaks at R = ~0.046 nm1 (i.e., at approximately the position of the
[1,1,0] equatorial reflection).
The 5.9- and 5.1-nm actin layer lines
Fig. 4 shows [1,1,0]-row line traces in the region of the 5.9- and 5.1-nm actin layer lines. It is apparent from the data that the centers of gravity of the layer lines at Po occur at larger spacings than at rest, which in turn are larger than at Vo. It is also noticeable that the relative spacing change of the 5.1-nm layer line is larger in all cases than that of the 5.9-nm layer line. These observations are ratified by the statistical analysis of the spacing changes in the individual patterns (Tables 1 and 2).
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1 and ~0.06 nm1, respectively. The most
notable features are the absence of any lattice sampling and that the
intensities at rest and Vo are essentially identical, while
the intensity at Po is noticeably higher. The intensity
distributions of both layer lines at Po have their center of gravity shifted toward the meridian relative to those at rest and
Vo.
Regarding the spacings (Fig. 5, B and D) one
finds that because of arching they increase progressively with
increasing R-values. This effect is less pronounced at
Po and, because of it, the spacing of the layer lines at
rest and Vo is the same or greater than that at
Po for values of R > ~0.08
nm1. At rest and Vo the spacing of the 5.9-nm
layer line is significantly larger in the neighborhood of the meridian,
i.e., for R-values <0.02 nm1. This is due to
the presence of meridional reflections with a nonhelical origin (see
Waka-bayashi et al., 1994, who reported similar observations).
However, it is clear that in the region of the [1,1,0]-rowline, i.e.,
for 0.035 nm1 < R < 0.06 nm1, the spacings of the layer lines at Po
are significantly larger than at rest, which in turn are larger than at
Vo.
The 2.7-nm actin layer line
Meridional profiles of the 2.7-nm actin meridional reflection at rest, Vo, and Po are shown in Fig. 6. One can see that the centroid of the reflection at Po corresponds to a larger spacing than at rest, which in turn is larger than that at Vo. These observations are ratified by the statistical analysis of the individual diffraction patterns (Tables 1 and 2).
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0.005 nm1 < R < 0.005 nm1.
Because of the relatively narrow strip used in the integration, one
obtains an axial half-width at rest and Vo which is
comparable to that at Po. Also, the reflections are fairly
symmetric around their centroid. However, as pointed out by Huxley et
al. (1998), if one chooses a wider region of integration (such as that
we had to use for the statistical analysis of the individual patterns, i.e., 0.02 nm1 < R < 0.02 nm1), then the traces at Vo and at rest
display a sharper inner edge due to a combination of arching and/or
broadening of the layer line. This is due to small but inevitable
differences in orientational disorder between the various states. As
shown by the spacing variation of the 5.9- and 5.1-nm layer lines,
layer-line arching tends to overestimate the spacing because with
increasing R-values the centroid moves closer to the origin.
However, Huxley et al. (1998) suggest that an increase of orientational
disorder at Vo moves part of the measured reflection to a
slightly higher z-value and gives it an apparent spacing
decrease. To establish the spacing of the layer lines, it is necessary
to find the spacing dependence with R with as high a
resolution as possible. The extrapolated values at R = 0 nm1 should be the best measure of the spacings. This
analysis proved impossible on the individual patterns, but it could be
carried out on the averaged diffraction patterns. The results are shown in Fig. 7.
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1 the spacing at
Vo is no more than ~0.05% smaller than that at rest,
which in turn is only ~0.15% smaller than at Po. The
conclusion, analogously to the case of the 5.9- and 5.1-nm layer lines,
is that if the spacings are determined from radially integrated
patterns, then because of arching and axial spreading the extent of the spacing differences at rest/Vo relative to Po
and Vo relative to rest tend to be underestimated.
Statistical analysis of actin layer line spacings at rest, Vo and Po
The analysis so far was concerned with averaged diffraction diagrams. However, the relative and absolute spacings for the 1A-LL at rest and Po, the 5.9- and the 5.1-nm actin layer lines, could be determined from the individual patterns from the traces of their [1,1,0]-row lines. The 1A-LL at Vo could not be analyzed this way because of the relative weakness of this layer line and, also, because of the dominant presence of the 1M-LL. However, the spacing of the 1A-LL at Vo can be indirectly derived from those of the 5.9- and 5.1-nm layer lines and used for the statistical analysis. Regarding the 2.7-nm actin meridional the statistical analysis could be done for radially integrated patterns in the region0.02 < R < 0.02 nm1. The results
of this analysis are given in Tables 1 and 2.
The values given in Tables 1 and 2 are statistically precise, as seen
from the relatively small standard deviations. However, because of
different amounts of layer-line arching and/or axial broadening, the
values in the tables are subject to systematic errors. The analysis
presented in the preceding sections show that arching effects are more
pronounced at Vo than at rest, and in both cases more
pronounced than at Po. Therefore, the values quoted in
Tables 1 and 2 for rest and Vo relative to those at Po are likely to be systematically underestimated because
of the width used in the radial integration.
A measure of the magnitude of the underestimate can be arrived at by
extrapolating the layer-line spacings shown in Fig. 5, B and
D, and 7 D toward the meridian. For example, the
values quoted for the 2.7-nm meridional reflection in Table 1 can only be compared with those in Fig. 7 by taking their intensity weighted average. When this is done the values in Table 1 and Fig. 7 coincide within error. However, one can estimate by extrapolation toward the
meridian of the values in Fig. 7 that the spacing at Vo may be ~0.17% smaller than at rest (as opposed to the ~0.13% obtained in Table 2).
In summary, we conclude that the data in Tables 1 and 2 reflect a
minimal difference in the spacing changes undergone by the various
actin layer lines. Despite this, and for the purpose of the discussion
that follows, we will use the data in Tables 1 and 2.
Time-resolved data collected at the SRS
Relative to rest and Vo, the intensity increase at Po of the 5.1- and 2.7-nm layer lines is somewhat larger (~×2.0 and ×2.4, respectively) than that of the 5.9-nm layer line (~×1.6; Fig. 8). During unloaded shortening, the intensities practically return to rest values. The spacing changes (Fig. 9) confirm an increase during Po and a decrease to values smaller than at rest during Vo. The time courses of the spacings and intensities of the 5.9- and 5.1-nm layer lines are similar to that of the tension development/redevelopment. The intensity, but not the spacing, increase of the 2.7-nm reflection may lead tension. The spacing and intensity changes occur simultaneously with the tension drop during the initial quick release.
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The data collection method used at the SRS (see Materials and Methods) results in less reliable absolute and, to a lesser extent, relative values of the spacings than those obtained at the ESRF. Nevertheless, the SRS data (Fig. 9) show that the spacing change in the 5.1- and 2.7-nm layer lines is larger than that of the 5.9-nm layer line. The ESRF data were collected for 20 ms after tension had reached zero (see Materials and Methods). Taking the mean value of the spacing percentage change during this period of time for the SRS data, one obtains relative spacing changes between Po and Vo of 0.35-0.4, 0.55-0.65, and 0.45-0.5% for the 5.9-, 5.1-, and 2.7-nm layer line, respectively. These values are not significantly different from those found in the ESRF data. However, during the quick release the relative spacing changes seem somewhat larger, and afterward there is a tendency (especially noticeable in the case of the 5.9 and 2.7) for the spacings to return to rest values. If these observations are confirmed one would have to conclude that the magnitude of filament extensibility is largest during the quick release and somewhat greater than that obtained from the time-averaged ESRF data.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Layer-line intensities at rest, Vo, and Po
The behavior of the actin and myosin layer lines corroborates that very few heads form an actomyosin (AM) complex at Vo
Martin-Fernandez et al. (1994) concluded from meridional data that
at Vo very few, if any, of the myosin heads form an AM complex. This conclusion is reinforced here because 1) the intensities of the 5.9-, 5.1, and 2.7-nm layer lines are much the same as at rest
(Figs. 5 and 8); 2) the actin-based layer lines characteristic of the
Po state are absent (Figs. 1 and 2); and 3) the myosin layer lines return and show relative intensities very similar to those
at rest (Fig. 1). Note that differences in absolute intensities can be
simply explained by different degrees of crystalline order. Also, if
allowance is made for sampling differences in the first myosin layer
line at rest and Vo, it is clear that the centroid of the
underlying Bessel term occurs at about the same radial position (Fig.
3). This implies that the average disposition of the myosin heads is
much the same in these two states.
The first actin and myosin layer lines suggest that there are two populations of heads at Po
The diffracted intensities depend on the fraction of heads in any given state and on the molecular transform of the average head. Assuming that differences in the molecular transform are not dominant at our relatively low resolution (an unproven assumption, but often made, for example, when comparing Po and rigor data), it is possible to estimate the fraction of heads in a given state from the intensities of the first myosin and actin layer lines. At Po there is substantial intensity in both the actin and the myosin layer lines (Figs. 1-3). Therefore, either there are two populations of myosin heads or a part of the mass of each head diffracts with actin and another part with myosin periodicities. The second explanation is unlikely, although it cannot be totally ruled out, because in general one would expect only one axially broad layer line with a spacing somewhere in between that of actin and myosin. The fact that we observe two separate layer lines tends to favor the first explanation. Even neglecting molecular transform effects, intensity comparisons between Po and rest are fruitless because of the much higher degree of crystallographic order in the latter. However, the degree of sampling at Vo is much less pronounced and comparable to that at Po (Fig. 2). Because of this, intensity comparisons between these two states are more significant. In the region where the contributions from C-protein and troponin are negligible (i.e., for R > 0.035 nm1;
Fig. 2) the integrated intensity of the myosin layer line at Po is ~1/4 of that at Vo (Fig. 3). The
square root of this ratio provides a measure of the fraction of myosin
heads leaving the myosin periodicity during the transition from
Vo to Po (i.e., ~50%). The square root of
the intensity increase
relative to Voof the actin layer
line at Po depends on the fraction of myosin heads that go
to form an AM complex. This value is also ~1/4 of that of the
integrated intensity in the first myosin layer line at Vo. So, ~50% of the myosin heads may acquire actin-based periodicities at Po. Because we have neglected molecular transform
effects, there may be significant errors in this deduction; however, it is unlikely that the simultaneous presence of a myosin- and actin-based layer line at Po, both with similar intensities overall
(Fig. 1), can be explained if the fraction of myosin heads forming an AM at Po was lower than, say, 30% or greater than, say,
70%. In the first case the actin layer line would be expected to be
~
of that of myosin, and ~5 times stronger in the second
case. Note that a 1:1 ratio between detachedor unspecifically
attachedheads and those forming an AM complex at least partly
explains why the movement of the leading edge of the 5.9- and 5.1-nm
layer lines toward the meridian is not as pronounced in the
rest/Vo to Po transition as it is in the
transition from rest to rigor (unpublished data). Because the intensity
profile of the first myosin layer line bears no resemblance to that at
rest or Vo, it may be concluded that the fraction of heads
not forming a specific AM complex has a very different configuration.
It is not yet possible to cleanly strip out the contributions of
C-protein and troponin to the first myosin and actin layer lines (Fig.
2). Therefore, the main current value of their detection is to show
that they must be considered in any attempt to analyze the layer-line
intensities. In fact, the co-existence of a troponin and actin layer
line may be the reason why in the electron microscopy study of Lenart
et al. (1996) it appeared as if the first actin layer line had a longer
spacing in the early stages of contraction than during the steady
state. Indeed, one would expect the troponin layer line to dominate in
the early stages of contraction, when the filament is activated but the
AM complex has not yet had time to fully form.
Layer-line spacings at rest, Vo, and Po
The actin filament extends during the transition from rest to Po and shortens by a greater amount from Po to Vo
Spacing changes must be interpreted as due to average changes in whatever periodic structures are responsible for their presence. Therefore, it is conceivable that some parts of the filaments and/or some filaments change their length by different amounts. With this qualification, it is clear that the average length of the actin filaments increases during isometric contraction and that at Vo decreases to a value smaller than at rest. The data reveal that relative to the mean rest length this elongation comes to at least 0.3 ± 0.1% when deduced from the 5.9- and 5.1-nm reflections, and to 0.29 ± 0.04% when measured directly from the 2.7-nm actin meridional reflection. These values are essentially those reported by Wakabayashi et al. (1994) and Huxley et al. (1994).
As deduced from the traces of the 5.9- and 5.1-nm reflections the axial
rise of the actin monomers at Vo becomes smaller by at
least 0.52 ± 0.1% relative to the mean value at Po,
or 0.22 ± 0.10% smaller than the mean value at rest. Similarly,
direct measurement of the 2.7-nm meridional reflection shows that the axial rise of the actin monomers becomes smaller by at least 0.42 ± 0.03% relative to the mean value at Po, or by 0.13 ± 0.03% relative to the mean value at rest (Table 2). Thus a minimum
change of 0.42% in the axial rise of the actin monomer between
Po and Vo takes place.
The SRS results (Fig. 9) confirm that in the release maneuver, the
spacings of the 2.7-nm actin meridional and those of the 5.9- and
5.1-nm actin layer lines decrease below their rest values by similar
amounts. In addition, the SRS data suggest that the length change might
be larger during the fast release.
The actin filament changes its helical symmetry during contraction
The analysis of the 1A-LL shows that at Po its spacing is ~37.0 nm, while it is only 36.0-36.5 nm at rest and Vo (Fig. 2 and Table 1). This difference of 3.2-1.8% is substantially larger than the 0.42% difference in the spacing of the 2.7 nm between Vo and Po, and the 0.29% difference between rest and Po (Table 2). This cannot be explained in terms of elongation (see formulas in Materials and Methods), and we conclude that, in addition, the actin filament must change its helical symmetry during contraction. The above can be quantified from the spacings of the 5.9- and 5.1-nm layer lines. The data in Tables 1 and 2 show that the fractional spacing change in the 5.1-nm layer line is consistently larger than that in the 5.9-nm layer line. This amounts to at least 0.09 ± 0.04% during the transition from rest to Po and to0.32 ± 0.08% from Po to Vo. Thus, the
5.1-nm layer line has a larger increase/decrease than the 5.9-nm layer
line, which is statistically significant and, therefore, one can
conclude that in the transition from rest to Po the actin
filament elongates relative to the rest state and changes its symmetry
by untwisting, while in the release the filament shortens and becomes
more twisted than both at Po and at rest. Application of
the formulas in Materials and Methods yields values for
n/n of 0.0059 ± 0.0026 and 0.0212 ± 0.0053 corresponding to the transitions rest-Po and
Po-Vo, respectively.
The spacing of the 1A-LL derived from those of the 5.9- and
5.1-nm layer lines (see Materials and Methods) are ~36.9, ~36.6, and ~36.0 nm at Po, rest, and Vo,
respectively. These are in agreement with the direct measurements of
the spacings of the 1A-LL of the averaged patterns and with the
statistical analysis of the individual patterns (Fig. 2 and Table 1).
Because of the untwisting, the spacings of the various actin layer
lines at Po fit, within error, with those of a 54/25 helix (i.e., 54 actin subunits in 25 turns of a left-handed genetic helix of
5.9-nm pitch). As actin occupies the trigonal positions in the
hexagonal arrangement of myosin filaments, a 54/25 actin helix has the
symmetry appropriate for the presentation of actin binding sites to the
myosin heads in each of the three thick filaments surrounding each
actin filament. This suggests that the strain resulting from binding of
the myosin heads forces the thin filament to acquire a more untwisted
symmetry than that of the rest or the activated, but unstrained, filament.
In summary, within the error of the respective measurements one
can estimate that the long actin helix changes its pitch from ~73.0
nm at rest (i.e., ~36.5 × 2 nm) to ~74.0 nm (i.e.,
~37.0 × 2 nm) at Po, while it reduces to ~72.0 nm
(i.e., ~36.0 × 2 nm) at Vo. Considering that
n/n = 
/, where is the helical
rotation per actin monomer, then with a 54/25 helix at Po
one deduces that the untwisting from rest to Po amounts to
0.98 ± 0.43° per actin monomer and that it twists by
3.53 ± 0.83° during the transition from Po to
Vo.
Effects due to activation processes
If there is a negligible fraction of attached heads at Vo (Martin-Fernandez et al., 1994, and Discussion above),
the structural state of actin should be comparable to that during
stimulation at non-overlap or during the early stages of contraction
when heads have not yet attached. Therefore, it can be concluded that the shortening and twisting of the helical structure of the actin filament relative to its rest state are due to activation. This conclusion is supported by two independent lines of evidence: 1) Huxley
et al. (1996) recorded a small decrease in the spacing of the 2.7-nm
axial repeat during the early activation phase of contraction; 2) in
experiments with muscles stimulated at non-overlap lengths, Wakabayashi
et al. (1994) observed spacing decreases of ~0.1%, 0.22%, and
0.04% in the 2.7-, 5.1-, and 5.9-nm actin layer lines, respectively,
and suggested that the actin filament shortens and twists under
conditions where it cannot interact with myosin heads.
Effects due to strain induced by attachment of myosin heads
The actin filament at Po is at its most untwisted and longest. We suggest that this is due to the strain induced on the actin filament by the attachment of the myosin heads. Two lines of evidence support this view: 1) the time-resolved experiments show that during the transition from rest to Po the spacing increase of the 2.7-, 5.1-, and 5.9-nm layer lines follows the same time course as tension rise; and 2) at Po there is an AM complex formed (Figs. 1 and 2). Reinforcing this interpretation there are the results of Wakabayashi et al. (1994) who, in experiments with muscles stimulated at full and half-overlap, observed spacing increases of
~0.25%, 0.25%, and 0.21%; and 0.15%, 0.23%, and 0.11% in the 2.7-, 5.1-, and 5.9-nm actin layer lines, respectively. Accordingly, they suggested that during the transition from rest to Po
the actin filament lengthens and untwists to an extent that depends on overlap.
Thin-filament compliance from activation to isometric contraction
A sarcomere length of ~2.3 µm and actin and myosin filament lengths of 1 µm and 0.8 µm, respectively, result in an overlap length of 0.65 µm. Therefore, the 0.42 ± 0.03% thin-filament extensibility at Po relative to the activated, but unstrained, filament at Vo indicates that in these conditions the compliance of the thin filament is 0.646 ± 0.046% per Po (i.e., (0.42 ± 0.03) · 1.0/0.65%). Most models of contraction assume that there is no filament compliance.| |
FOOTNOTES |
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Received for publication 10 September 1998 and in final form 19 August 1999.
Address reprint requests to Dr. Joan Bordas, LLS-IFAE, Edifici Ciencies Nord, Campus UAB, E-08193 Bellaterra, Barcelona, Spain. Tel.: 34-93-581-30-76; Fax: 34-93-581-32-13; E-mail: jbordas{at}ifae.es.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Biophys J, December 1999, p. 3197-3207, Vol. 77, No. 6
© 1999 by the Biophysical Society 0006-3495/99/12/3197/11 $2.00
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