Axial Dispositions and Conformations of Myosin Crossbridges Along Thick Filaments in Relaxed and Contracting States of Vertebrate Striated Muscles by X-ray Fiber Diffraction

doi:10.1016/j.jmb.2006.12.036

J. Mol. Biol. (2007) 367, 275–301

Axial Dispositions and Conformations of Myosin Crossbridges Along Thick Filaments in Relaxed and Contracting States of Vertebrate Striated Muscles by X-ray Fiber Diffraction Kanji Oshima 1 , Yasunori Takezawa 1 , Yasunobu Sugimoto 1 Takakazu Kobayashi 2 , Thomas C. Irving 3 and Katsuzo Wakabayashi 1 ⁎ 1

Division of Biophysical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan 2

Department of Electronic Engineering, Shibaura Institute of Technology, Koto-ku, Tokyo 135-8543, Japan 3

BioCAT and CSRRI, Department of Biological, Chemical and Physical Sciences, Illinois Institute of Technology, Chicago, IL 60616, USA

X-ray diffraction patterns from live vertebrate striated muscles were analyzed to elucidate the detailed structural models of the myosin crown arrangement and the axial disposition of two-headed myosin crossbridges along the thick filaments in the relaxed and contracting states. The modeling studies were based upon the previous notion that individual myosin filaments had a mixed structure with two regions, a “regular” and a “perturbed”. In the relaxed state the distributions and sizes of the regular and perturbed regions on myosin filaments, each having its own axial periodicity for the arrangement of crossbridge crowns within the basic period, were similar to those reported previously. A new finding was that in the contracting state, this mixed structure was maintained but the length of each region, the periodicities of the crowns and the axial disposition of two heads of a crossbridge were altered. The perturbed regions of the crossbridge repeat shifted towards the Z-bands in the sarcomere without changing the lengths found in the relaxed state, but in which the intervals between three successive crowns within the basic period became closer to the regular 14.5-nm repeat in the contracting state. In high resolution modeling for a myosin head, the two heads of a crossbridge were axially tilted in opposite directions along the three-fold helical tracks of myosin filaments and their axial orientations were different from each other in perturbed and regular regions in both states. Under relaxing conditions, one head of a double-headed crossbridge pair appeared to be in close proximity to another head in a pair at the adjacent crown level in the axial direction in the regular region. In the perturbed region this contact between heads occurred only on the narrower inter-crown levels. During contraction, one head of a crossbridge oriented more perpendicular to the fiber axis and the partner head flared axially. Several factors that significantly influence the intensities of the myosin based-meridional reflections and their relative contributions are discussed. © 2006 Elsevier Ltd. All rights reserved.

*Corresponding author

Keywords: conformation of myosin crossbridge; thick myosin filament; muscle contraction; X-ray fiber diffraction; synchrotron radiation

Introduction

E-mail address of the corresponding author: [email protected]

Energy transduction in muscle contraction is carried out by the interaction between thin actincontaining filament and thick myosin-containing filament using the free energy delivered by the

0022-2836/$ - see front matter © 2006 Elsevier Ltd. All rights reserved.

276 hydrolysis of ATP. Structural changes of both filaments in contracting muscle are thought to couple to one another and to participate directly in the force generation mechanism. Knowledge of the basic structures of both filaments is indispensable for understanding the dynamic, molecular changes of contractile proteins underlying muscle contraction. Detailed, atomic-resolution, structural models of thin actin filaments incorporating the troponin– tropomyosin complex have been proposed on the basis of three-dimensional reconstruction of electron micrographs1,2 and X-ray fiber diffraction.3–5 However, far less is known about the precise structure of myosin filaments of vertebrate skeletal muscle because of its inherent complexity, although detailed structural analyses of fish muscle thick filaments have been presented very recently.6 In the thick filament, the long α-helical tails of myosin molecules self-assemble to form a filament backbone, from which the globular myosin heads protrude. The vertebrate thick filament has a threestranded structure in which each of the three strands consists of nine pairs of myosin heads per helical turn of ∼129 nm-pitch with an axial rise of ∼14.3 nm forming a 9/1 helix.7–9 Because of the three-start arrangement, the thick filament has a crystallographic period for every three axial rises (42.9 nm = 14.3 nm × 3), where the planes with a 14.3 nm axial repeat (often referred to as crowns) are rotated by 40° around the filament axis to go to the next crown level along the helix. The basic period is 43.5 nm (14.5 nm × 3) in the contracting state. In the relaxed state of vertebrate skeletal muscle, there are numerous layer-line reflections arising from thick filaments with the above-mentioned structure, occurring at different axial spacings from the thin actin filaments in the X-ray diffraction diagrams. 11,12 Various investigators have attempted to analyze the intensity distributions of these myosin reflections in order to elucidate the structures of the two-headed crossbridges in relaxed and isometrically contracting states of live skeletal muscles.6,13–17 There is a series of reflections indexing on the basic period of 42.9 nm observed on the meridian in the resting Xray diffraction pattern,11,12 indicating that there are significant departures from the regular symmetry; the so-called forbidden meridional reflections on the layer-lines such as 1, 2, 4, 5, 7 etc. of the basic period that are introduced by the presence of a systematic perturbation of the three successive crown repeats within the basic period,18,19 not by variations in the sizes or shapes of myosin crowns themselves.14 Such a perturbation does not occur on the myosin filaments of insect flight muscle or other invertebrate muscles. In addition, the thick filaments emanate from either side of the so-called M-line with opposite polarities in the sarcomere. In the region where the 1 μm long thin filaments emanating from the Z-bands overlap with half of the 1.6 μm long thick filaments, the two kinds of filaments are packed in a hexagonal array of a superlattice form.11,20 Thus, these myosin-based

Myosin Filaments in Vertebrate Skeletal Muscle

reflections are sampled partially but strongly in the radial direction by the interference function due to the hexagonal filament array and sampled also in the axial direction by the mirror-image structure of myosin filaments across the M-line.21,22 During contraction, the forbidden meridional reflections as well as most of the myosin-based layer-lines are much less intense but the meridional reflections indexing as multiples of three times the basic period remain with strong intensity and still show axial interference sampling. Recently, the intensity and spacing changes of the axial interference fringes of the 14.5 nm meridional reflection during a rapid length perturbation applied to contracting muscle fibers have been a matter of considerable interest, because analysis of them has enabled us to probe the conformational changes of a myosin crossbridge that are associated with the force generation at atomic-scale resolution. 23–26 Very recently, perplexing intensity behaviors of the myosin-based meridional reflections upon the application of rapid length perturbation to contracting whole muscle have been reported.27,28 As has been discussed,7,10,29–31 the difficulty in interpreting these data is that the intensities of myosin meridional reflections are determined by multiple factors, including interference between the two heads of an individual crossbridge, interference between the diffraction from the crossbridge projecting from the backbone and that from structures within the backbone itself, as well as the changing interference by the mirror image structure of the thick filaments across the M-line. We have no clear information on the relative importance of these various contributions that would allow unambiguous reconstruction of the axial mass projection of the myosin crossbridges onto the fiber axis. Thus it is not possible, in a straightforward way, to interpret their intensity changes solely in terms of the crossbridge conformation. Furthermore, the intensities of the meridional reflections are affected by changes in lateral coherence between myofilaments. In addition, skeletal muscle myosin filaments contain accessory proteins such as C-protein, connectin/titin among others and these accessory proteins are bound to the filament backbone with periodicities very similar to that of the myosin filaments.7,32 For these reasons, precise modeling of the filament structure has not been easy to do and the periodicity of the myosin crowns, the axial disposition of two-headed crossbridges and their structure remain to be elucidated in detail. Malinchik and Lednev introduced the concept that the vertebrate myosin filament has a mixed structure, with two different periodicities of the crossbridge arrangement in order to explain the presence of forbidden meridional reflections. 14 Here, we report the results of much detailed modeling studies, using their model as a starting point, aimed at elucidating the axial dispositions and conformations of two-headed myosin crossbridges projecting from the thick filament backbone by simulating the intensities of myosin-based meridional reflections

Myosin Filaments in Vertebrate Skeletal Muscle

in high angular resolution X-ray diffraction patterns from relaxed and isometrically contracting frog skeletal muscles. The meridional reflections from C-protein and/or connectin/titin could be separated from the myosin-based reflections and were not included in the analysis. In modeling, we used an incremental approach, first fitting our model to the axially integrated intensities and then fitting it to the axial intensity profiles of the myosin meridional reflections. Finally, the structure of the myosin crossbridges on the thick filaments was elucidated to sub-nanometer resolution using the protein crystallographic data for myosin heads. For the resting crossbridge structure, the off-meridional layer-line intensities, free of lattice sampling effects, were also included in the simulations. On the basis of our structural models, we explore mechanisms of inhibition of actomyosin interaction in the resting state, and conformational changes of myosin crossbridges and the performance of a double-headed crossbridge during an isometric contraction. We examined closely which structural parameters dominate in potentially affecting the calculated intensities of myosin meridional reflections. These studies represent a substantial improvement over the modeling studies that we reported previously in preliminary form,29,30 providing structural information required for the interpretation of dynamic X-ray data taken during muscle contraction.

Results Myosin-based X-ray diffraction patterns in the relaxed and contracting states Figure 1(a) and (b) show a comparison of X-ray diffraction patterns from relaxed and isometrically contracting frog skeletal muscles with their meridional axes coincident. The X-ray diffraction pattern in the relaxed state shows a strong series of myosinbased layer-lines that index on a crystallographic period of 42.9 nm (denoted by the letter M), separated, for the most part, from the other reflections. The dominant feature of the myosin layer-line pattern is a ladder-like appearance that may be attributed to the perturbed helical structure of the three-stranded myosin filaments with differing crossbridge crown repeats within the crystallographic period (see Materials and Methods). During an isometric contraction, these myosin layer-lines became much weaker, but meridional reflections whose orders are multiples of three (3M) retained strong intensities on the meridian in spite of the fact that the myosin projections swung towards the neighboring thin actin filaments, which are located at the trigonal positions in the hexagonal array of the A-band in the sarcomere to interact with actin. In order to elucidate the structures of the myosin crossbridges projecting from the thick myosin filament backbones in the relaxed and isometrically contracting states, we have analyzed the myosin-

277 based meridional reflections from live frog skeletal muscles in both states. As seen in the X-ray diffraction patterns (Figure 1), a series of meridional reflections with the 42.9 nm period was observed in the relaxed state, and a similar series of merdional reflections was still observed but now with an increased period of 43.5 nm in the isometrically contracting state. The meridional reflections on the layer-lines except for those at spacings of 3n/ 43.5 nm−1 (n, integers) should be forbidden11,12 from the idealized filament structure with a 3-fold rotation axis and a 9/1 helical symmetry. As noted above, the appearance of forbidden reflections has been interpreted as due to a systematic perturbation of the myosin crown repeats from the regular 14.3 nm distance in the relaxed state within the crystallographic period. 18, 19 All myosin-based reflections were sampled partially but strongly in the radial direction by the superlattice form of the hexagonal filament array.20 In addition, these meridional reflections, which are crystalline reflections, were sampled axially by interference between the two symmetrical halves of the myosin filaments across the M-line in the sarcomere.12,21,22 Furthermore, the meridional X-ray patterns included the diffraction from accessory proteins, particularly from C-protein, connectin/titin and other components that are bound to thick filament backbones with closely similar periodicities.7 In high angular resolution X-ray patterns (Figure 1(b)), we were able, for the most part, to account for and remove the contributions of C-protein (and possibly connectin/ titin) from the intensities of myosin-based meridional reflections by separating the intensity profiles by the Gaussian deconvolution method (see Materials and Methods),33 since the periodicities of these myosin-binding proteins are slightly longer than the myosin periodicity (Table 1).19,21 It was still difficult, however, to assign the first-order myosin meridional reflection at 1/43.02 nm−1 (M1) because it sat at the foot of the peak of the first-order C-protein reflection at ∼1/44.0 nm−1 (C1) in the relaxed state (Figure 2(a)) and the profiles shifted towards the low-angle side during contraction (Figure 2(b)). Since both M1 and C1 reflections were axially sampled, it was hard to separate the M1 intensity profile from the intensity profile of the C1 reflection. An additional complication is that the region of these reflections was influenced by the form factor of the thick filament having a finite length (see Materials and Methods). For these reasons, we did not use the intensity of the M1 reflection in the analysis. The intensity of the M1 reflection, however, was predicted to be weaker than that of the M2 reflection in both states, as observed. The spacings and intensities of the observed meridional reflections are summarized in Table 1. The forbidden meridional reflections in the transition of muscle to an isometric contraction We measured intensities in a narrow range of reciprocal space close to the meridian to produce

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Myosin Filaments in Vertebrate Skeletal Muscle

Figure 1. (a) X-ray diffraction patterns in the relaxed and contracting states of frog skeletal muscles taken at the Photon Factory. The background intensity was subtracted. The left side is the relaxed state and the right side is the contracting state with the meridional axis coincident. The fiber axis is vertical. M1 to M11 denote the first to the 11th-order myosin-based reflections with a crystallographic period of 42.9 nm (the relaxed state) or 43.5 nm (the contracting state). The values in parentheses are axial spacings in real space. M, the meridional axis and E, the equatorial axis. (b) High angular resolution X-ray diffraction patterns in the relaxed (left side) and contracting (right side) states taken at the Advanced Photon Source. In the very low-angle region in (b) (with much reduced background) the sampling pattern due to the sarcomere repeat faded away in both states.76 M1 to M6 denote the first to the sixth-order myosin-based meridional reflections with a basic period of 42.9 nm or 43.5 nm. C1 to C5 denote the first to the fifth-order C-protein-based meridional reflections. (c) Axial intensity distributions of the meridional reflections in the relaxed (red) and contracting states (blue). Axial profiles of a series of meridional reflections are finely sampled by interference between the crossbridge arrays on two symmetrical halves of the thick filament across the M-line in the sarcomere.

279

Myosin Filaments in Vertebrate Skeletal Muscle Table 1. Spacings and relative intensities of the thick filament-based meridional reflections Spacings (nm)

Relative intensities

Order

Rest

Contraction

Rest

Contraction

M1/C1

46.69 44.46

0.30 1.00

C2 C2 C2 M2 M2 C3 C3 M3 M3 M3 C4 C4 C4 M4 M4 C5 C5 M5 M5 M5 M6 M6 M7 M8 M8 M8 M9 M9 M9 M10 M10 M11 M11 M11

23.93 23.17 22.27 21.54 21.00 15.42 15.04 14.59 14.36 14.14 11.22 11.02

47.52 44.67 42.87 24.27 23.49 22.71 21.96 21.51

0.33 1.00 0.25 0.41 0.51 0.51 0.32 1.00

10.84 10.68 9.13 9.02 8.68 8.59 8.49 7.20 7.14 6.15 5.40 5.35 5.31 4.80 4.29 3.92 3.90 3.87

14.64 14.44 11.34 11.16 11.01

8.71 7.31 7.25 5.44 4.87 4.84 4.81 4.38 4.34 3.97 3.95

0.29 0.62 0.72 1.00 0.18 0.56 0.10 0.05 1.00 0.17 0.33 0.44 0.09 1.00 0.36 0.36 0.23 1.00 0.09 1.00 0.49 1.00 0.74 1.00 0.26 1.00 1.00 0.62 1.00 0.51

1.00 0.57 0.17 0.26 1.00

1.00 1.00 0.42 1.00 0.29 1.00 0.34 1.00 0.65 1.00 0.47

The first column identifies the reflections from various structures (C, C-protein; M, myosin) with the order of their basic periods. Because of interference sampling, intensity centered at various diffraction orders appeared as a cluster of peaks. The second and third columns are the spacings of peaks in each cluster in the relaxed state (Rest) and in the contracting state (Contraction), respectively. The fourth and fifth columns are the intensities of peaks in a given cluster relative to the most intense peak, which is taken as unity, in the relaxed (Rest) and contracting states (Contraction), respectively.

axial profiles. The positions and integrated intensities of myosin-based reflections were separated from the other reflections by modeling them as overlapping Gaussian functions. When muscle went from the relaxed to the contracting state, widths of the meridional reflections increased in the radial direction, depending upon the order of reflections, as a result of reduced lateral coherence between myofilaments.21 After a correction for this spreading both in the relaxed and contracting states (see Materials and Methods), the corrected intensities of the reflections except for the M1 reflection (Figure 2) were normalized to the total intensities of all myosin-based reflections measured and shown in Figure 3. At the plateau of isometric tension, the intensities of the 3M reflections increased and the forbidden

reflections, apart from the M4 reflection, became much weaker than at rest but did not disappear. The M2 reflection decreased in intensity at least by a factor of 5 or 7 at the plateau of isometric tension. On the other hand, the intensity of the M4 reflection increased slightly. The lateral width of the forbidden reflections broadened as in the case of 3M reflections. Although uncertainties in exact physiological state may be unavoidable for whole muscles,12,21 we found that this residual intensity was quite apparent in the X-ray diffraction patterns from fresh muscles taken at maximal stimulation in a very short exposure showing little or no significant sign of fatigue (see Materials and Methods). All peaks of the myosin reflections including layer-lines shifted together towards the low-angle side due to an elongation of the thick filaments as a result of activation during contraction.33–35 So it seems that the forbidden meridional reflections do not arise from inactive fibers. This observation suggests strongly that the thick filaments still preserve the perturbed periodicity of the crown levels within the crystallographic period in the force-generating state and that a rearrangement of the myosin crown configuration occurs in the transition of resting muscle to an isometric contraction. The axial interference patterns of the myosin-based meridional reflections in the relaxed and contracting states We first investigated the axial interference patterns of myosin-based meridional reflections in order to understand the interference properties of the thick filament on each side of the M-line in the sarcomere. Figure 4(a) and (b), and (c) and (d) compare the axial intensity profiles of M2 and M5 forbidden reflections in the relaxed and contracting states, respectively, taken from high angular resolution X-ray diffraction patterns (Figure 1(b) and (c)). Figure 4(e) and (f), and (g) and (h) show those of M3 and M6 3M reflections in both states, respectively. The interference peaks on these reflections were separated by the Gaussian deconvolution method.33 The interference separation tended to be longer with increasing the order of reflections, as reported by Juanhuix et al.36 The distances in real space derived from the interference separations of these fine peaks are given in Table 2. The distance measured from the separation between the fine peaks on M2 and M5 reflections was, on average, 820(±40) nm in the relaxed state, and increased to 1010(±40) nm in the contracting state (Table 2). The distance measured from the separation between the fine peaks on M3 and M6 reflections was, on average, 890(±50) nm in the relaxed state and increased to 1010(±40) nm in the contracting state. Thus, the distance derived from the forbidden reflections is different from that from the 3M reflections in the relaxed state but is almost the same in the contracting state. The observation that the distance from the forbidden reflections appeared to be shorter than the center-tocenter distance (∼890 nm) between the crossbridge

280

Myosin Filaments in Vertebrate Skeletal Muscle

Figure 2. Axial intensity distributions around the M1 reflection. (a) The relaxed state and (b) the contracting state. The observed intensity distributions are shown by red dots in (a) and by blue dots in (b), and the calculated distributions from the final models are shown by the continuous curves. The locations of the M1 reflection expected from the observed spacing of the M3 reflection in the relaxed and contracting states are shown by the vertical lines. Note that the peak intensity at Z = 0.0225 nm−1 due to C-proteins in the relaxed state is normalized to 1 and the most intense peak in the calculated intensity clusters of the M1 reflection is normalized to the peak height at Z = 0.0225 nm−1 in the relaxed state and to that at Z = 0.0224 nm−1 in the contracting state.

arrays on the myosin filament at each side of the Mline in the relaxed state suggests that not all of the crossbridges on the myosin filament are axially perturbed. This observation leads to the notion assumed by Malinchik and Lednev 14 that the myosin filament has a mixed structure with two different periodicities of the crossbridge arrangement, i.e., there are both perturbed and regular regions on individual myosin filaments. The differ-

ence in the distance obtained from the forbidden and 3M reflections may also suggest the coexistence of such regions. In the contracting state, the distance derived from the interference separation of the forbidden reflections became larger and was closer to that from the interference separation of the 3M reflections, implying an alteration of the perturbed structure. However, the interference spacings alone do not tell us that the myosin filament has a mixed structure without assuming what the model is set up to prove, because there are many structural parameters contributing to the meridional reflections that need to be considered (see below). Modeling using an incremental approach of the integrated intensity fitting and the intensity profile fitting to the myosin-based meridional reflections

Figure 3. Comparisons of the observed and calculated integrated intensities of the myosin-based meridional reflections from the final models by the incremental fitting of the models first to the integrated intensities and then to the intensity profiles. Experimental intensities of the meridional reflections are shown by red bar graphs in the relaxed state and by blue bar graphs in the contracting state. Calculated intensities from the final models are shown by marks (⊗, relaxed state and ⊕, contracting state). The observed intensities were corrected for lattice disordering effects (see the text). These intensities are normalized so that the sum of the intensities from the M2 to the M11 (second to 11th-order) meridional reflections is identical for the relaxed state and the contracting state. Vertical lines on the bar graphs are standard deviation of the mean from four data. Note that the corrected intensity of the “forbidden” M4 reflection tended to increase during contraction.

In our analysis of the meridional patterns, as a starting point we assumed, following Malinchik and Lednev,14 that the myosin filament has a mixed structure with two different periodicities of the crossbridge arrangement (i.e., both perturbed and regular regions coexist on individual thick filaments, whose projected densities onto the fiber axis have 42.9 nm and 14.3 nm, respectively). This assumption, however, was not made in structural modeling for fish muscle thick filament.6 In order to construct detailed models for the myosin crown arrangement and the axial disposition of myosin heads along the filament backbone in the relaxed and contracting states, both the axially integrated intensities and the axial intensity profiles of myosin-based meridional reflections were analyzed. Firstly, we simulated the integrated intensities of the meridional reflections with onedimensional models (see Materials and Methods). Given the presence of a mixed population of both regular and perturbed regions on the thick filaments, we can make the distance measured from the interference peaks on M2 and M5 reflections res-

Myosin Filaments in Vertebrate Skeletal Muscle

281

Figure 4. Axial intensity distributions of M2 and M5 “forbidden” meridional reflections and M3 and M6 “3M” meridional reflections. (a) and (c) The M2 intensity profiles in the relaxed and contracting states, respectively, and (b) and (d) the M5 intensity profiles in the relaxed and contracting states, respectively. (e) and (g) The M3 intensity profiles in the relaxed and contracting states, respectively, and (f) and (h) the M6 intensity profiles in the relaxed and contracting states, respectively. In (a)–(h), the experimental intensity profiles are denoted by red dots in the relaxed state and by blue dots in the contracting state. The fitting Gaussian functions are shown by continuous curves.

ponsible for the apparent center-to-center distance between the perturbed regions on the myosin filaments across the M-line. The integrated intensities of the meridional reflections from the models set up were calculated by varying the values of all parameters as was done in our preliminary study,30 with the additional constraints that the center-tocenter distance between the perturbed regions should be less than the experimentally determined value because of the displacement produced by sampling steeply sloping intensity curves,28,37 and the intensity of the M1 reflection is required to be smaller than the M2 intensity (see above). We started with a model having regular regions on either side of the perturbed region in a half part of the filaments

as neither the length of the perturbed region nor that of the regular region is known a priori. In our modeling the configurations of myosin crossbridges were assumed to be different in both regions but same in the perturbed region. The most probable values of these parameters were finally determined by minimizing the R-factor of equation (6) in Materials and Methods between calculated and observed M2 to M11 reflection intensities. They are given in Table 3 together with our previous results. As shown in Table 3, we thus confirmed that the myosin filament has a mixed structure consisting of perturbed and regular regions in the relaxed state, as proposed by Malinchik and Lednev,14 and that this mixed structure persists even in the contracting state.

282

Myosin Filaments in Vertebrate Skeletal Muscle

Table 2. The distances measured from the interference separations on M2 and M5 reflections (left) and those from M3 and M6 reflections (right) Distance (nm) Order

Relaxed state

Contracting state

M2 M5 Average

840 ± 30 (n = 4) 790 ± 20 (n = 3) 820 ± 40 (n = 7)

1010 ± 40 (n = 3) 1010 ± 40 (n = 3)

M3 M6 Average

930 ± 20 (n = 4) 840 ± 20 (n = 4) 890 ± 50 (n = 8)

1040 ± 30 (n = 4) 980 ± 10 (n = 4) 1010 ± 40 (n = 8)

The first column identifies the reflections. The second and third columns show the distances (mean ± SD and n, the number of fibers) in the relaxed and contracting states, respectively. The distances are measured from the separation between fine sampling peaks on these reflections.

Next, we adopted the parameter sets for all models that yielded R-factors up to ∼5% larger than the minimal R-factor obtained using the above fitting approach as acceptable windows for calculating the axial intensity profiles of the meridional reflections. For this fitting procedure, we adjusted these parameters so as to obtain improved fits between the calculated and observed intensity profiles of the M2 to the M6 (second to sixth order) meridional reflections by minimizing the Rpr-factor of equation (7) in Materials and Methods. The models with the best fit to the observed intensity profiles yielded a different projected density of a crossbridge onto the fiber axis in each of the regular and perturbed regions in each of the relaxed and

contracting states. The minimal Rpr value was ∼0.52 in the relaxed model and it was ∼0.51 in the contracting model. The best-fit parameter sets are given in Table 3. Furthermore, in order to derive a more detailed structure of a myosin crossbridge to sub-nanometer resolution, we introduced the crystallographic model38 of a myosin subfragment 1 (S1). Here, we used an approximated atomic model for a myosin crossbridge to reproduce the obtained density distributions of two-headed crossbridges, which were previously expressed by two Gaussian functions in integrated fitting. In the calculation, the mass projection of head pairs was calculated with the 68-sphere model for an S1 crystal structure of chicken skeletal muscle myosin, similar to what was done in insect flight muscle modeling by Al-Khayat et al.,39 (see Figure 12(a) in Materials and Methods). Finally, we recalculated the intensity profiles of the meridional reflections using the 68-sphere model of a myosin head so obtained and refined the axial configuration of a myosin crossbridge. We refer to such a refined model in this incremental approach as the final model. We selected the parameter set of a model giving the minimum value of the Rpr-factor by taking into consideration the above-mentioned additional constraints. Figure 5 shows the axial intensity distributions from the M2 to the M6 reflections in the final models in the relaxed and contracting states in comparison with the observed values. The minimal Rpr value was ∼0.45 in the relaxed model and it was ∼0.38 in the contracting model, both being lower than the respective values obtained using the Gaussian models in integrated fitting described above. Almost

Table 3. Parameters used to define the structure of a myosin crossbridge on the thick filament in the modelling calculation Best model (previous) Parameter Width, ar (nm) Width, br (nm) Distance between heads, dr (nm) Width, ap (nm) Width, bp (nm) Distance between heads, dp (nm) Deviation from the regular repeat, δ1 (nm) Deviation from the regular repeat, δ2 (nm) Number of crowns in the inner region, l Number of crowns in the perturbed region, 3k Total number of crowns, Nc

Best model (intensity)

Best model (profile)

Range

Rest

Contraction

Rest

Contraction

Rest

Contraction

5 ≤ ar ≤ 18 5 ≤ br ≤ 18 0 ≤ dr ≤ 18 5 ≤ ap ≤ 18 5 ≤ bp ≤ 18 0 ≤ dp ≤ 18 −5 ≤ δ1 ≤ 5 −5 ≤ δ2 ≤ 5 0 ≤ l ≤ 51 12 ≤ 3k ≤ 51 49 ≤ Nc ≤ 51

6.0 5.0 5.0 15.0 5.0 5.0 −1.0 2.0 4 39 49

5.0 5.0 5.0 8.0 5.0 2.0 −1.0 0.0 11 33 49

6.0 5.0 5.0 12.0 5.0 4.0 −2.0 1.0 1 36 49

8.0 5.0 4.0 5.0 12.0 6.0 1.0 −1.0 14 18 50

9.8 6.1 6.3 5.0 9.9 4.5 −0.6 2.9 0 36 51

5.0 5.0 4.1 6.0 18.0 6.5 0.5 −0.7 7 36 50

The first column denotes the parameters used in the modeling calculation where subscripts r and p of parameters correspond to those of the regular and perturbed regions, respectively. The second column shows the ranges over which the parameters were allowed to vary in the calculation. The third and fourth columns present the values of parameters for the best models in the relaxed and contracting states in the previous calculation by Oshima et al.30 The fifth and sixth columns present the values of the best models in both states in the present calculations by fitting to the integrated intensities. The value of the Rpr-factor was 0.96 in the relaxed state and 0.98 in the contracting state. The seventh and eighth columns present the best-fit values for the parameters for both states in the present calculation by incrementally fitting first to the integrated intensities and then to the intensity profiles. The value of the Rpr-factor was 0.52 in the relaxed state and 0.51 in the contracting states. Nc is the total number of crowns in a half thick filament and given by Nc = l + 3k + m. Note that the models obtained by integrated intensity fitting are very similar to our previous models for the relaxed state but differ markedly from those for the contracting state. Nc was 51 in the relaxed state and 50 in the contracting state. Although Nc must be the same value in both relaxed and contracting models, it was chosen to be 51 (an integer multiple of three) in the relaxed model for the brevity of calculation of the layer-line intensities.

Myosin Filaments in Vertebrate Skeletal Muscle

283

Figure 5. Comparisons of the observed axial intensity profiles of the M2 to the M6 (second to sixth order) meridional reflections and the calculated profiles from the final models. (a) and (f), (b) and (g), (c) and (h), (d) and (i), (e) and (j) show M2, M3, M4, M5 and M6 reflections in the relaxed and contracting states, respectively. In (a)–(j), the experimental intensity distributions are shown by red dots in the relaxed state and by blue dots in the contracting state and the calculated ones are shown by the continuous curves.

all calculated profiles of the meridional reflections showed a good agreement with the observed profiles except for the M6 reflection in both states. In the contracting state, the peaks of the meridional reflections moved towards the low-angle side in Figure 5 due to ∼1.6% elongation of the thick filaments. The agreement between the calculated and observed profiles of the M6 reflection was poor,

in spite of the fact that its integrated intensity calculated from the final models yielded a good fit to that observed in both states (see Figure 3); the height of the two peaks was the reverse of what was seen experimentally and their peaks shifted more towards the low-angle side than did the observed peak positions. Presumably, some additional modifying factors such as interference between structures

284 within the backbone and the crossbridges might be involved in the M6 reflection. This is consistent with the suggestion by Huxley et al., that the bulk of the intensity of the M6 reflection must include strong contributions from some fixed components within the backbone in addition to the myosin heads.24,28,40 Note that, in the present model, the myosin filament backbone was approximated by a uniform cylinder with a length of 1.46 μm and the contribution from such a structureless backbone appears only in the low-angle region around the C1/M1 reflections modifying the intensity distribution there (Figure 2). The intensity profile and integrated intensity of the M4 reflection were similar to those observed in both states, although the axial profile shifted towards the lower-angle side in the relaxed state and towards the higher-angle side in the contracting state than did the observed profiles. Comparisons between the observed integrated intensities of the meridional reflections and those calculated from the final models in the relaxed and contracting states are shown in Figure 3. A satisfactory agreement between them was obtained in both states. The calculated intensity of the M2 reflection was greater than that observed in the relaxed state. This is due partly to the fact that the low-angle side peaks of the main peak were regarded as the C2 reflection in the observed data (Figure 5(a)). Although intensity profile fitting was done using the intensities of M2–M6 reflections, the integrated intensities of M10 and M11 reflections were deduced from this fitting approach. They were very different from those observed (Figure 3). This indicates that there may be some contribution to these reflections from structures within the backbone.41,42 Recently, it has been suggested that the part close to the M11 reflection is affected by the domain structure of connectin/titin.7 Locations of the perturbed and regular regions on a myosin filament and the crossbridge repeats in the triplet in the relaxed and contracting states Figure 6 shows the locations of the perturbed and regular regions on a myosin filament in the sarcomere in both relaxed and contracting states, which were derived from the final models for the myosin filaments. In the relaxed model (Figure 6(a)), the perturbed regions were ∼516 nm long, having 12 triplet levels of the 42.9 nm period. The regular regions were located at the distal ends (towards the Z-bands) of the perturbed regions and their lengths are ∼215 nm. Thus, the length of the perturbed region was about 2.4 times longer than that of the regular region. This result is consistent with the result reported by Malinchik and Lednev.14 In the contracting model (Figure 6(b)), the lengths of the perturbed regions were almost the same as those of the regions in the relaxed model. The lengths were ∼524 nm in which 12 triplet levels of the 43.5 nm period are involved. The perturbed regions shifted towards the Z-bands, with the regular regions

Myosin Filaments in Vertebrate Skeletal Muscle

Figure 6. Distributions of the crossbridge arrays along the thick filament across the M-line in the sarcomere, which were derived from the final models. (a) The model in the relaxed state and (b) the model in the contracting state.

growing on the M-line side and shrinking at the distal ends (Z-bands) both of length ∼102 nm. Thus, the perturbed regions are sandwiched between the regular regions. The total lengths of the regular regions were also almost the same as those in the relaxed state. The lengths of the perturbed region were about 70% of the total length of the crossbridge arrangement on the myosin filament in both states. Thus, the details of a mixed structure of the myosin filament were clarified in both states, and it was clear that the perturbed region was maintained with its proportional length unchanged when muscle went from the relaxed to the contracting state. The true interference spacings are longer than the apparent separations between the fine peaks on the forbidden and 3M reflections for the reasons as mentioned above. Comparisons of the distance between the perturbed regions across the M-line in the final model and the apparent distance derived from the interference peaks on the forbidden reflections calculated from the final model showed that the ratio of the apparent distance to the true one is, on average, 1.24 in the relaxed state and 1.19 in the contracting state. When we divide the experimentally obtained distance (Table 2) by these ratios in order to estimate the true distance, it is 660(±40) nm in the relaxed state and 850(±40) nm in the contracting state, close to the center-to-center distance between the perturbed regions across the Mline in the final model. However, we could not derive the true distances between the perturbed regions and the regular regions from the 3M reflections because of a mixture of interference of diffraction from several regions such as the interference between the regular regions, the perturbed regions, and the regular and perturbed regions.

Myosin Filaments in Vertebrate Skeletal Muscle

285

Figure 7. Part of the radial projection of the crossbridges in the perturbed regions; (a) and (b) show those in the relaxed and contracting states, respectively. The blue-filled and circles show respectively the shifted and regular the locations of the center of gravity of crossbridges with the 9/1 helix. The displacements of the axial perturbation from the regular repeat of a helical symmetry are shown. The bottom of the Figure is towards the M-line.

Figure 7 shows part of the radial projections (the radial nets) of the helical arrangement of crossbridges in the perturbed region on a myosin filament in the relaxed and contracting models. The distances among the crossbridge crowns in the triplet were 17.24 nm, 10.84 nm and 14.94 nm in the relaxed model (Figure 7(a)) and they were 13.87 nm, 15.77 nm and 14.07 nm in the contracting model (Figure 7(b)). The inter-crown distance in the regular region was 14.34 nm in the relaxed model and 14.57 nm in the contracting model. In the contracting state, the displacement of each crown from the regular repeat became smaller than in the relaxed state. The axial orientation of two-headed crossbridges on a myosin filament to the fiber axis in the relaxed and contracting states The axial dispositions of two-headed myosin crossbridges, which were derived using the approximate crystal model of S1, are depicted in Figure 8. In modeling, the two heads were assumed to be in contact at their innermost ends. A remarkable feature is that the configurations of the two-heads in a pair in a crossbridges along the thick filament differed from each other in each of the regular and perturbed regions in each of relaxed and contracting models. In a modeling study on relaxed muscle by Malinchik and Lednev, the structures of a crossbridge in both regions were assumed to be identical.14 In the case of plaice muscle by Hudson et al., the structures of three crowns in the perturbed region, however, were shown to differ from each other.16 Each head tilted in an opposite direction along the 3-fold helical tracks of thick filaments to a different extent (see Figure 10), generating a highly asymmetric profile for the projected density. One head of a crossbridge in either the regular or the perturbed regions oriented more perpendicular to the fiber axis than the partner head in both states. This feature became more prominent in the per-

turbed region in the contracting state, resulting in more asymmetric and broader density projections. Thus our modeling analysis reveals that the asymmetry of a crossbridge structure projected onto the fiber axis increases considerably during contraction. Determination of the azimuthal orientation of a myosin crossbridge around the z-axis by the use of a cylindrically averaged Patterson function In the above analysis, we could not obtain information concerning the azimuthal orientation of the myosin crossbridge around the filament axis because the density distribution of a crossbridge projected onto the z-axis (parallel with the filament axis) (see Figure 12(b) in Materials and Methods) remains unchanged for a rotation of crossbridges around this axis. In order to determine the orientation of a crossbridge around the z-axis, it is necessary to analyze the off-meridional layer-line intensities. Unfortunately, such analysis was limited to the relaxed state because the intensities of the offmeridional layer-lines were too weak to measure in the contracting state. By placing the origin of a crossbridge at the innermost joint of two myosin heads, we calculated the intensities of M1–M6 (first to sixth-order) off-meridional layer-lines using the structure of a crossbridge of the final relaxed model in the framework of a mixed structure obtained above. We then compared them to the observed layer-line intensity data, because it is known that the filament backbone contributes nothing to the offmeridional parts.11–13,43 We employed the intensities of the myosin layer-lines in the X-ray diffraction patterns from overstretched semitendinosus muscles in place of those data from sartorius muscles at fulloverlap length, because the X-ray diffraction patterns from both muscles are very similar in general appearance and there are much less sampling effects on the off-meridional layer-lines from overstretched muscles, more suitable for modeling studies.12–14 Figure 9(a) shows the X-ray diffraction pattern taken

286

Myosin Filaments in Vertebrate Skeletal Muscle

Figure 8. The axial orientations and the projected densities of a myosin crossbridge derived from the final models using the 68-sphere model of S1. (a) and (e) Those in the regular region; and (b) and (f) those in the perturbed region in the relaxed state. (c) and (g) Orientations and densities in the regular region, and (d) and (h) those in the perturbed region in the contracting state. In (a)–(d), the two heads of a crossbridge are depicted by two groups of red and purple spheres. In (e)–(h), the projected density profiles derived using the 68-sphere model of S1 are shown by red circles in the relaxed state and by blue circles in the contracting states, and those calculated from two Gaussian functions are shown by red curves in the relaxed state and by blue curves in the contracting state, respectively. The z-axis orients in the direction of the Z-band in the sarcomere and passes through the joint of two heads, being parallel with the filament axis. Note that orientation of a myosin crossbridge around the z-axis is arbitrary in both regions in the contracting state but that of a crossbridge in the relaxed state was determined by the analysis using the intensities of layer-line reflections (see the text).

from overstretched semitendinosus muscles and Figure 9(b) shows the intensity distributions from M1–M6 layer-lines. The intensity of the M1 reflection near the meridian could not be measured for the reason as mentioned above. The layer-line intensities are still affected by residual sampling effects. In order to compare the off-meridional layer-line intensities from the model structure to those observed, it is desired to use the sampling-free intensity data of layer-lines. For this purpose, a cylindrically averaged Patterson function 44,45 was used to derive the layerline intensity data of single myosin filaments without any sampling effects of the filament lattice array. It was calculated using the intensity data of M1–M6

layer-lines from overstretched muscles in the radial range of R < 0.157 nm−1 using the following equations in cylindrical coordinates:44  6 Z 0:157 2X DQðr; zÞ ¼ Il ðRÞJ0 ð2kRrÞ2kRdR c l¼1 0   2klz  cos ð1Þ c DQðr; f; zÞ ¼ Qðr; f; zÞ  Q ¯ ðr; fÞ ¯ ðr; fÞ ¼ Q

1 c

Z 0

c

Qðr; f; zÞdz

ð2Þ ð3Þ

287

Myosin Filaments in Vertebrate Skeletal Muscle

Figure 9. (a) Low-angle part of X-ray diffraction patterns in the relaxed state obtained from overstretched frog semitendinosus muscles. (b) The observed intensity distributions along the M1 to the M6 (first to sixth-order) myosinbased layer-lines as shown by red curves. X-ray diffraction patterns show residual sampling effects on the off-meridional layer-line reflections due to the hexagonal filament array. (c) The r-z map of a cylindrically averaged difference Patterson function (ΔQ(r,z)) calculated from the intensities of the M1 to the M6 layer-lines. The map is contoured at levels between 0 and 430 at the intervals of 5. Only positive peaks are shown in the map and some positive peaks in a region beyond a red line (r > ∼32 nm) come largely from inter-crossbridge vectors between thick filaments (see the text). (d) Comparisons of the intensity distributions (red) of the M1 to the M6 layer-line reflections obtained from the Fourier-Bessel transformation of the truncated ΔQt(r,z) and the calculated ones (blue) derived from the final model (see the text). These intensities are normalized so that the sum of the intensities of the M1 to the M6 layer-lines except for the region close to the meridian (R < 0.0254 nm−1) is identical for the observed data and the calculated data.

where ΔQ(r,z) is the cylindrical average of ΔQ(r,ϕ,z), and c and l denote the basic repeat and the layer-line index, respectively. ΔQ(r,ϕ,z) is defined in equation (2) as the Patterson function (Q(r,ϕ,z)) minus its zaverage, and we refer to this expression as the cylindrically averaged difference Patterson function. 45 This function expresses the difference between the overall Patterson function of the thick filaments and that of the structure of thick filaments projected onto the equatorial plane. Thus, it can be calculated without the use of the equatorial data (l = 0) which are Bragg reflections. The grid size used to make the map of a difference Patterson function was 0.2 nm (Figure 9(c)). The obtained map represents the r-z section of the cylindrically averaged difference Patterson function where negative peaks were omitted. Positive peaks appeared clearly on the map, corresponding to the vectors between the mass

centers of crossbridges on a three-stranded helical arrangement. Some weak positive peaks appeared in the region of r > ∼32 nm have been interpreted, for the most part, as inter-crossbridge vectors between different thick filaments by our modeling studies (not shown). Therefore, we removed these outer peaks due to inter-crossbridge vectors sitting outside the red curve in Figure 9(c) from the map to recalculate the intensity data of the layer-lines from single thick filaments without the sampling effects using the equations:  Z c Z 2 DQt ðr; zÞJ0 ð2kRrÞ2krdr DI ðR; ZÞ ¼ 2 0

 cos2kzZdz cos2kzZdz ð4Þ DIðR; ZÞ ¼ IðR; ZÞ  IðR; 0Þ

ð5Þ

288 where ΔI(R,Z) is the cylindrical average of ΔI(R,Φ,Z) and ΔQt(r,z) is the truncated cylindrically averaged difference Patterson function. Although the peaks around r∼30 nm in the ΔQt(r,z) map were still affected by some inter-crossbridge vectors within the hexagonal unit cell, the recalculated intensity data from ΔQt(r,z) were very similar to the original observed intensity data, except on and near the meridian confirming that the lattice sampling influenced strongly the intensities of the meridional part in the X-ray diffraction pattern from overstretched muscles. From the comparison of the obtained ΔQ(r,z) map with the theoretical Q(r,z) map of a myosin filament model of a three-stranded 9/1 helix of two-headed crossbridges, the radial position of a crossbridge mass center along a helix could be estimated from the peak around (r, z) = (∼22 nm, 0 nm) to be ∼12.6 nm. We used this value as the helical radius of a crossbridge mass center to carry out the intensity calculation of the layer-lines by the Fourier-Bessel transformation of a helical arrangement of crossbridges around a myosin filament consisting of a mixed population of crossbridge arrangements (see the Appendix). Indeed, similar calculations using the truncated layer-line intensity data from sartorius muscle at full-overlap length revealed comparable intensity distributions of the

Myosin Filaments in Vertebrate Skeletal Muscle

layer-lines except on and near the meridian to those from overstretched semitendinosus muscle (unpublished results). Note that, for instance, the intensity of the M3 reflection at R = 0 could be a factor of 4 greater than that from single thick filaments, indicating that the strong and radially sharp intensities of the meridional reflections in muscle at full filamentoverlap between myofilaments are governed primarily by lateral coherence between the myofilaments. A more detailed discussion of the ΔQt(r,z) analysis will be presented elsewhere. In the intensity calculation, we searched for the optimum azimuthal orientation of each head of crossbridges by rotating each myosin head of crossbridges independently around the z-axis in the final model. The helical radii of crossbridges in each region were also refined by translating crossbridges in the radial direction (see Materials and Methods). Figure 9(d) shows a comparison of the layer-line intensities of M1–M6 layer-lines derived from ΔQt(r,z) and those calculated from the best-fit model having Rl ∼ 0.28 (Rl, see equation (8) in Materials and Methods). The results showed that the helical radius of a crossbridge mass center was ∼11.2 nm in the regular region and it was almost the same (∼11.4 nm) in the perturbed region. Finally the orientations of a crossbridge around the filament axis were determined using the

Figure 10. Arrangements and configurations of myosin crossbridges along the thick filament. (a) and (b) The final model in the regular region and that in the perturbed region, respectively, in the relaxed state. (c) and (d) The final model in the regular region and that in the perturbed region, respectively, in the contracting state. The backbone is described as a structureless cylinder. A thick filament model is seen from the direction perpendicular to the filament axis in side view and is seen from the direction parallel with the filament axis in top view. A top view model could not be produced for contracting muscle (see the text). In (a)–(d), the z-axis orients in the direction of the Z-band in the sarcomere and is parallel with the filament axis. In top view in (a) and (b), central circles denote the backbones of thick filaments and double-ended arrows connect the center of the thick filament and a mass center of a two-headed crossbridge. Note that orientations of a crossbridge around the filament axis are arbitrary in both regions in the contracting state (see the text).

Myosin Filaments in Vertebrate Skeletal Muscle

68-sphere model of the S1 structure. The results are shown in top view in Figure 10(a) and (b), which shows also the configurations of crossbridges within the basic period. Each head of a crossbridge had a different orientation around the z-axis in both regions. In the relaxed model, when viewed from the top, the distal ends of two heads of a crossbridge had a dramatically different orientation in the regular region from that in the perturbed region and their centers of gravity reside at different radii. The helical radii of purple and red heads in a pair were 9.8 nm and 12.6 nm, respectively, in the regular region and 11.8 nm and 11.0 nm, respectively, in the perturbed region. In top view, two heads of a crossbridge flared, forming a windmill-like shape in the regular region (Figure 10(a)), and one head of a crossbridge almost came in contact with the partner head at their outer ends with the concave side of both heads facing towards each other in the perturbed region, making a U-shaped structure at the same axial level (Figure 10(b)). In side view, one of a pair of heads seemed to be almost in contact with the other head in a pair at an adjacent crown level along the filament axis in the regular region (Figure 10(a)) and, in the perturbed region (Figure 10(b)), one head appeared to make contact with the other on the adjacent crown but only on the narrower inter-crown levels. Earlier X-ray studies using a simplified model for a crossbridge in relaxed frog muscles by Haselgrove,13 Malinchik and Lednev,14 and three-dimensional reconstruction of electron microscopic images by Stewart et al.46 and Hashiba et al.47 have indicated an axially flared structure of crossbridges consistent with our model. The arrangement of heads in the regular region in the relaxed state is very similar to the structure revealed by cryo-electron microscopic three-dimensional reconstruction of tarantula thick filament,48 but quite different from the thick filament structure of plaice muscle by a single-particle analysis of electron micrograph images 4 9 and X-ray diffraction analysis,6 and that of insect flight muscle by X-ray diffraction analysis.39

Discussion The intent of this article is to provide more precise structural information on myosin crossbridges that may be needed for the interpretation of the results of dynamic X-ray experiments aimed at understanding the molecular mechanism of force generation in muscle. We elaborated the earlier study on relaxed muscles by Malinchik and Lednev14 in substantial ways and extended the modeling approach to the analysis of isometrically contracting muscle, something that has not been attempted previously. The proposition that there are both regular and perturbed regions of the crossbridge arrangement along myosin filaments is necessitated by the observation of so-called forbidden meridional reflections in contracting muscle, although the presence of forbidden meridional reflections has not been considered previously in the analysis of the active state.

289 The question arises of whether these are genuine features of contracting muscle or an artifact due to fatigue or insufficient stimulation in contracting whole muscle. In X-ray diffraction patterns from whole muscle recorded during a small number of repetitive cycles of activation (even in one single tetanus) and in a very short X-ray exposure time (even in one single 100-ms-exposure) we were able to measure all the myosin-based meridional reflections. There was no appreciable difference in X-ray patterns between a single exposure for 100 ms and five repetitions of a single exposure for 100 ms. The intensities of most of the forbidden meridional reflections showed a large decrease but did not disappear at the plateau of isometric tension. In addition, all peaks of the myosin reflections shifted towards the low-angle side as a result of activation during contraction.33–35 Thus, it is clear that these residual intensities are apparent in fresh muscles showing no significant indication of fatigue. In previous experiments on contracting intact frog single fiber,22 the M2 reflection is frequently not seen. We believe this is because, in these experiments, the M2 reflection had decreased to a level that was too small to measure during contraction, because the same exposure time was used for a fiber during contraction that was used for the resting fiber. In the case of permeabilized rabbit and frog skeletal fiber using parallel arrays of single fibers,50–52 clear forbidden myosin meridional reflections can be seen during activation. Thus, the appearance of the forbidden meridional reflections observed during contraction of whole muscle is a genuine feature of contracting muscle, implying that the perturbed structure on the myosin filaments is maintained during contraction. This fact may be consistent with electron microscopic observations that suggest that the perturbations of the crossbridge array are an intrinsic feature of isolated skeletal muscle myosin filaments.53 Thus, our analysis of the rearrangement of the myosin crown configuration in terms of the perturbed and regular regions in the active state is justified. In our modeling studies, an incrementally fitting approach allowed us to search for the most plausible model of a myosin filament in a much shorter calculation time than had we started with the intensity profile fitting at the outset and showed that the detailed peak shapes, as reflected in the intensity profiles, contain important information that needs to be considered in order to derive detailed structures. We then conducted the modeling procedure using an atomic model of a myosin crossbridge in order to obtain a more detailed conformation of the two-headed crossbridge to sub-nanometer resolution in both relaxed and contracting states. The meridional reflections were well reproduced by this modeling approach. Interference effects on M3 and M6 meridional reflections According to the proposed structure of a myosin filament consisting of the regular and perturbed

290 regions in both relaxed and contracting states, the samplings of the 3M order reflections, such as M3 and M6 reflections, originate from mixed interference between multiple regions across the M-line. In the final model (see Figure 6), the center-to-center distance between the perturbed regions and that between the outer regular regions across the M-line in the relaxed state were ∼688 nm and ∼1420 nm, respectively. In the contracting state, the center-tocenter distance between the perturbed regions increased to ∼903 nm, with the result that the distance between the inner regular regions and that between the outer regular regions were ∼277 nm and ∼1530 nm, respectively. The average of these periods weighted simply by their lengths was ∼903 nm in both states. On the other hand, sampling analysis of these reflections in the observed X-ray diffraction patterns showed that the apparent distance was 890(±50) nm in the relaxed state, whereas it was 1010(±40) nm in the contracting state (Table 2 and Figure 4(e)–(h)). The average period did not change in the transition of resting muscle to the contracting state, but the apparent center-to-center distance altered between the relaxed state and the contracting state. However, the apparent center-to-center distance between the perturbed regions was close to the distances measured from M2 and M5 forbidden reflections in both states (Table 2). This implies that the sampling of M3 and M6 reflections is dominated by interference between heads in the perturbed regions across the M-line, with other interference between heads on a myosin filament making less contribution to the observed sampling. Perturbed structures of the myosin filament in the relaxed and contracting states The forbidden meridional reflections are caused by the systematic perturbations in the axial repeat of myosin crossbridges from the regular repeat.14,18,19 In the contracting model, the perturbed region moved towards the Z-band and maintained the length it had in the relaxed state, so that a new regular region was born on the M-line side, with the result that the perturbed region was surrounded between two regular regions. As shown in Table 3, the number of the triplets in the perturbed region in both models was 12, very close to the value (13) in the relaxed model described by Malinchik and Lednev,14 and the locations of the regular and perturbed regions on the filament in our relaxed model were also similar to theirs. The axial repeats (17.2 nm, 10.8 nm and 14.9 nm) among crown levels in the triplet of the perturbed region in the relaxed model (Figure 10(a)) were somewhat different from those (16.7 nm, 13.1 nm and 13.1 nm) determined by Malinchik and Lednev14 (where they assumed symmetrical displacements of the crowns), optical diffraction analysis of the cryo-sectioned A-bands from human muscles (16.3 nm, 12.8 nm and 13.8 nm) by Squire et al.,54 and analysis of the low-angle X-ray diffraction from plaice muscles (17.9 nm, 13.3 nm

Myosin Filaments in Vertebrate Skeletal Muscle

and 11.7 nm) by Hudson et al.16 In the contracting model, these repeats became 13.9 nm, 15.8 nm and 14.1 nm (Figure 10(b)), each crown repeat in the triplet became closer to the regular repeat. This factor can explain the weakening of the forbidden reflections and relative strengthening of the 14.5 nmbased meridional reflections observed during contraction. If these axial perturbations are accompanied by azimuthal displacements, the 3-fold 9/1 helix of a myosin filament could have a sinusoidal variation with a period of a 42.9 nm or a 43.5 nm such as observed in the dahlemense strain of tobacco mosaic virus.55 Myosin crossbridge structures in the relaxed and force generating states Our modeling results suggest that in both relaxed and contracting states of frog skeletal muscle, the two heads of a myosin crossbridge are axially tilted in opposite direction along the 3-fold helical tracks of myosin filaments (Figure 10). In the relaxed model, the appearance in the perturbed region that one head of a crossbridge almost comes in contact with the partner head at their outer ends invokes an intramolecular interaction between heads of a crossbridge. In the axial direction, one of a pair of heads seems to be in contact with the other head in a pair at an adjacent crown level in the regular region, and one head seems to make contact with the other on the adjacent crown only on the narrower inter-crown levels in the perturbed region. Such an appearance suggests an intermolecular interaction between heads of crossbridges in the axial direction in resting myosin filaments. Thus, the interaction between heads in resting frog muscle myosin filaments appears to involve interactions both within a crown and between crowns. These interactions appear to be different from those in plaice muscle myosin,6,49 where the interaction is between heads of the same molecule, in insect flight muscle,39 where the interaction occurs between heads of adjacent myosin molecules in the same crown and in tarantula (and Limulus) muscle,48 where the interaction is between heads in different crowns. From the spacings of the (100) and (110) equatorial reflections in the X-ray diffraction pattern from relaxed muscles, the distance between thick filaments in the hexagonal array was estimated to be ∼43.2 nm in the relaxed state of muscle at fulloverlap length between myofilaments. Therefore, the distance between a thick filament and a thin filament is ∼25.0 nm. Then the distances between the actin-binding sites of individual myosin heads of a crossbridge and the thick filament axis are ∼15.4 nm and ∼17.7 nm in the regular region, and they are ∼17.2 nm and ∼16.2 nm in the perturbed region. Assuming that the diameter of an actin monomer is about 4.5 nm,56 the shortest distance between the surface of the actin filament and the actin-binding site of a myosin head of the crossbridge projecting from the backbone is ∼20.5 nm,

Myosin Filaments in Vertebrate Skeletal Muscle

showing that, on average, the myosin heads sit far away from the actin filament surface. In addition, the general intensity distributions of the myosin layer-line diffraction pattern from overstretched muscles were very similar to those from muscles at full-overlap length after correcting for the influences of the lattice sampling. A strong inference from these results is that the dispositions of two-headed crossbridges are stabilized, in the relaxed state, predominantly by an intramolecular interaction between two heads of crossbridges and/or an intermolecular interaction between heads of different crown levels in the axial direction rather than by an electrostatic balance between the thick and thin filaments. Such interactions between myosin heads could be related to a mechanism for the inhibition of actomyosin interaction in the relaxed state, similar to those proposed to be operating in insect flight muscle39 and tarantula muscle.48 As noted above, however, the interactions between heads in resting myosin filaments appear to be different in different muscles. The different organizations of the myosin heads may be adaptations for the specific functions of the heads in these muscles. When muscles go from the relaxed state to the contracting state, the release of such resting interactions between myosin heads, perhaps by Ca2+-binding to myosin light chains,57 would allow myosin heads to translocate to interact with Ca2+activated thin actin filaments. In the contracting model, one head of a crossbridge is oriented more perpendicular to the fiber axis while keeping its own axial periodicity and the other head flared axially. Thus, the asymmetric nature of the crossbridge density, when projected onto the fiber axis, became more prominent than in the relaxed state, implying that there exist two populations of myosin heads during contraction. This is another factor that can help explain the weakening of the forbidden reflections and strengthening of the 14.5 nm-based meridional reflections during contraction. The asymmetric profile of the projected density of a crossbridge in the perturbed region in the contracting model (Figure 8(d)) is consistent with the report by Juanhuix et al.,36 although they did not distinguish their profiles in terms of the perturbed and regular regions on the filament. If the more perpendicularly oriented heads contribute to the remnant intensity of the M1 layer-line (∼20% of the original resting intensity),12,21,33 the squareroot of this intensity implies that ∼50% of the total heads assume this configuration during an isometric contraction. Taking into consideration that individual myosin heads cycle asynchronously during the hydrolysis of ATP, the heads that appeared to be axially flared may represent an average conformation over the heads cycling at different times. It might be just the more perpendicularly inclined heads that are in the pre-forceproducing state (myosin.ADP.Pi state, where Pi is inorganic phosphate) 52,58 that then work in a coordinated fashion in the process of force redevelopment during quick length change, mediating the

291 extensibility accompanying twisting of the thin actin filaments during contraction.33,34,59 This evokes the concept that the two heads of the crossbridge play alternate roles for the generation of contractile force. Implication of the perturbation of myosin crossbridge arrangement during an isometric contraction The majority of crossbridges on the myosin filament in the relaxed state appeared to be in a perturbed region, taking up about 70% of the total length of the filament. In contracting muscle, there was still a perturbed region of about the same length but it translocated on the filament so that it was surrounded on both sides by regular regions. This confirms that a rearrangement in the systematic perturbation of the helical arrangement of crossbridges on the thick filament occurs upon activation. It has been suggested that the existence of the perturbed regions may be associated with the existence of C-proteins in the central part of the perturbed region on the thick filament.7,14,19 A difficulty with this notion is that electron microscopy has shown that the length of the C-protein region on a half thick filament is about 300 nm,19 which is shorter than that of the perturbed region on myosin filament of frog muscle (Figure 6). Very recently, however, the structural configuration of C-protein has been investigated by single-particle analysis of electron micrograph images of the thick filaments, revealing evidence that C-protein might be responsible for the perturbation from regular helical symmetry in the vertebrate myosin crossbridge arrangement to facilitate interactions of myosin heads with surrounding actin filaments in relaxed muscle.49,60 The meridional reflections attributed to C-proteins became much weaker in intensity during an isometric contraction (Figures 1(b) and 2(b)), implying that C-proteins tethered on the myosin filaments become much more mobile in the active state. Malinchik and Lednev discussed the possibility that the perturbation in relaxed muscle may be caused by the interaction between myosin heads and C-proteins, and that the release of interactions between them would much diminish the perturbation when muscle is activated.14 However, under low ionic strength conditions of skinned muscle fibers in the relaxed state,15,61 and upon Ca2+activation of skinned fibers under low ionic strength conditions (H. Iwamoto (JASRI), personal communication), a similar translocation of myosin heads towards the thin filaments to form a weak/strong binding state is not accompanied by the weakening of the intensities of the forbidden meridional reflections. A plausible explanation for these observations may be that a rearrangement in the systematic perturbation of the helical arrangement of crossbridges on the thick filament during contraction yields a more optimal geometrical relationship for active interaction between actin and myosin heads in the framework of their incommensurate

292 periodicities. The loosening of C-protein-containing structures on the myosin filament may be responsible for this rearrangement of crossbridges upon activation. Major contributions of structural parameters to the myosin-based meridional intensity profiles In the present modeling studies, the best fit to the observed intensity data was obtained by allowing a relatively large number of parameters to vary. In order to examine which parameters dominate in affecting the intensities of myosin-based meridional reflections, we investigated the variation (sensitivity) of the Rpr-factor (equation (7) in Materials and Methods) when the parameters of the final models in the relaxed and contracting states were altered individually in the region of the final, best-fit parameter sets. As shown in Figure 11, this inspection revealed that the value of the Rpr-factor was influenced primarily by the crossbridge shifts from the regular repeat distance in the triplet (Figure 11(c) and (g)) and rotations of a twoheaded crossbridge around the x and y axes in both singlet and triplets (Figure 11(a) and (e)), together with the lengths of the regular and perturbed regions and their disposition (Figure 11(d) and (h)), because these changes contribute significantly to the alteration of the electron density distribution of a myosin filament projected onto the fiber axis. On the other hand, a rotation around the long axis of a myosin head had little affect on the Rpr-factor (Figure 11(b) and (f)), because these changes have less affect on the projected density of heads onto the fiber axis. The results demonstrate that the intensity distribution of the meridional reflections is sensitive to axial orientational changes of a twoheaded crossbridge and to changes in other structural components or their combination, such as the deviation of crowns from the regular repeat and the length and the disposition of the perturbed regions. Thus, care should be taken when interpreting the intensity changes of myosin meridional reflections when rapid23–26,28,62 or slow63,64 length perturbations are applied to contracting muscle. In these cases, the way in which these other structural parameters, additional to the orientational parameters of crossbridges, respond to these perturbations must be ascertained. A careful examination of the changes in the lateral width of meridional reflections will also be needed. Recently, when a rapid length release was imposed on contracting whole muscle, a significant increase in the intensity of M2 and M6 meridional reflections in contrast to an intensity decrease of the M3 reflection was observed without a delay with respect to the tension change. 27,28 This behavior of the M2 intensity implies that a rearrangement of the myosin crown configuration could occur in the process of force redevelopment. The intensity increase of the M6 reflection suggests that inferring structural changes from intensity change of the M3 reflection alone may be overly simplistic. The

Myosin Filaments in Vertebrate Skeletal Muscle

possible orientational changes of myosin heads in relation to intensity changes of M3 and M6 reflections during a rapid length perturbation,28 and in shortening muscle,65 have been discussed extensively by Huxley and colleagues. It may be worth mentioning that there is little indication of a reappearance of the M2 reflection when a rapid stretch is applied to contracting muscle,27,28 or when a slow length oscillation is applied to contracting muscle, the M6 intensity changes in phase with the M3 intensity in response to the tension changes.64

Conclusions Both regular and perturbed regions of the crossbridge arrangement co-exist along the thick myosin filaments in isometrically contracting muscles as well as in relaxed muscles. In the transition of resting muscle to the contracting state, the structure and the disposition of perturbations on the myosin filaments alter while maintaining the length they had in the relaxed state, and are now surrounded by two regular regions. The perturbed regions in both relaxed and contracting muscles occupy about 70% of the total length of a myosin filament. The decrease in displacement of each crown repeat in the triplets from the regular repeat distance, and the increased asymmetry in the densities of crossbridges projected onto the fiber axis in the perturbed region, together with the translocation of the perturbed region on the myosin filaments cause the weakening of the forbidden reflections and relative strengthening of the 14.5 nm-based meridional reflections in the contracting state. The altered perturbed structure in the contracting state may allow the myosin crossbridges to interact optimally with the actin filaments with their different periodicity. Detailed modeling analysis reveals that the conformation of the myosin crowns is different in the regular and perturbed regions in both states, and that one head in a pair of a crossbridge orients more perpendicularly to the thin actin filaments, and the partner head flares axially in the perturbed region in the contracting state. These results suggest that the two heads of the crossbridges could play alternate roles in the generation of force. Analysis of crossbridge conformations in the relaxed state indicates that one head of a crossbridge comes into close proximity to the partner head at their outer end and to the other head in a pair at the adjacent crown level in the axial direction. Both intramolecular and intermolecular interactions between two heads of crossbridges could provide a mechanism for the inhibition of the actomyosin interaction in the relaxed state. The actual values of the intensities of the myosin-based meridional reflections depend significantly upon a number of factors; axial orientations of the two-headed myosin crossbridges themselves, and the inter-crown distances in the triplets along the filament, together with the length

Myosin Filaments in Vertebrate Skeletal Muscle

293

Figure 11. The sensitivity of the various parameters to the Rpr-factor by shifting them in the regions of their values of the final models. (a) and (e) The changes in Rpr-factor against the rotations (α, β) of a crossbridge around x and y-axes in the relaxed and contracting states, respectively. (b) and (f) Those in Rpr-factor against the rotations (γ) of a crossbridge around the long axis connecting the proximal end (Pro840) and the mass center of a myosin head in the relaxed and contracting states, respectively. (c) and (g) Those in Rpr-factor against the shifts (δ1, δ2) from a regular repeat within the unit cell in the relaxed and contracting states, respectively. (d) and (h) Those in Rpr-factor against the change of the number (3k) of the crowns in the perturbed regions without changing the distance between the perturbed regions in the relaxed and contracting states, respectively. Horizontal broken lines are drawn at the level of 5% (acceptable windows) above the minimal Rpr-factor of the final model.

and the disposition of the perturbed region in the filament. The results of the present modeling study provide more precise structural information needed

for the proper interpretation of the dynamic X-ray data upon the application of length perturbation to contracting muscle and during shortening.

294

Materials and Methods Muscle preparation and experimental protocols Bullfrogs (Rana catesbeiana) were killed by decapitation, followed by destruction of the spinal cord. Live sartorius and semitendinosus muscles were dissected and used for X-ray diffraction experiments. Sartorius muscles at full-overlap length between thin and thick filaments in the sarcomere (adjusted to ∼2.3 μm sarcomere length by light diffraction with He-Ne laser) were used for experiments involving a contracting state. Sartorius muscles were ∼50 mm long and ∼10 mm wide, and semitendinosus muscles were ∼35 mm long and ∼3 mm wide. The pelvic end or the tendon end, respectively, was connected to a force transducer and the other ends were fixed to the chamber. They were mounted vertically in a specimen chamber with two mylar windows for X-rays to pass through. Chilled frog Ringer solution (0.85 mM NaH2PO4 (pH 7.2), 115 mM NaCl, 2.5 mM KCl, 1.8 mM CaCl2, 2.15 mM Na2HPO4) was circulated through the chamber. Muscles were stimulated electrically at 10 °C under isometric conditions for 1.4 s with a train of 1 ms duration supramaximal current pulses at ∼33 Hz. X-ray diffraction experiments were performed using collimated synchrotron X-rays with a wavelength of 0.150 nm on beamline 15A1 at the Photon Factory (PF), High Energy Accelerator Research Organization, Tsukuba, Japan.66–68 The temperature of ∼10 °C was chosen because this is where the X-ray diffraction pattern is best conserved in repetitive cycles.21,33 The size of the X-ray beam was 0.5 mm vertically and 1.5 mm horizontally at the specimen. The flux of X-ray beam was ∼1011 photons·s−1. Two-dimensional X-ray diffraction patterns from relaxed muscles, isometrically contracting muscles and overstretched relaxed muscles (see below) were recorded with an image plate67 (type BAS-III, Fuji Film Co., Tokyo, Japan) at a specimen-to-detector distance of ∼2.4 m to measure the first to the 11th-order myosinbased meridional reflections as described.33 X-ray diffraction data from relaxed muscles were collected in a 10 s exposure in total. After moving the muscle specimen vertically, X-ray data were collected in a 1 s exposure when the tension had reached its plateau phase during an isometric contraction, and the measurements were repeated ten times with resting intervals of 90 s between contractions to accumulate X-ray data on the same image plate. The X-ray data were accepted until the tension declined to a level of ∼85% of the initial value. The X-ray data from four muscles were used after applying a scaling by the total intensity of the diffraction pattern, except for the strong equatorial region and the part around the beam stop for relaxed and contracting pairs.33 Semitendinosus muscles stretched to non-overlap between myofilaments in the sarcomere (>4.0 μm) (referred to as overstretched muscle) were prepared for measurement of the myosin-based layer-line reflections in the relaxed state. The influence of the hexagonal lattice sampling on the myosin-based layer-lines was much reduced in the X-ray diffraction patterns from overstretched muscles, except for the meridional reflections due to the considerable decrease in lateral coherence between filaments by stretch. The X-ray data from overstretched muscles were collected in a 20 s exposure by shifting the position of muscle vertically every 5 s of exposure. The X-ray data from three muscles were summed.

Myosin Filaments in Vertebrate Skeletal Muscle

In order to measure precisely the separation between fine sampling peaks of myosin-based meridional reflections arising from interference between the arrays in the two halves of each myosin filament across the M-line, an additional set of X-ray diffraction experiments was done at BioCAT beamline18ID at a third-generation source, the Advanced Photon Source (APS), Argonne, USA. Here, the optics provided highly collimated synchrotron X-rays (wavelength, λ = 0.1033 nm) with a flux of 10 13 photons·s−1 from the multipole undulator source.69,70 The beam size (FWHM) was ∼37 μm vertically and ∼190 μm horizontally at the detector plane. Sartorius muscles from R. catesbeiana were stimulated electrically using the protocol described above. During X-ray exposure, the specimen chamber was moved up and down at a speed of ∼1 mm·s−1 to minimize the radiation damage of muscles. X-ray diffraction patterns of muscles were recorded with a CCD detector71 with a spatial resolution of ∼60 μm (FWHM) at a specimen-to-detector distance of ∼5 m to measure the first to the sixth-order myosin-based reflections. X-ray diffraction data with much higher angular resolution (∼6000 nm order-toorder) than were obtainable previously were collected in 100 ms to 500 ms exposure time from fresh relaxed and contracting muscles showing little sign of fatigue. The data from four muscles were used. Analysis of X-ray diffraction data After the X-ray exposure, image plates were scanned with an image plate reader (BAS 2000, Fuji Film Co., Tokyo, Japan) using a pixel size of 100 μm. Digital intensity data from the image plates were analyzed on graphics workstations (O2, Silicon Graphics Inc., USA and Power Macintosh G4, Apple Computer Inc., USA). After determining the origin and correcting the inclination angle of each image, the four quadrants of the patterns were folded and averaged.33 The X-ray diffraction data from four muscles were used separately. The axial intensity distributions of the meridional reflections in the X-ray diffraction patterns were obtained after radial integration of the data in the very narrow range of 0 < R < 8.48 × 10−4 nm−1 on either side of the meridional axis where R = 2sinθ/λ (2θ is the diffraction angle and λ is the wavelength of the X-rays used) denotes the reciprocal radial coordinate along the equator. The intensities of the meridional reflections were sampled with intervals of 2.826 × 10−4 nm−1. For an intensity measurement, a linear background was drawn by connecting two background points on each side of the reflection or cluster of reflections and subtracted. The intensity profile of each reflection was deconvoluted by modeling it as overlapping Gaussian functions, providing integrated intensity and peak position (a Gaussian deconvolution method).33 The mean axial spacing of the reflection was determined as the mean of the spacings of the component peaks weighted by their intensities. Axial spacings were calibrated internally by the relaxed spacing of the third-order meridional reflection as 14.34 nm.12 The total integrated intensity of the sampled reflection was measured as the sum of their areas of the sampling components. The intensities of the myosin-based layer-lines from overstretched muscles in the relaxed state were measured by radial integration of the appropriate width of the stripes parallel with the meridian in appropriate radial ranges (∼4.24 × 10−3 nm−1), and intensity distributions across the several layer-lines were obtained in the axial direction.33

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Myosin Filaments in Vertebrate Skeletal Muscle

After the background intensity was subtracted, the overlapping intensity peak profile was deconvoluted as described above, providing the integrated intensity. The integrated intensity of each reflection was plotted as a function of the reciprocal radial coordinate R. The layerline intensities were finally sampled with intervals of 4.24 × 10−3 nm−1. X-ray diffraction data collected on the CCD detector at the APS were analyzed using the FIT2D program†.72 The origin and inclination angle of two-dimensional images were determined by measuring the center of the overlapping reflections by the first-order myosin-based and C-protein-based reflections on the meridian on each side of the equator and the (100) Bragg reflections on the equator on each side of the origin, and the images were aligned. The axial intensity distribution of myosin-based meridional reflections was obtained by radial integration of the data in the region of 8.48 × 10–4 nm–1 on either side of the meridional axis as described above. The intensity profiles of the meridional reflections were sampled with intervals of 4.677 × 10−5 nm−1. After applying the scaling and the background subtraction, the intensity profile of each reflection was summed from four muscles and plotted as a function of the reciprocal axial coordinate Z = sin2θ/λ. The axial intensity broadening due to the convolution of the X-ray beam profile was negligible because of the sharpness of the X-ray beam at the 18ID beamline of the APS. In order to correct the effect due to the increase in the disorder of the axial register of filaments on the crystalline intensities of the myosin-based meridional reflections (integrated in the very vicinity of the meridian) from relaxed and contracting muscles, the axial integrated intensity and the axial intensity profile of each reflection were multiplied by the square of each radial width to compensate for the different sampling of peaks by the Ewald sphere. Modeling calculations Fitting the model to the integrated intensities of the myosin-based meridional reflections Modeling calculations of the myosin crown periodicity and the axial disposition of two-headed myosin crossbridges along the thick filaments were initially carried out using the axially integrated intensities of the myosin-based reflections on the meridian to construct one-dimensional structural models of the myosin filaments projected onto the fiber axis as described.30 For modeling the crossbridge arrangement along the whole thick filament, we used the integrated intensities of the second-order (M2) to the 11thorder (M11) myosin-based reflections with the basic period of 42.9 nm in the relaxed state and those of the reflections with the 43.5 nm period in the contracting state. Here, the backbone structure was simply approximated by a uniform cylinder with a finite length of 1.46 μm, because the structure of the backbone is not known in any detail. According to electron microscopic data, about 50 crossbridge crowns are located in each half thick filament, with an average repeat of 14.3 nm with a bare zone lacking crossbridges in the center of the filament that is ∼160 nm long.7 In the simulation, we assumed that the elongation of a thick filament during contraction is uniform along a thick filament, and that the axial periodicity of the crossbridge arrangement and the length of the bare zone become longer by ∼1.6% in proportion to the elongation of the † http://www.esrf.fr/computing/scientific/FIT2D

thick filaments in the transition of muscle from the relaxed state to the contracting state.33–35 In modeling studies, we considered a mixed structure consisting of triplet and singlet repeating units of crossbridge arrays within the basic period (a unit cell), as did Malinchik and Lednev.14 The triplet structure of crossbridges has a 42.9 nm periodicity, within which the three myosin crown levels deviate from a regular 14.3 nm interval. The singlet structure has a true 14.3 nm periodicity. The triplet structure and singlet structure regions are referred to as perturbed regions and regular regions on the filament, respectively.14 The same definitions applied to contracting muscle (see the text), but the singlet repeat is now 14.5 nm and the triplet repeat is 43.5 nm. The location of the perturbed regions on the filament was estimated by analyzing the sampling period of M2 and M5 forbidden meridional reflections.14 Initially, we assumed that the perturbed region is arrayed successively on the thick filament without a separation and that the regular regions with a 14.3 nm repeat can reside both inside and outside the perturbed region. As neither the length of the perturbed region or that of the regular region on the myosin filament is known a priori, the number of crossbridge levels in each region was allowed to vary. The projected densities of individual heads of a two-headed crossbridge were initially modeled as overlapping Gaussian functions. The following 11 parameters in total were allowed to vary independently; the Gaussian widths (4σ) (ar, br and ap, bp) of projected density of each pair of myosin heads, the axial distances (dr, dp) between two heads of a crossbridge (the subscripts r and p denote the regular region and the perturbed region, respectively), the axial shifts (δ1, δ2) of the crown levels from the regular repeat (14.3 nm or 14.5 nm) in the triplets, the number of the crowns (l, 3k) in the singlet and triplet regions, respectively. The total number (Nc) of the crossbridge crown levels in a half thick filament was varied between 49, 50 and 51. They are given in Table 3 and the Appendix. The variation stepsizes allowed for these parameters in the fitting calculation were 1 nm. It was assumed that each crown structure in three successive crowns within the unit cell is the same in both regions. The most probable values of these parameters were determined by searching for the best fit between the calculated (Ii,calc) and observed (Ii,obs) integrated intensities of the meridional reflections in order to minimize the following R-factor: 11 X Ii;obs 11 1X jIi;obs  sc Ii;calc j Sc ¼ i¼2 ð6Þ R¼ 11 X N i¼2 Ii;obs Ii;calc i¼2

in which sc is a scale factor and the summation of i is performed over the M2 to M11 meridional reflections (N = 10 in the relaxed state and N = 9 in the contracting state). Ii,calc was derived by axial integration of the intensity of the ith meridional reflection (I(0,Z)) as described in the Appendix. The axial ranges of integration of each reflection are given below. Our simulation searched for the global minimum of R-factor in a parameter space consisting of 11 parameters using ten or nine observed data with the two additional constraints that the center-to-center distances between perturbed regions are shorter than the experimentally determined distances, and that the intensity of the M1 reflection is required to be less than that of the M2 reflection in both the relaxed and contracting states (see the text). The range over which the parameters were allowed to vary was restricted within physically reasonable boundaries (Table 3).

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Myosin Filaments in Vertebrate Skeletal Muscle

Fitting the model to the axial intensity profiles of the myosin-based meridional reflections In order to refine our modeling further, we calculated the axial intensity profiles of M2–M6 (second to sixthorder) reflections using the parameter sets of the above models as starting points for fitting to the observed intensity profiles of the meridional reflections from the high angular resolution X-ray diffraction patterns taken at the APS. Using all parameter sets of the obtained models with the R-factors being up to ∼5% (corresponding to SEM of the observed integrated intensity data) higher than the lowest value as the acceptable windows, we searched for the intensity profile fitting models in both the relaxed and contracting states that give the lowest value of the following Rpr-factor: 6 Z ei X jIobs ðZÞ  sc Icalc ðZÞjdZ Rpr ¼

i¼2

si

6 Z X i¼2

ei

ð7Þ Iobs ðZÞdZ

si

in which sc is the same scale factor as in equation (6) and si and ei are described below. Iobs(Z) is the observed intensity of the meridional reflection and Icalc(Z), the calculated intensity described as I(0,Z) in the Appendix. In the refinement, the range over which the parameters were allowed to vary was in the neighboring region of each value of parameter sets as described above. In this way, all parameters in the above integrated intensity fitting were refined. The axial integration ranges (si ≤ Z ≤ ei) of five meridional reflections used for the intensity profile fitting were; 0.0445 ≤ Z ≤ 0.0485 nm−1 for M2, 0.0678 ≤ Z ≤ 0.0717 nm−1 for M3, 0.0910 ≤ Z ≤ 0.0949 nm−1 for M4, 0.1143 ≤ Z ≤ 0.1182 nm −1 for M5 and 0.1375 ≤ Z ≤ 0.1414 nm−1 for M6 in the relaxed state, while the corresponding ranges in the contracting state were smaller by ∼1.6% than those of the relaxed state due to the elongation of the thick filaments. These ranges were determined to cover the range of the intensity profile contributing to the integrated intensity of the meridional reflections (see Figure 5). In the present simulation, we used nine or ten observed intensity data and two experimental conditions for optimization of 11 parameters, and the final models were assessed by the least-squares fitting (Rpr-factor) between the observed and calculated intensity profiles. The first stage of fitting only to the integrated intensities has fewer observables than parameters, so this stage of the fitting may be under-determined. Inclusion of the peak shape information as observables in the second stage of the simulation, however, ensured that overall fitting process was not under-determined. Calculation of projected densities of myosin head pairs of crossbridges using the crystal structure of a myosin head For the projected densities of crossbridges in the regular and perturbed regions of the myosin filaments in modeling, we constructed the axial density distributions of crossbridges in the relaxed and contracting states by calculating the mass projection of pairs of the crystallographically determined structure of a chicken skeletal muscle myosin subfragment 1 (S1) (PDB ID 2MYS),38 because the crystal structure of the muscle frog myosin S1 has not been determined. A chicken myosin head consists of 1072 Cα atoms. The Cα atoms of each head in a pair were translated so that the origin of Cartesian coordinates was placed at the Cα of Pro 840, which resides close to the

joint of two heads of a myosin molecule. The two heads were assumed to be in contact at their innermost ends. The simulation started from the structure of a two-headed myosin molecule obtained by energy minimization as reported by Offer and Knight.73 To reduce computation time, a set of ∼16 Cα atoms in an S1 was grouped and approximated by one equivalent sphere, similar to what was done by Al-Khayat et al.,39 resulting in an S1 consisting of 68 spheres (referred to as the 68-sphere model of S1). In the calculation, the density of each sphere was expressed as a Gaussian function with 2σ of 0.72 nm. A correlation coefficient between the computed Fourier transform of a myosin filament constructed using the 68-sphere model of S1 and that of the 1072 Cα model was 0.999 in the present meridional fitting region. The long axis connecting the center of the mass density of S1 and the joint (Pro840) of a pair of two S1 molecules passed through the z-axis in the initial structure (Figure 12(a)). The z-axis was assumed to be parallel with the filament axis, onto which the mass projection of two-headed crossbridges was performed. The myosin heads were rotated around the x, y and long axes, respectively, without changing the internal structure in the ranges; 0 ≤ α ≤ 90°, 0 ≤ β ≤ 90° and 0 ≤ γ ≤ 360°. Thereafter, the mass projection onto the z-axis was derived by summing the projected densities of the Gaussians. The calculated mass projection was plotted in 0.1 nm units and the variation step-size of the rotation was 15°. The resulting mass projection onto the z-axis was then compared with the experimentally determined mass projections. Optimization of the fit between the experimentally determined and the calculated mass projections was carried out by the procedure employed above. Finally, we recalculated the intensity profile of the meridional reflections using the 68sphere model of S1 in order to refine the axial configuration of myosin crossbridges. Determination of the orientation parameters of a resting crossbridge around the z-axis Since the orientation of a crossbridge around the z-axis parallel with the filament axis cannot be determined from intensity analysis of the meridional reflections, we used the intensities of the myosin-based layer-lines from overstretched muscles in the relaxed state, which contained much less lattice sampling than at full-overlap lengths, to determine the orientation of a crossbridge with respect to the z-axis by rotating each myosin head of a crossbridge independently around this axis. Off-meridional parts of layer-lines involve no contribution from the backbone structure, because frog skeletal muscles in rigor at any sarcomere length show no indication of off-meridional reflections.11–13,43 Similar analysis of contracting muscle data could not be done, because the intensities of the myosin-based layer-lines were too weak to measure during contraction. In this calculation, we used the intensity data of the myosin layer-line reflections, from which the influence of the sampling by the hexagonal array of the thick filaments was largely eliminated (see Results). The simulation started from the best-fit structural model of a thick filament obtained by incrementally fitting the myosin-based meridional reflections using the 68-sphere model of S1. The calculation is somewhat complicated, because the structure of a myosin crossbridge differs in the regular and perturbed regions (see below). In the present study, an idealized helical symmetry of the myosin molecules in the filaments was assumed, except in the perturbed region; in frog skeletal muscle, three successive crossbridges consisting of two myosin heads in pairs per

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Myosin Filaments in Vertebrate Skeletal Muscle

Figure 12. Representation of a two-headed myosin crossbridge in terms of a 68-sphere model of S1 (ID 2MYS). (a) The volume of these spheres, each having a radius of 0.72 nm is chosen to produce the overall structure of a two-headed portion of a crossbridge. The z-axis is parallel with the filament axis. The two heads of a crossbridge are rotated independently around the x, y and long axes by α, β and γ, respectively, in the simulation of the density of a crossbridge projected onto the filament axis. (b) The two heads of a crossbridge are rotated around the z-axis by ε, respectively, in the simulation of the intensities of the layer-lines in the relaxed state. Thin actin filaments sit towards the positive direction of the y-axis and the backbone of a myosin filament orients in the negative direction of the y-axis. Note that the z-axis is different from the filament axis, because the z-axis passes through the joint of two heads, although being parallel with the filament axis, while the filament axis passes through the center of the thick filament. crown are arrayed to form a three-stranded helix with a helical repeat of ∼129 nm with an axial rise of ∼14.3 nm and nine crown levels within the helical repeating unit.10 In the perturbed region, it was assumed for simplicity that each level in the three successive crowns deviates only axially from the regular disposition, and this set of crowns was treated as a unit cell that is helically arranged. Therefore, each level of crossbridges rotates azimuthally by 40° when going to the next crown level in both regions. In this simulation, the rotation angle (ε) of each head around the z-axis in each region was allowed to vary and the other parameters were fixed. The variation step-size of the rotation angles in the fitting process was 15°. The range over which the rotation angles were allowed to vary was restricted, so that each of the long axes connecting the mass center of S1 and the joint (Pro840) directs towards the side of the thin filaments (Figure 12(b)). Using equations (A4)–(A6) of the Fourier-Bessel transform74,75 of the model in the Appendix, the layer-line intensity calculations were carried out up to the M6 layerline (∼0.142 nm−1) in the axial direction and up to 0.157 nm−1 in the radial direction where the intensity measurements were done. Only 3n (n, integers) order Bessel functions contribute to every layer-line due to the 3fold rotational symmetry of the thick filament of vertebrate skeletal muscles. All 3n order Bessel functions also govern all of the layer-line intensities due to the axial perturbation of the crossbridge arrangement, causing a ladder-like appearance in the X-ray diffraction pattern. Bessel functions up to the ninth order were taken into consideration in the calculation because higher-order Bessel functions contribute little to the layer-line intensities in the range of R < 0.157 nm−1. The radius of the helical arrangement of the crossbridges but with the two heads at different radii was varied around ∼12.6 nm, which was estimated from the cylindrically averaged difference Patterson function calculated from the observed layer-line intensity data (see Results).45 The calculated intensity distribution of each layer-line (Ii,calc(R)) was derived by axial integration of I(R, Z) in the same axial range as was done in intensity profile fitting, and was plotted in radial intervals of 4.24 × 10−3 nm−1. For this modeling calculation, we used all the intensities on the layer-lines except for a region of R < 0.0254 nm−1 close to the meridian, where the intensities were affected by the residual sampling by the hexagonal filament array and by structures within the backbone.

Goodness of the simulation was assessed in the above range of the radial coordinate by the Rl-factor defined as: 6 Z 0:157 X jIi;obs ðRÞ  scl Ii;calc ðRÞj dR R1 ¼

i¼1

0:0254

6 Z X i1

6 Z X

Scl ¼

i¼1

6 Z X i¼1

0:157

Ii;obs ðRÞdR

0:0254 0:157

ð8Þ Ii;obs ðRÞdR

0:0254 0:157

Ii;calc ðRÞdR

0:0254

in which scl is a scale factor and the summation of i is performed over M1–M6 (first to sixth-order) layer-lines. The best structure was obtained by searching for a model giving the lowest value of the Rl-factor, where Ii,obs(R) is the observed intensity distribution of the ith layer-line. It is unlikely that the crossbridges are positioned precisely with no form of disorder. Since the effect of disorder introduced by small random movements is just to decrease the intensity of the outer parts of the X-ray diffraction pattern, the models described here contained no provision for disorder effects.

Acknowledgements The authors thank Dr H. Tanaka for his continuous help with physiological and X-ray experiments at the Photon Factory and Dr D. B. Gore and other members of the BioCAT staff for their help in setting the optics at the Advanced Photon Source. This work was approved by the Photon Factory Advisory Committee, and supported, in part, by the Special Coordination Funds from the Ministry of Education, Science, Sports and Culture of Japan. Use of the Advanced Photon Source was supported by the US Department of Energy, Basic Energy Sciences, Office of Energy Research, under contract no. W-31-109-ENG-38. BioCAT is an NIH-supported Research Center (RR08630).

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Appendix A All calculations were made using cylindrical coordinates (r, ϕ, z) in real space where the z-axis is parallel to the fiber axis. Fourier transforms F(R,Φ,Z) in cylindrical coordinates in reciprocal space (R,Φ,Z) were calculated using the following equation:74,75 X FðR; A; ZÞ ¼ F ðR; ZÞexpðin AÞ ðA1Þ n n where Fn(R,Z) is written by: n k o X  Fn ðR; ZÞ ¼ j exp in  fj fj ðR; ZÞJn 2krj R 2   exp 2kizj Zexpð2kizj ZÞ ðA2Þ in which fj (R,Z) is the atomic scattering factor of the jth atom, rj, ϕj, zj are cylindrical coordinates of the jth atom and Jn(2πrjR) is the nth order Bessel function of argument 2πrjR. The sum of n up to the ninth order was taken into consideration. The cylindrically averaged intensity was then calculated as the sum of the squares of the absolute values of the Fourier transform:74,75 X hIðR; A; ZÞiA ¼ IðR; ZÞ ¼ jF ðR; ZÞj2 ðA3Þ n n The myosin filaments were assumed to have a mixed structure with two different axial periodicities of the crossbridge arrangement when their structures are projected onto the fiber axes. The filament backbone itself was a structureless cylinder with a finite length (1.46 μm). The cylindrically averaged intensity is then written by: X jF ðR; ZÞ þ Fpn ðR; ZÞ IðR; ZÞ ¼ n rn þ Fb ðR; ZÞj2

ðA4Þ

where Frn(R,Z) is the structure factor of the regular region of which the projected density has a 14.3 nm periodicity and Fpn(R,Z) is that of the perturbed region of which the projected density has a 42.9 nm periodicity. Fb(R,Z) is the structure factor of a backbone and was neglected in the calculation of the offmeridional layer-line intensities because the uniform cylinder with a finite length contributes only to the low-angle region. Under the condition that crossbridge structures in the inner and outer regular regions are identical, Frn(R,Z) and Fpn(R,Z) are written by: n k o X  Frn ðR; ZÞ ¼ 2 jr exp in  fjr fjr ðR; ZÞJn 2krjr R 2

  sinðkNr1 cZÞ  cos k 2zjr þ Cr1 Z sinðkcZÞ   sinðkNr2 cZÞ þ cos k 2zjr þ Cr2 Z sinðkcZÞ ðA5Þ n k o X Fpn ðR; ZÞ ¼ 2 jp exp in  fjp fjp ðR; ZÞ 2 sinðkNp cZÞ     Jn 2krjp R cos k 2zjp þ Cp Z sinðkcZÞ ðA6Þ where Nr1·c and Nr2·c are the lengths of the inner and outer regular regions in a half thick filament in the

sarcomere, respectively, and Np·c is the length of the perturbed region and c is the crystallographic period (42.9 nm in the relaxed state or 43.5 nm in the contracting state). Cr1, Cr2 and Cp are the center-tocenter distances between the inner regular regions,the outer regular regions, and the perturbed regions, respectively. The atomic scattering factors (fjr(R,Z) and fjp(R,Z)) for each atom in the regular and perturbed regions were approximated by the normalized form factor of the sphere having a Gaussian density distribution by: f ðR; ZÞ ¼ expð2k2 j2 ðR2 þ Z2 ÞÞ

ðA7Þ

where 2σ corresponds to a half of the diameter of the sphere. When the 68-sphere model of S1 is used, the value of 2σ was 0.72 nm. The intensities of the meridional reflections were calculated from Frn(R,Z) and Fpn(R,Z) at R = 0 and with n = 0 because only the zero-order Bessel function contributes to the meridional reflections and from the form factor (Fb(R,Z)) of the backbone at R = 0:

 sinðkNr1 cZÞ Ms1X Z f ð 0; Z Þ cos k 2z þC Fr0ð0; ZÞ¼ jr r1 jr sinðkcZÞ 34

  sinðkNr2 cZÞ þcos k 2zjr þ Cr2 Z sinðkcZÞ ðA8Þ Fp0 ð0; ZÞ ¼ 

  Ms1 X f ð0; ZÞcos k 2zjp þ Cp Z jp 34

sinðkNp cZÞsinðkNp cZÞ  sinðkcZÞ sinðkcZÞ Fb ð0; ZÞ ¼

3Mrod sinðkLZÞ kZ c

ðA9Þ ðA10Þ

in which Ms1 is the molecular mass of an S1 (130 kDa) and Mrod is that of the rod portion of S1 (210 kDa) and L is the length of the backbone (=2(Nr1 + Np + Nr2)c). When the density of a two-headed crossbridge projected onto the fiber axis was approximated by two Gaussian functions (Gaussian model) in integrated intensity fitting, equations (A8) and (A9) may be greatly simplified as described below. The Fourier transform of the structure of the regular region Frn(R, Z) at R = 0 and with n = 0 is written by:

 2 2 2 Ms1 k ar Z Fr0ð0; ZÞ¼ exp 34 8 sinðklcr ZÞ  cosfkðCr1 þ dr ÞZg sinðkcr ZÞ  2 2 2 k br Z sinðklcr ZÞ þexp cosfkðCr1  dr ÞZg sinðkcr ZÞ 8  2 2 2 k ar Z sinðkmcr ZÞ þexp cosfkðCr2 þ dr ÞZg sinðkcr ZÞ 8  2 2 2

k br Z sinðkmcr ZÞ þexp cosfkðCr2  dr ÞZg sinðkcr ZÞ 8 ðA11Þ

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where cr is a 14.3 nm repeat, l and m are the numbers of the crowns in the inner and outer regular regions in a half thick filament in the sarcomere, respectively, ar and br are the widths (4σ) of the density of a head projected onto the fiber axis and dr is the distance between paired heads of a crossbridge in the regular region. On the assumption that the projected densities of crossbridges in the triplet are identical, the Fourier transform of the structure in the perturbed region Fpn (R,Z) at R = 0 and with n = 0 is written as:

  k2 a2p Z2 Ms1 Fp0 ð0; ZÞ ¼ exp 34 8  cos  cos ½k½fkCfpC 2ðc 2ðc y1yÞ1þ Þ þdpdgZ p r r p Z   þ cos k Cp þ dp Z     sinðkkcZÞ þ cos k Cp þ 2ðcr þ y2 Þ þ dp Z sinðkcZÞ   k2 b2p Z2    þ exp cos k Cp  2ðcr  y1 Þ  dp Z   8 þ cos k Cp  dp Z

    sinðkkcZÞ þ cos k Cp þ 2ðcr þ y2 Þ  dp Z sinðkcZÞ ðA12Þ where 3k is the number of the crowns in the perturbed region, ap and bp are the widths (4σ) of the density of a head projected onto the fiber axis, dp is the distance between the mass centers of two heads of a crossbridge, and δ1 and δ2 are the deviations of crown levels from the regular repeat within the unit cell in the perturbed region.

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Edited by M. Moody (Received 28 July 2006; received in revised form 9 December 2006; accepted 12 December 2006) Available online 19 December 2006