X-ray study of myosin heads in contracting frog skeletal muscle

Using synchrotron radiation, the behaviour of the diffuse X-ray scatter was investigated in the relaxed and active phases of auxotonic and isometric contractions. Muscles were stimulated tetanically for 0.75 of a second, leaving intervals of three minutes between successive contractions. In isometric contractions the scatter is very asymmetric, which means that the myosin heads have a strongly preferred orientation. During tension rise the scatter expands in the meridional direction and contracts in the equatorial direction, the maximal local intensity change being about 20%. The shape change indicates that on average the myosin heads become oriented more perpendicularly to the fibre axis. The distribution of orientations at peak tension is quite different from that we found previously in X-ray scattering data from rigor muscles. In auxotonic contractions where muscles shorten against an increasing tension the scatter is practically circularly symmetrical. This suggests that during shortening the myosin heads go evenly through a wide range of orientations. It is concluded that the results from both the auxotonic and isometric experiments provide strong support for the rotating myosin head model. In isometric contractions the transition between the relaxed phase and peak tension is accompanied by an overall increase in scattering intensity of about 10%: this corresponds to a relative increase in the fraction of disordered myosin heads by almost 30%.     

X-ray studies of order-disorder transitions in the myosin heads of skinned rabbit psoas muscles.

Using x-rays from a laboratory source and an area detector, myosin layer lines and the diffuse scattering between them in the moderate angle region have been recorded. At full overlap, incubation of rigor muscles with S-1 greatly reduces the diffuse scattering. Also, three of the four actin-based layer lines lying close to the meridian (Huxley, H. E., and W. Brown, 1967. J. Mol. Biol. 30:384-434; Haselgrove, J. C. 1975. J. Mol. Biol. 92:113-143) increase, suggesting fuller labeling of the actin filaments. These results are consistent with the idea (Poulsen, F. R., and J. Lowy, 1983. Nature [Lond.]. 303:146-152) that some of the diffuse scattering in rigor muscles is due to a random mixture of actin monomers with and without attached myosin heads (substitution disorder). In relaxed muscles, regardless of overlap, lowering the temperature from 24 to 4 degrees C practically abolishes the myosin layer lines (a result first obtained by Wray, J.S. 1987. J. Muscle Res. Cell Motil. 8:62 (a). Abstr.), whilst the diffuse scattering between these layer lines increases appreciably. Similar changes occur in the passage from rest to peak tetanic tension in live frog muscle (Lowy, J., and F.R. Poulsen. 1990. Biophys. J. 57:977-985). Cooling the psoas demonstrates that the intensity relation between the layer lines and the diffuse scattering is of an inverse nature, and that the transition occurs over a narrow temperature range (12-14 degrees C) with a sigmoidal function. From these results it would appear that the helical arrangement of the myosin heads is very temperature sensitive, and that the disordering effect does not depend on the presence of actin. Measurements along the meridian reveal that the intensity of the diffuse scattering increases relatively little and does so in a nearly linear manner: evidently the axial order of the myosin heads is much less temperature sensitive. The combined data support the view (Poulsen, F. R., and J. Lowy. 1983. Nature [Lond.]. 303:146-152) that in relaxed muscles a significant part of the diffuse scattering originates from disordered myosin heads. The observation that the extent of the diffuse scattering is greater in the equatorial than in the meridional direction suggests that the disordered myosin heads have an orientation which is on average more parallel to the filament axis.     

The M.ADP.P(i) state is required for helical order in the thick filaments of skeletal muscle

The thick filaments of mammalian and avian skeletal muscle fibers are disordered at low temperature, but become increasingly ordered into an helical structure as the temperature is raised. Wray and colleagues (Schlichting, I., and J. Wray. 1986. J. Muscle Res. Cell Motil. 7:79; Wray, J., R. S. Goody, and K. Holmes. 1986. Adv. Exp. Med. Biol. 226:49-59) interpreted the transition as reflecting a coupling between nucleotide state and global conformation with M.ATP (disordered) being favored at 0 degrees C and M.ADP.P(i) (ordered) at 20 degrees C. However, hitherto this has been limited to a qualitative correlation and the biochemical state of the myosin heads required to obtain the helical array has not been unequivocally identified. In the present study we have critically tested whether the helical arrangement of the myosin heads requires the M.ADP.P(i) state. X-ray diffraction patterns were recorded from skinned rabbit psoas muscle fiber bundles stretched to non-overlap to avoid complications due to interaction with actin. The effect of temperature on the intensities of the myosin-based layer lines and on the phosphate burst of myosin hydrolyzing ATP in solution were examined under closely matched conditions. The results showed that the fraction of myosin mass in the helix closely followed that of the fraction of myosin in the M.ADP.P(i) state. Similar results were found by using a series of nucleoside triphosphates, including CTP and GTP. In addition, fibers treated by N-phenylmaleimide (Barnett, V. A., A. Ehrlich, and M. Schoenberg. 1992. Biophys. J. 61:358-367) so that the myosin was exclusively in the M.ATP state revealed no helical order. Diffraction patterns from muscle fibers in nucleotide-free and in ADP-containing solutions did not show helical structure. All these confirmed that in the presence of nucleotides, the M.NDP.P(i) state is required for helical order. We also found that the spacing of the third meridional reflection of the thick filament is linked to the helical order. The spacing in the ordered M.NDP.P(i) state is 143.4 A, but in the disordered state, it is 144. 2 A. This may be explained by the different interference functions for the myosin heads and the thick filament backbone.     

"Crystalline" myosin cross-bridge array in relaxed bony fish muscle. Low-angle x-ray diffraction from plaice fin muscle and its interpretation

Detailed structural analysis of muscles normally used to study myosin cross-bridge behavior (e.g., frog sartorius muscle, insect flight muscle) is extremely difficult due to the statistical disorder inherent in their myosin filament arrays. Bony fish muscle is different from all other muscle types in having a myosin filament (A-Band) array with good three-dimensional (crystalline) regularity that is coherent right across each myofibril. Rigorous structure analysis is feasible with fish muscle. We show that low-angle x-ray diffraction patterns from plaice fin muscle contain characteristic vertebrate layer lines at orders of 429 (+/- 0.2) A, that these layer lines are well sampled by row-lines from a simple hexagonal lattice of a-spacing 470 (+/- 2.0) A at rest length and that there are meridional reflections, due to axial perturbations of the basic helix of myosin heads, similar in position to those from frog muscle but differing in relative intensities. Clear trends based on modeling to a resolution of 130 A of the observed intensities in the low angle x-ray diffraction pattern from relaxed plaice fin muscle suggest that: (a) the pattern out to 130 A is more sensitive to the distribution of the two heads than it is to details of the head shape, (b) both heads in one myosin molecule probably tilt axially in the same direction by approximately 20-40 degrees relative to a normal to the thick filament backbone, (c) the center of mass of the heads is at 145 to 160 A radius, and (d) the two heads form a compact structure by lying closely adjacent to each other and almost parallel. Little rotational disorder of the heads can occur. Because of its crystallinity, bony fish muscle provides a uniquely useful structural probe of myosin cross-bridge behavior in other muscle states such as rigor and active contraction.     

Comparison of Orientation and Rotational Motion of Skeletal Muscle Cross-bridges Containing Phosphorylated and Dephosphorylated Myosin Regulatory Light Chain

Calcium binding to thin filaments is a major element controlling active force generation in striated muscles. Recent evidence suggests that processes other than Ca²⁺ binding, such as phosphorylation of myosin regulatory light chain (RLC) also controls contraction of vertebrate striated muscle (Cooke, R. (2011) Biophys. Rev. 3, 33–45). Electron paramagnetic resonance (EPR) studies using nucleotide analog spin label probes showed that dephosphorylated myosin heads are highly ordered in the relaxed fibers and have very low ATPase activity. This ordered structure of myosin cross-bridges disappears with the phosphorylation of RLC (Stewart, M. (2010) Proc. Natl. Acad. Sci. U.S.A. 107, 430–435). The slower ATPase activity in the dephosporylated moiety has been defined as a new super-relaxed state (SRX). It can be observed in both skeletal and cardiac muscle fibers (Hooijman, P., Stewart, M. A., and Cooke, R. (2011) Biophys. J. 100, 1969–1976). Given the importance of the finding that suggests a novel pathway of regulation of skeletal muscle, we aim to examine the effects of phosphorylation on cross-bridge orientation and rotational motion. We find that: (i) relaxed cross-bridges, but not active ones, are statistically better ordered in muscle where the RLC is dephosporylated compared with phosphorylated RLC; (ii) relaxed phosphorylated and dephosphorylated cross-bridges rotate equally slowly; and (iii) active phosphorylated cross-bridges rotate considerably faster than dephosphorylated ones during isometric contraction but the duty cycle remained the same, suggesting that both phosphorylated and dephosphorylated muscles develop the same isometric tension at full Ca²⁺ saturation. A simple theory was developed to account for this fact.     

Temperature-induced structural changes in the myosin thick filament of skinned rabbit psoas muscle.

By using synchrotron radiation and an imaging plate for recording diffraction patterns, we have obtained high-resolution x-ray patterns from relaxed rabbit psoas muscle at temperatures ranging from 1 degree C to 30 degrees C. This allowed us to obtain intensity profiles of the first six myosin layer lines and apply a model-building approach for structural analysis. At temperatures 20 degrees C and higher, the layer lines are sharp with clearly defined maxima. Modeling based on the data obtained at 20 degrees C reveals that the average center of the cross-bridges is at 135 A from the center of the thick filament and both of the myosin heads appear to wrap around the backbone. At 10 degrees C and lower, the layer lines become very weak and diffuse scattering increases considerably. At 4 degrees C, the peak of the first layer line shifts toward the meridian from 0.0047 to 0.0038 A(-1) and decreases in intensity approximately by a factor of four compared to that at 20 degrees C, although the intensities of higher-order layer lines remain approximately 10-15% of the first layer line. Our modeling suggests that as the temperature is lowered from 20 degrees C to 4 degrees C the center of cross-bridges extends radially away from the center of the filament (135 A to 175 A). Furthermore, the fraction of helically ordered cross-bridges decreases at least by a factor of two, while the isotropic disorder (the temperature factor) remains approximately unchanged. Our results on the order/disordering effects of temperature are in general agreement with earlier results of Wray [Wray, J. 1987. Structure of relaxed myosin filaments in relation to nucleotide state in vertebrate skeletal muscle. J. Muscle Res. Cell Motil. 8:62a (Abstr.)] and Lowy et al. (Lowy, J., D. Popp, and A. A. Stewart. 1991. X-ray studies of order-disorder transitions in the myosin heads of skinned rabbit psoas muscles. Biophys. J. 60:812-824). and support Poulsen and Lowy's hypothesis of coexistence of ordered and disordered cross-bridge populations in muscle (Poulsen, F. R., and J. Lowy. 1983. Small angle scattering from myosin heads in relaxed and rigor frog skeletal muscle. Nature (Lond.). 303:146-152.). However, our results added new insights into the disordered population. Present modeling together with data analysis (Xu, S., S. Malinchik, Th. Kraft, B. Brenner, and L. C. Yu. 1997. X-ray diffraction studies of cross-bridges weakly bound to actin in relaxed skinned fibers of rabbit psoas muscle. Biophys. J. 73:000-000) indicate that in a relaxed muscle, cross-bridges are distributed in three populations: those that are ordered on the thick filament helix and those that are disordered; and within the disordered population, some cross-bridges are detached and some are weakly attached to actin. One critical conclusion of the present study is that the apparent order <--> disorder transition as a function of temperature is not due to an increase/decrease in thermal motion (temperature factor) for the entire population, but a redistribution of cross-bridges among the three populations. Changing the temperature leads to a change in the fraction of cross-bridges located on the helix, while changing the ionic strength at a given temperature affects the disordered population leading to a change in the relative fraction of cross-bridges detached from and weakly attached to actin. Since the redistribution is reversible, we suggest that there is an equilibrium among the three populations of cross-bridges.     

Myosin Heads Contribute to the Maintenance of Filament Order in Relaxed Rabbit Muscle

Raising the temperature of rabbit skeletal muscle from ∼0°C to ∼20°C has been shown to enhance the helical organization of the myosin heads and to change the intensities of the 10 and 11 equatorial reflections. We show here by time-resolved x-ray diffraction combined with temperature jump that the movement of the heads to enhance the organized myosin helix occurs at the same fast rate as the change in the intensities of the equatorial reflections. However, model calculations indicate that the change in the equatorials cannot be explained simply in terms of the movement of myosin heads. Analysis of electron micrographs of transverse sections of relaxed muscle fibers cryofixed at ∼5°C and ∼35°C shows that in addition to the reorganization of the heads the thin and thick filaments are less constrained to their positions in the hexagonal filament lattice in the warm muscle than in the cold. Incorporating the changes in filament order in model calculations reconciles these with the observed changes in equatorial reflections. We suggest the thin filaments in the cold muscle are boxed into their positions by the thermal movement of the disordered myosin heads. In the warmer muscle, the packed-down heads leave the thin filaments more room to diffuse laterally.     

3D structure of relaxed fish muscle myosin filaments by single particle analysis

To understand the structural changes involved in the force-producing myosin cross-bridge cycle in vertebrate muscle it is necessary to know the arrangement and conformation of the myosin heads at the start of the cycle (i.e. the relaxed state). Myosin filaments isolated from goldfish muscle under relaxing conditions and viewed in negative stain by electron microscopy (EM) were divided into segments and subjected to three-dimensional (3D) single particle analysis without imposing helical symmetry. This allowed the known systematic departure from helicity characteristic of vertebrate striated muscle myosin filaments to be preserved and visualised. The resulting 3D reconstruction reveals details to about 55 A resolution of the myosin head density distribution in the three non-equivalent head 'crowns' in the 429 A myosin filament repeat. The analysis maintained the well-documented axial perturbations of the myosin head crowns and revealed substantial azimuthal perturbations between crowns with relatively little radial perturbation. Azimuthal rotations between crowns were approximately 60 degrees , 60 degrees and 0 degrees , rather than the regular 40 degrees characteristic of an unperturbed helix. The new density map correlates quite well with the head conformations analysed in other EM studies and in the relaxed fish muscle myosin filament structure modelled from X-ray fibre diffraction data. The reconstruction provides information on the polarity of the myosin head array in the A-band, important in understanding the geometry of the myosin head interaction with actin during the cross-bridge cycle, and supports a number of conclusions previously inferred by other methods. The observed azimuthal head perturbations are consistent with the X-ray modelling results from intact muscle, indicating that the observed perturbations are an intrinsic property of the myosin filaments and are not induced by the proximity of actin filaments in the muscle A-band lattice. Comparison of the axial density profile derived in this study with the axial density profile of the X-ray model of the fish myosin filaments which was restricted to contributions from the myosin heads allows the identification of a non-myosin density peak associated with the azimuthally perturbed head crown which can be interpreted as a possible location for C-protein or X-protein (MyBP-C or -X). This position for C-protein is also consistent with the C-zone interference function deduced from previous analysis of the meridional X-ray pattern from frog muscle. It appears that, along with other functions, C-(X-) protein may have the role of slewing the heads of one crown so that they do not clash with the neighbouring actin filaments, but are readily available to interact with actin when the muscle is activated.     

Studies of the diffuse x-ray scattering from contracting frog skeletal muscles.

Using x-rays from synchrotron radiation, we studied diffuse scattering, sometimes together with the myosin layer lines. With an area detector, sartorius muscles and a time resolution of 150 ms, earlier results from semitendinosus muscles contracting isometrically at 6 degrees C (Lowy, J., and F. R. Poulsen. 1987. J. Mol. Biol. 194:595-600) were confirmed and extended. Evidence from intensity changes both in the diffuse scattering and in the myosin layer lines showed that the majority of the heads become disordered at peak tetanic tension. With a linear detector and a time resolution of 5 ms, it was found that during tension rise the intensity increase of the diffuse scattering (which amounted maximally to 12% recorded near the meridian) runs approximately 20 ms ahead of the mechanical change, comparing half-completion times. This suggests that an appreciable number of heads change orientation before peak tension is reached. In quick release experiments the diffuse scattering intensity showed very little change. Recorded near the meridian during rapid shortening, however, it decreased progressively with a half-time of approximately 40 ms. This change amounted to approximately 35% of that observed during the initial tension rise. We interpret this to indicate that during rapid shortening a certain number of heads assume an orientation characteristic of the relaxed state. Viewed in the context of the behavior of the first myosin layer line and the (1, 1) equatorial reflection in similar experiments (Huxley, H. E., M. Kress, A. R. Faruqi, and R. M. Simmons. 1988.(ABSTRACT TRUNCATED AT 250 WORDS)     

Blebbistatin stabilizes the helical order of myosin filaments by promoting the switch 2 closed state

Blebbistatin is a small-molecule, high-affinity, noncompetitive inhibitor of myosin II. We have used negative staining electron microscopy to study the effects of blebbistatin on the organization of the myosin heads on muscle thick filaments. Loss of ADP and Pi from the heads causes thick filaments to lose their helical ordering. In the presence of 100 μM blebbistatin, disordering was at least 10 times slower. In the M·ADP state, myosin heads are also disordered. When blebbistatin was added to M·ADP thick filaments, helical ordering was restored. However, blebbistatin did not improve the order of thick filaments lacking bound nucleotide. Addition of calcium to relaxed muscle homogenates induced thick-thin filament interaction and filament sliding. In the presence of blebbistatin, filament interaction was inhibited. These structural observations support the conclusion, based on biochemical studies, that blebbistatin inhibits myosin ATPase and actin interaction by stabilizing the closed switch 2 structure of the myosin head. These properties make blebbistatin a useful tool in structural and functional studies of cell motility and muscle contraction.     

3D Structure of fish muscle myosin filaments

Myosin filaments isolated from goldfish (Carassius auratus) muscle under relaxing conditions and viewed in negative stain by electron microscopy have been subjected to 3D helical reconstruction to provide details of the myosin head arrangement in relaxed muscle. Previous X-ray diffraction studies of fish muscle (plaice) myosin filaments have suggested that the heads project a long way from the filament surface rather than lying down flat and that heads in a single myosin molecule tend to interact with each other rather than with heads from adjacent molecules. Evidence has also been presented that the head tilt is away from the M-band. Here we seek to confirm these conclusions using a totally independent method. By using 3D helical reconstruction of isolated myosin filaments the known perturbation of the head array in vertebrate muscles was inevitably averaged out. The 3D reconstruction was therefore compared with the X-ray model after it too had been helically averaged. The resulting images showed the same characteristic features: heads projecting out from the filament backbone to high radius and the motor domains at higher radius and further away from the M-band than the light-chain-binding neck domains (lever arms) of the heads.     

Temperature and ligand dependence of conformation and helical order in myosin filaments

Mammalian myosin filaments are helically ordered only at higher temperatures (>20 degrees C) and become progressively more disordered as the temperature is decreased. It had previously been suggested that this was a consequence of the dependence of the hydrolytic step of myosin ATPase on temperature and the requirement that hydrolysis products (e.g., ADP.P(i)) be bound at the active site. An alternative hypothesis is that temperature directly affects the conformation of the myosin heads and that they need to be in a particular conformation for helical order in the filament. To discriminate between these two hypotheses, we have studied the effect of temperature on the helical order of myosin heads in rabbit psoas muscle in the presence of nonhydrolyzable ligands. The muscle fibers were overstretched to nonoverlap such that myosin affinity for nucleotides was not influenced by the interaction of myosin with the thin filament. We show that with bound ADP.vanadate, which mimics the transition state between ATP and hydrolysis products, or with the ATP analogues AMP-PNP or ADP.BeF(x)() the myosin filaments are substantially ordered at higher temperatures but are reversibly disordered by cooling. These results reinforce recent studies in solution showing that temperature as well as ligand influence the equilibrium between multiple myosin conformations [Málnási-Csizmadia, A., Pearson, D. S., Kovács, M., Woolley, R. J., Geeves, M. A., and Bagshaw, C. R. (2001) Biochemistry 40, 12727-12737; Málnási-Csizmadia, A., Woolley, R. J., and Bagshaw, C. R. (2000) Biochemistry 39, 16135-16146; Urbanke, C., and Wray, J. (2001) Biochem. J. 358, 165-173] and indicate that helical order requires the myosin heads to be in the closed conformation. Our results suggest that most of the heads in the closed conformation are ordered, and that order is not produced in a separate step. Hence, helical order can be used as a signature of the closed conformation in relaxed muscle. Analysis of the dependence on temperature of helical order and myosin conformation shows that in the presence of these analogues one ordered (closed) conformation and two disordered conformations with distinct thermodynamic properties coexist. Low temperatures favor one disordered conformation, while high temperatures favor the ordered (closed) conformation together with a second disordered conformation.     

X-ray diffraction studies of the contractile mechanism in single muscle fibres

The molecular mechanism of muscle contraction was investigated in intact muscle fibres by X-ray diffraction. Changes in the intensities of the axial X-ray reflections produced by imposing rapid changes in fibre length establish the average conformation of the myosin heads during active isometric contraction, and show that the heads tilt during the elastic response to a change in fibre length and during the elementary force generating process: the working stroke. X-ray interference between the two arrays of myosin heads in each filament allows the axial motions of the heads following a sudden drop in force from the isometric level to be measured in situ with unprecedented precision. At low load, the average working stroke is 12 nm, which is consistent with crystallographic studies. The working stroke is smaller and slower at a higher load. The compliance of the actin and myosin filaments was also determined from the change in the axial spacings of the X-ray reflections following a force step, and shown to be responsible for most of the sarcomere compliance. The mechanical properties of the sarcomere depend on both the motor actions of the myosin heads and the compliance of the myosin and actin filaments.     

Probing Muscle Myosin Motor Action: X-Ray (M3 and M6) Interference Measurements Report Motor Domain Not Lever Arm Movement

The key question in understanding how force and movement are produced in muscle concerns the nature of the cyclic interaction of myosin molecules with actin filaments. The lever arm of the globular head of each myosin molecule is thought in some way to swing axially on the actin-attached motor domain, thus propelling the actin filament past the myosin filament. Recent X-ray diffraction studies of vertebrate muscle, especially those involving the analysis of interference effects between myosin head arrays in the two halves of the thick filaments, have been claimed to prove that the lever arm moves at the same time as the sliding of actin and myosin filaments in response to muscle length or force steps. It was suggested that the sliding of myosin and actin filaments, the level of force produced and the lever arm angle are all directly coupled and that other models of lever arm movement will not fit the X-ray data. Here, we show that, in addition to interference across the A-band, which must be occurring, the observed meridional M3 and M6 X-ray intensity changes can all be explained very well by the changing diffraction effects during filament sliding caused by heads stereospecifically attached to actin moving axially relative to a population of detached or non-stereospecifically attached heads that remain fixed in position relative to the myosin filament backbone. Crucially, and contrary to previous interpretations, the X-ray interference results provide little direct information about the position of the myosin head lever arm; they are, in fact, reporting relative motor domain movements. The implications of the new interpretation are briefly assessed.     

X-ray diffraction studies of the thick filament in permeabilized myocardium from rabbit

Low angle x-ray diffraction patterns from relaxed permeabilized rabbit cardiac trabeculae and psoas muscle fibers were compared. Temperature was varied from 25 degrees C to 5 degrees C at 200 mM and 50 mM ionic strengths (mu), respectively. Effects of temperature and mu on the intensities of the myosin layer lines (MLL), the equatorial intensity ratio I(1,1)/I(1,0), and the spacing of the filament lattice are similar in both muscles. At 25 degrees C, particularly at mu = 50 mM, the x-ray patterns exhibited up to six orders of MLL and sharp meridional reflections, signifying that myosin heads (cross-bridges) are distributed in a well-ordered helical array. Decreasing temperature reduced MLL intensities but increased I(1,1)/I(1,0). Decreases in the MLL intensities indicate increasing disorder in the distribution of cross-bridges on the thick filaments surface. In the skeletal muscle, order/disorder is directly correlated with the hydrolysis equilibrium of ATP by myosin, [M.ADP.P(i)]/[M.ATP]. Similar effects of temperature on MLL and similar biochemical ATP hydrolysis pathway found in both types of muscles suggest that the order/disorder states of cardiac cross-bridges may well be correlated with the same biochemical and structural states. This implies that in relaxed cardiac muscle under physiological conditions, the unattached cross-bridges are largely in the M.ADP.P(i) state and with the lowering of the temperature, the equilibrium is increasingly in favor of [M.ATP] and [A.M.ATP]. There appear to be some differences in the diffraction patterns from the two muscles, however. Mainly, in the cardiac muscle, the MLL are weaker, the I(1,1)/I(1,0) ratio tends to be higher, and the lattice spacing D(10), larger. These differences are consistent with the idea that under a wide range of conditions, a greater fraction of cross-bridges is weakly bound to actin in the myocardium.     

Direct modeling of X-ray diffraction pattern from contracting skeletal muscle

A direct modeling approach was used to quantitatively interpret the two-dimensional x-ray diffraction patterns obtained from contracting mammalian skeletal muscle. The dependence of the calculated layer line intensities on the number of myosin heads bound to the thin filaments, on the conformation of these heads and on their mode of attachment to actin, was studied systematically. Results of modeling are compared to experimental data collected from permeabilized fibers from rabbit skeletal muscle contracting at 5°C and 30°C and developing low and high isometric tension, respectively. The results of the modeling show that: i), the intensity of the first actin layer line is independent of the tilt of the light chain domains of myosin heads and can be used as a measure of the fraction of myosin heads stereospecifically attached to actin; ii), during isometric contraction at near physiological temperature, the fraction of these heads is ∼40% and the light chain domains of the majority of them are more perpendicular to the filament axis than in rigor; and iii), at low temperature, when isometric tension is low, a majority of the attached myosin heads are bound to actin nonstereospecifically whereas at high temperature and tension they are bound stereospecifically.     

Cooperative actions between myosin heads bring effective functions

A recent study with single molecule measurements has reported that muscle myosin, a molecular motor, stochastically generates multiple steps along an actin filament associated with the hydrolysis of a single ATP molecule [Kitamura, K., Tokunaga, M., Esaki, S., Iwane, A.H., Yanagida, T., 2005. Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro. Biophysics 1, 1-19]. We have built a model reproducing such a stochastic movement of a myosin molecule incorporated with ATPase reaction cycles and demonstrated that the thermal fluctuation was a key for the function of myosin molecules [Esaki, S., Ishii, Y., Yanagida, T., 2003. Model describing the biased Brownian movement of myosin. Proc. Jpn. Acad. 79 (Ser B), 9-14]. The size of the displacement generated during the hydrolysis of single ATP molecules was limited within a half pitch of an actin filament when a single myosin molecules work separately. However, in muscle the size of the displacement has been reported to be greater than 60 nm [Yanagida, T., Arata, T., Oosawa, F., 1985. Sliding distance of actin filament induced by a myosin crossbridge during one ATP hydrolysis cycle. Nature 316, 366-369; Higuchi et al., 1991]. The difference suggests cooperative action between myosin heads in muscle. Here we extended the model built for an isolated myosin head to a system in which myosin heads are aligned in muscle arrangement to understand the cooperativity between heads. The simulation showed that the rotation of the actin filament [Takezawa, Y., Sugimoto, Y., Wakabayashi, K., 1998. Extensibility of the actin and myosin filaments in various states of skeletal muscles as studied by X-ray diffraction. Adv. Exp. Med. Biol. 453, 309-317; Wakabayashi, K., Ueno, Y., Takezawa, Y., Sugimoto, Y., 2001. Muscle contraction mechanism: use of X-ray synchrotron radiation. Nat. Enc. Life Sci. 1-11] associated with the release of ATPase products and binding of ATP as well as interaction between myosin heads allowed the myosin filament to move greater than a half pitch of the actin filament while a single ATP molecule is hydrolyzed. Our model demonstrated that the movement is loosely coupled to the ATPase cycle as observed in muscle.     

Application of potential energy calculations to the determination of muscle structure from X-ray data with special reference to the configuration of myosin heads

A method that relates molecular structure to the forces that maintain it and to its X-ray diffraction pattern is described and applied to muscle. In a computer model, the potential energy of the moveable components (here the myosin heads) is minimized by letting them move down the steepest gradient in three dimensions from a variety of starting positions. Initial values are assumed for the parameters that determine the forces, and for those that define the structure and arrangement of the fixed components. The X-ray pattern expected from the resulting structures can be calculated in a straightforward manner and compared with relevant observed data. Discrepancies can then be minimized by varying the values initially assumed for the parameters, as in the conventional “trial and error” method.This first application of the present method is concerned with the effects of the hexagonal lattice on the myosin head configuration in thick filaments of the type found in vertebrate skeletal muscle. For that purpose, a very simple model was used with the following main features: smooth cylinders for the thin filaments and for the thick filament backbones, two spherical heads attached by Hookean springs to each point of a $\text{9}\text{3}$ helix on the surface of the backbone, and repulsive forces of the electrostatic double-layer type acting between each head and all other surfaces.The myosin head configuration was calculated for an isolated thick filament and a study was made of the effects of packing such filaments into a hexagonal lattice of various side spacings in the presence or absence of thin filaments. For the isolated filament, it was found that the $\text{9}\text{3}$ helical symmetry is maintained in the myosin head configuration and that the two heads of each molecule are splayed azimuthally. When such filaments are packed into the hexagonal lattice with thin filaments present, the $\text{9}\text{3}$ helical symmetry of the myosin head configuration is lost. As the lattice side spacing is reduced, the myosin heads become increasingly displaced not only in the radial and azimuthal directions but also in the axial direction, although they interact primarily with smooth cylinders. The axial separation of the two heads in each molecule becomes different in one level from that in the other two in the 43 nm axial repeat, thus increasing the repeat in projection onto the axis from 14.3 to 43 nm. This effect may contribute to the “forbidden meridionals” described by Huxley & Brown (1967). In the absence of thin filaments, the displacements of the myosin heads are much smaller, even when the lattice side spacing is reduced to that present in muscles stretched to non-overlap.Applying the method based on potential energy minimization to the evaluation of X-ray data from muscles in hypertonic Ringer reveals that, even in the case of patterns apparently free of lattice sampling (and thus normally considered to represent diffraction from single filaments), the interpretation must include the nearest myosin heads from neighbouring filaments, and that this may be necessary also for unsampled patterns obtained from muscles in normal Ringer. Furthermore, the method helps to explain several other major features of X-ray results obtained from muscles in the hypertonic state and from muscles stretched in normal Ringer to long sarcomere lengths including non-overlap. It is concluded that the method provides a powerful tool for the interpretation of muscle X-ray patterns.     

X-ray interference studies of crossbridge action in muscle contraction: evidence from quick releases

We have used a high-resolution small angle X-ray scattering system, together with a high-performance CCD camera, on the BioCAT beamline at the APS synchrotron radiation facility at the Argonne National Laboratory, to study X-ray interference effects in the meridional reflections generated by the arrays of myosin crossbridges in contracting muscle. These give information about axial movements of the myosin heads during contraction with sub-nanometer resolution. Using whole intact muscle preparations (frog sartorius) we have been able to record the detailed behavior of M3 (the first order meridional reflection from the myosin crossbridges, at 14.56 nm) at each of a number of quick releases of increasing magnitude, on the same specimen, and at the same time make similar measurements on higher order myosin meridional reflections, particularly M6. The latter provides information about the dispersion of lever arm angles of the actin-attached myosin heads. The observations show that in isometric contraction the lever arm angles are dispersed through +/- 20-25 degrees on either side of a mean orientation that is about 60 degrees away from their orientation at the end of the working stroke: and that they move towards that orientation in synchronized fashion, with constant dispersion, during quick releases. The relationship between the shift in the interference fringes (which measures the shift of the myosin heads scattering mass towards the center of the sarcomere, and the changes in the total intensity of the reflections, which measures the changes in the axial profile of the heads, is consistent with the tilting lever arm mechanism of muscle contraction. Significant fixed contributions to the meridional reflections come from unattached myosin heads and from backbone components of the myosin filaments, and the interaction of these with the contributions from actin-attached myosin heads determines the behavior of these reflections.