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.     

Strong binding of myosin heads stretches and twists the actin helix

Calculation of the size of the power stroke of the myosin motor in contracting muscle requires knowledge of the compliance of the myofilaments. Current estimates of actin compliance vary significantly introducing uncertainty in the mechanical parameters of the motor. Using x-ray diffraction on small bundles of permeabilized fibers from rabbit muscle we show that strong binding of myosin heads changes directly the actin helix. The spacing of the 2.73-nm meridional x-ray reflection increased by 0.22% when relaxed fibers were put into low-tension rigor (<10 kN/m(2)) demonstrating that strongly bound myosin heads elongate the actin filaments even in the absence of external tension. The pitch of the 5.9-nm actin layer line increased by approximately 0.62% and that of the 5.1-nm layer line decreased by approximately 0.26%, suggesting that the elongation is accompanied by a decrease in its helical angle (approximately 166 degrees) by approximately 0.8 degrees. This effect explains the difference between actin compliance revealed from mechanical experiments with single fibers and from x-ray diffraction on whole muscles. Our measurement of actin compliance obtained by applying tension to fibers in rigor is consistent with the results of mechanical measurements.     

Structural changes of actin-bound myosin heads after a quick length change in frog skeletal muscle

Changes in the x-ray diffraction pattern from a frog skeletal muscle were recorded after a quick release or stretch, which was completed within one millisecond, at a time resolution of 0.53 ms using the high-flux beamline at the SPring-8 third-generation synchrotron radiation facility. Reversibility of the effects of the length changes was checked by quickly restoring the muscle length. Intensities of seven reflections were measured. A large, instantaneous intensity drop of a layer line at an axial spacing of 1/10.3 nm(-1) after a quick release and stretch, and its partial recovery by reversal of the length change, indicate a conformational change of myosin heads that are attached to actin. Intensity changes on the 14.5-nm myosin layer line suggest that the attached heads alter their radial mass distribution upon filament sliding. Intensity changes of the myosin reflections at 1/21.5 and 1/7.2 nm(-1) are not readily explained by a simple axial swing of cross-bridges. Intensity changes of the actin-based layer lines at 1/36 and 1/5.9 nm(-1) are not explained by it either, suggesting a structural change in actin molecules.     

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.     

The "roll and lock" mechanism of force generation in muscle

Muscle force results from the interaction of the globular heads of myosin-II with actin filaments. We studied the structure-function relationship in the myosin motor in contracting muscle fibers by using temperature jumps or length steps combined with time-resolved, low-angle X-ray diffraction. Both perturbations induced simultaneous changes in the active muscle force and in the extent of labeling of the actin helix by stereo-specifically bound myosin heads at a constant total number of attached heads. The generally accepted hypothesis assumes that muscle force is generated solely by tilting of the lever arm, or the light chain domain of the myosin head, about its catalytic domain firmly bound to actin. Data obtained suggest an additional force-generating step: the "roll and lock" transition of catalytic domains of non-stereo-specifically attached heads to a stereo-specifically bound state. A model based on this scheme is described to quantitatively explain the data.     

Structure of insect fibrillar flight muscle in the presence and absence of ATP

Low-angle X-ray diffraction pictures were taken of Lethocerus flight muscle in one or other of its two inactive states, relaxation and rigor. They showed more detail than previous pictures and the parameters of the actin and myosin helices could be deduced from the spacings of the observed layer lines. Subunits consisting of actin monomers and of myosin heads were arranged on helices so as to conform to these parameters, and the diffraction patterns from these models were calculated. When these model systems resembled the structures observed in the electron microscope, the calculated diffraction patterns had layer Unes similar in radial distribution and relative intensity to those observed, with certain exceptions. The fit was quite critical, in that variation of the size and orientation of the subunits affected it considerably. The results support the idea that in rigor (i.e. without ATP) all of the myosin heads attach to actin monomers in a regular angled configuration. In contrast, on relaxation (i.e. on addition of ATP but no Ca²⁺) most or all of the myosin heads detach from the actin and are arranged with a specific symmetry around the myosin filament. It is not necessary, however, to assume that they change shape or move far from the actin filament in this process. Features of the X-ray diffraction pattern which remained unaccounted for by this model can be explained on the basis of an arrangement of actin helices on a further helix around a thick filament. Types of extended lattices containing actin helices in statistical axial or azimuthal positions are discussed.     

Energetics of the actomyosin bond in the filament array of muscle fibers.

The interaction between actin and myosin in the filament array of glycerinated muscle fibers has been monitored using paramagnetic probes and mechanical measurements. Both fiber stiffness and the spectra of probes bound to a reactive sulfydral on the myosin head were measured as the actomyosin bond was weakened by addition of magnesium pyrophosphate (MgPPi) and glycerol. In the absence of MgPPi, all myosin heads are attached to actin with oriented probes. When fibers were incubated in buffers containing MgPPi, a fraction of the probes became disordered, and this effect was greater in the presence of glycerol. To determine whether the heads with disordered probes were detached from actin, spin-labeled myosin subfragment-1 (MSL-S1) was diffused into unlabeled fibers, and the fractions bound to actin and free in the medium were correlated with the oriented and disordered spectral components. These experiments showed that the label was oriented when MSL-S1 was attached to actin in a ternary complex with the ligand and that all heads with disordered probes were detached from actin. Thus the fraction of oriented labels could be used to determine the fraction of heads attached to actin in a fiber in the presence of ligand. The fraction of myosin heads attached to actin decreased with increasing [MgPPi], and in the absence of glycerol approximately 50% of the myosin heads were dissociated at 3.3 mM ligand with little change in fiber stiffness. In the presence of 37% glycerol plus ligand, up to 80% of the heads could be detached with a 50% decrease in fiber stiffness. The data indicate that there are two populations of myosin heads in the fiber. All the data could be fit with a model in which one population of myosin heads (comprising approximately 50% of the total) sees an apparent actin concentration of 0.1 mM and can be released from actin with little change in fiber stiffness. A second population of myosin heads (approximately 50%) sees a higher actin concentration (5 mM) and is only released in the presence of both glycerol and ligand.     

The influence of filament elasticity on transients after sudden alteration of length of muscle or load

The duration of phase 2 of a transient after sudden reduction of the length of a muscle or a load on it decreases rapidly with increasing amplitude of the jump. This is mainly due to the increasing role of the superfast relaxation processes with a characteristic time of about 0.1 ms. Mainly in order to explain this effect, Huxley and Simmons proposed their famous model of force generation in 1971. The present paper examines the effect of elasticity of filaments on relaxation processes. It is shown that if the filaments are not perfectly elastic, the superfast tension transient may result from a delay of redistribution of stresses within actin and/or myosin filaments at the beginning of phase 2. Corresponding redistribution of deformations within the actin filaments leads to non-uniform shifts of the attached myosin heads and changes in the X-ray diffraction pattern. Additionally, we discuss a change in the experimental technique that allows suppression of the elastic vibrations that obscure the contributions of other sources to the superfast tension transient.     

Movement of smooth muscle tropomyosin by myosin heads.

It has been proposed that during the activation of muscle contraction the initial binding of myosin heads to the actin thin filament contributes to switching on the thin filament and that this might involve the movement of actin-bound tropomyosin. The movement of smooth muscle tropomyosin on actin was investigated in this work by measuring the change in distance between specific residues on tropomyosin and actin by fluorescence resonance energy transfer (FRET) as a function of myosin head binding to actin. An energy transfer acceptor was attached to Cys374 of actin and a donor to the tropomyosin heterodimer at either Cys36 of the beta-chain or Cys190 of the alpha-chain. FRET changed for the donor at both positions of tropomyosin upon addition of skeletal or smooth muscle myosin heads, indicating a movement of the whole tropomyosin molecule. The changes in FRET were hyperbolic and saturated at about one head per seven actin subunits, indicating that each head cooperatively affects several tropomyosin molecules, presumably via tropomyosin's end-to-end interaction. ATP, which dissociates myosin from actin, completely reversed the changes in FRET induced by heads, whereas in the presence of ADP the effect of heads was the same as in its absence. The results indicate that myosin with and without ADP, intermediates in the myosin ATPase hydrolytic pathway, are effective regulators of tropomyosin position, which might play a role in the regulation of smooth muscle contraction.     

Changes in the X-ray diffraction pattern from rigor muscles by application of external length changes

The effect of external force on the X-ray pattern from frog muscles in rigor was studied by a time-resolved diffraction technique. When sinusoidal length changes (1.5–3% of the muscle length, 5Hz) were applied to the muscle, the 14.3 nm intensity decreased during the releasing phase and increased during the stretching phase. The intensity ratio of the equatorial 1,0 and 1,1 reflections did not change, nor were there any appreciable intensity changes in the 5.9 nm and 5.1 nm reflections during the length change. Experiments were also done with the relaxed muscles and no change was seen in any reflection, indicating that the rigor linkages are needed to produce the 14.3 nm intensity change. Thus the distinct effect of the length change was detected only on the 14.3 nm reflection. These results suggest no large conformational changes are induced in both the distal part of the myosin head attached to actin and the actin filament during the oscillation. It is therefore most probable that the proximal portion of myosin heads including S-2 contributes to the intensity change in response to the length change (see, also ref.21). When the muscle was stretched beyond the filament overlap, the 14.3 nm intensity change was suppressed to less than 50% of that of the slack length. It was also found that the tension change delayed the intensity change during the length oscillation. However, this delay of the tension change as observed in the muscle at the slack length was lacking in the overstretched muscle, indicating that the 14.3 nm intensity change may arise partly from a portion other than the crossbridges.     

X-ray diffraction indicates that active cross-bridges bind to actin target zones in insect flight muscle.

We report the first time-resolved study of the two-dimensional x-ray diffraction pattern during active contraction in insect flight muscle (IFM). Activation of demembranated Lethocerus IFM was triggered by 1.5-2.5% step stretches (risetime 10 ms; held for 1.5 s) giving delayed active tension that peaked at 100-200 ms. Bundles of 8-12 fibers were stretch-activated on SRS synchrotron x-ray beamline 16.1, and time-resolved changes in diffraction were monitored with a SRS 2-D multiwire detector. As active tension rose, the 14.5- and 7.2-nm meridionals fell, the first row line dropped at the 38.7 nm layer line while gaining a new peak at 19.3 nm, and three outer peaks on the 38.7-nm layer line rose. The first row line changes suggest restricted binding of active myosin heads to the helically preferred region in each actin target zone, where, in rigor, two-headed lead bridges bind, midway between troponin bulges that repeat every 38.7 nm. Halving this troponin repeat by binding of single active heads explains the intensity rise at 19.3 nm being coupled to a loss at 38.7 nm. The meridional changes signal movement of at least 30% of all myosin heads away from their axially ordered positions on the myosin helix. The 38.7- and 19.3-nm layer line changes signal stereoselective attachment of 7-23% of the myosin heads to the actin helix, although with too little ordering at 6-nm resolution to affect the 5.9-nm actin layer line. We conclude that stretch-activated tension of IFM is produced by cross-bridges that bind to rigor's lead-bridge target zones, comprising < or = 1/3 of the 75-80% that attach in rigor.     

Direct modeling of x-ray diffraction pattern from skeletal muscle in rigor

Available high-resolution structures of F-actin, myosin subfragment 1 (S1), and their complex, actin-S1, were used to calculate a 2D x-ray diffraction pattern from skeletal muscle in rigor. Actin sites occupied by myosin heads were chosen using a "principle of minimal elastic distortion energy" so that the 3D actin labeling pattern in the A-band of a sarcomere was determined by a single parameter. Computer calculations demonstrate that the total off-meridional intensity of a layer line does not depend on disorder of the filament lattice. The intensity of the first actin layer A1 line is independent of tilting of the "lever arm" region of the myosin heads. Myosin-based modulation of actin labeling pattern leads not only to the appearance of the myosin and "beating" actin-myosin layer lines in rigor diffraction patterns, but also to changes in the intensities of some actin layer lines compared to random labeling. Results of the modeling were compared to experimental data obtained from small bundles of rabbit muscle fibers. A good fit of the data was obtained without recourse to global parameter search. The approach developed here provides a background for quantitative interpretation of the x-ray diffraction data from contracting muscle and understanding structural changes underlying muscle contraction.     

Calcium regulates scallop muscle by changing myosin flexibility

Muscle myosins are molecular motors that convert the chemical free energy available from ATP hydrolysis into mechanical displacement of actin filaments, bringing about muscle contraction. Myosin cross-bridges exert force on actin filaments during a cycle of attached and detached states that are coupled to each round of ATP hydrolysis. Contraction and ATPase activity of the striated adductor muscle of scallop is controlled by calcium ion binding to myosin. This mechanism of the so-called “thick filament regulation” is quite different to vertebrate striated muscle which is switched on and off via “thin filament regulation” whereby calcium ions bind to regulatory proteins associated with the actin filaments. We have used an optically based single molecule technique to measure the angular disposition adopted by the two myosin heads whilst bound to actin in the presence and absence of calcium ions. This has allowed us to directly observe the movement of individual myosin heads in aqueous solution at room temperature in real time. We address the issue of how scallop striated muscle myosin might be regulated by calcium and have interpreted our results in terms of the structures of smooth muscle myosin that also exhibit thick filament regulation. This paper is not being submitted elsewhere and the authors have no competing financial interests     

Structural changes of cross-bridges on transition from isometric to shortening state in frog skeletal muscle

Structural changes in the myosin cross-bridges were studied by small-angle x-ray diffraction at a time resolution of 0.53 ms. A frog sartorius muscle, which was electrically stimulated to induce isometric contraction, was released by approximately 1% in 1 ms, and then its length was decreased to allow steady shortening with tension of approximately 30% of the isometric level. Intensity of all reflections reached a constant level in 5-8 ms. Intensity of the 7.2-nm meridional reflection and the (1,0) sampling spot of the 14.5-nm layer line increased after the initial release but returned to the isometric level during steady shortening. The 21.5-nm meridional reflection showed fast and slow components of intensity increase. The intensity of the 10.3-nm layer line, which arises from myosin heads attached to actin, decreased to a steady level in 2 ms, whereas other reflections took longer, 5-20 ms. The results show that myosin heads adapt quickly to an altered level of tension, and that there is a distinct structural state just after a quick release.     

Cross-bridge number, position, and angle in target zones of cryofixed isometrically active insect flight muscle

Electron micrographic tomograms of isometrically active insect flight muscle, freeze substituted after rapid freezing, show binding of single myosin heads at varying angles that is largely restricted to actin target zones every 38.7 nm. To quantify the parameters that govern this pattern, we measured the number and position of attached myosin heads by tracing cross-bridges through the three-dimensional tomogram from their origins on 14.5-nm-spaced shelves along the thick filament to their thin filament attachments in the target zones. The relationship between the probability of cross-bridge formation and axial offset between the shelf and target zone center was well fitted by a Gaussian distribution. One head of each myosin whose origin is close to an actin target zone forms a cross-bridge most of the time. The probability of cross-bridge formation remains high for myosin heads originating within 8 nm axially of the target zone center and is low outside 12 nm. We infer that most target zone cross-bridges are nearly perpendicular to the filaments (60% within 11 degrees ). The results suggest that in isometric contraction, most cross-bridges maintain tension near the beginning of their working stroke at angles near perpendicular to the filament axis. Moreover, in the absence of filament sliding, cross-bridges cannot change tilt angle while attached nor reach other target zones while detached, so may cycle repeatedly on and off the same actin target monomer.     

Ca2+-sensitive cross-bridge dissociation in the presence of magnesium pyrophosphate in skinned rabbit psoas fibers.

We find that at 6 degrees C in the presence of 4 mM MgPPi, at low or moderate ionic strength, skinned rabbit psoas fibers exhibit a stiffness and an equatorial x-ray diffraction pattern similar to that of rigor fibers. As the ionic strength is increased in the absence of Ca2+, both the stiffness and the equatorial x-ray diffraction pattern approach those of the relaxed state. This suggests that, as in solution, increasing ionic strength weakens the affinity of myosin cross-bridges for actin, which results in a decrease in the number of cross-bridges attached. The effect is Ca2+-sensitive. Assuming that stiffness is a measure of the number of cross-bridge heads attached, in the absence of Ca2+, the fraction of attached cross-bridge heads varies from approximately 75% to approximately 25% over an ionic strength range where ionic strength in solution weakens the binding constant for myosin subfragment-1 binding to unregulated actin by less than a factor of 3. Therefore, this phenomenon appears similar to the cooperative Ca2+-sensitive binding of S1 to regulated actin in solution (Greene, L. E., and E. Eisenberg, 1980, Proc. Natl. Acad. Sci. USA, 77:2616). By comparing the binding constants in solution and in the fiber under similar conditions, we find that the "effective actin concentration," that is, the concentration that gives the same fraction of S1 molecules bound to actin in solution as cross-bridge heads are bound to actin in a fiber, is in the millimolar range.(ABSTRACT TRUNCATED AT 250 WORDS)     

Why Muscle is an Efficient Shock Absorber

Skeletal muscles power body movement by converting free energy of ATP hydrolysis into mechanical work. During the landing phase of running or jumping some activated skeletal muscles are subjected to stretch. Upon stretch they absorb body energy quickly and effectively thus protecting joints and bones from impact damage. This is achieved because during lengthening, skeletal muscle bears higher force and has higher instantaneous stiffness than during isometric contraction, and yet consumes very little ATP. We wish to understand how the actomyosin molecules change their structure and interaction to implement these physiologically useful mechanical and thermodynamical properties. We monitored changes in the low angle x-ray diffraction pattern of rabbit skeletal muscle fibers during ramp stretch compared to those during isometric contraction at physiological temperature using synchrotron radiation. The intensities of the off-meridional layer lines and fine interference structure of the meridional M3 myosin x-ray reflection were resolved. Mechanical and structural data show that upon stretch the fraction of actin-bound myosin heads is higher than during isometric contraction. On the other hand, the intensities of the actin layer lines are lower than during isometric contraction. Taken together, these results suggest that during stretch, a significant fraction of actin-bound heads is bound non-stereo-specifically, i.e. they are disordered azimuthally although stiff axially. As the strong or stereo-specific myosin binding to actin is necessary for actin activation of the myosin ATPase, this finding explains the low metabolic cost of energy absorption by muscle during the landing phase of locomotion.     

Submillisecond rotational dynamics of spin-labeled myosin heads in myofibrils.

The rotational motion of crossbridges, formed when myosin heads bind to actin, is an essential element of most molecular models of muscle contraction. To obtain direct information about this molecular motion, we have performed saturation transfer EPR experiments in which spin labels were selectively and rigidly attached to myosin heads in purified myosin and in glycerinated myofibrils. In synthetic myosin filaments, in the absence of actin, the spectra indicated rapid rotational motion of heads characterized by an effective correlation time of 10 microseconds. By contrast, little or no submillisecond rotational motion was observed when isolated myosin heads (subfragment-1) were attached to glass beads or to F-actin, indicating that the bond between the myosin head and actin is quite rigid on this time scale. A similar immobilization of heads was observed in spin-labeled myofibrils in rigor. Therefore, we conclude that virtually all of the myosin heads in a rigor myofibril are immobilized, apparently owing to attachment of heads to actin. Addition of ATP to myofibrils, either in the presence or absence of 0.1 mM Ca2+, produced spectra similar to those observed for myosin filaments in the absence of actin, indicating rapid submillisecond rotational motion. These results indicate that either (a) most of the myosin heads are detached at any instant in relaxed or activated myofibrils or (b) attached heads bearing the products of ATP hydrolysis rotate as rapidly as detached heads.     

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.