X-ray diffraction measurements of the extensibility of actin and myosin filaments in contracting muscle.

We have used a small angle scattering system assembled on the high flux multipole wiggler beam line at CHESS (Cornell) to make very accurate spacing measurements of certain meridional and layer-line reflections from contracting muscles. During isometric contraction, the actin 27.3 A reflection increases in spacing from its resting value by approximately 0.3%, and other actin reflections, including the 59 and 51 A off-meridional reflections, show corresponding changes in spacing. When tension is augmented or diminished by applying moderate speed length changes to a contracting muscle, changes in spacing in the range of 0.19-0.24% (when scaled to full isometric tension) can be seen. The larger difference between the resting and isometric spacings suggests either nonlinearity at low tension levels or the presence of a component related to activation itself. Myosin filaments also show similar increases in axial period during slow stretch, in addition to the well known larger change associated with activation. An actin spacing change of 0.25-0.3% can also be measured during a 2 ms time frame immediately after a quick release, showing that the elastic behavior is rapid. These observations of filament extensions totaling 2-3 nm per half-sarcomere may necessitate some significant revision of the interpretation of a number of mechanical experiments in muscle, in which it has usually been assumed that virtually all of the elasticity resides in the cross-bridges.     

The stiffness of skeletal muscle in isometric contraction and rigor: the fraction of myosin heads bound to actin.

Step changes in length (between -3 and +5 nm per half-sarcomere) were imposed on isolated muscle fibers at the plateau of an isometric tetanus (tension T0) and on the same fibers in rigor after permeabilization of the sarcolemma, to determine stiffness of the half-sarcomere in the two conditions. To identify the contribution of actin filaments to the total half-sarcomere compliance (C), measurements were made at sarcomere lengths between 2.00 and 2.15 microm, where the number of myosin cross-bridges in the region of overlap between the myosin filament and the actin filament remains constant, and only the length of the nonoverlapped region of the actin filament changes with sarcomere length. At 2.1 microm sarcomere length, C was 3.9 nm T0(-1) in active isometric contraction and 2.6 nm T0(-1) in rigor. The actin filament compliance, estimated from the slope of the relation between C and sarcomere length, was 2.3 nm microm(-1) T0(-1). Recent x-ray diffraction experiments suggest that the myosin filament compliance is 1.3 nm microm(-1) T0(-1). With these values for filament compliance, the difference in half-sarcomere compliance between isometric contraction and rigor indicates that the fraction of myosin cross-bridges attached to actin in isometric contraction is not larger than 0.43, assuming that cross-bridge elasticity is the same in isometric contraction and rigor.     

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.     

Non-specific termination of simian virus 40 DNA replication.

Axial X-ray diffraction patterns have been studied from relaxed, contracted and rigor vertebrate striated muscles at different sarcomere lengths to determine which features of the patterns depend on the interaction of actin and myosin. The intensity of the myosin layer lines in a live, relaxed muscle is sometimes less in a stretched muscle than in the muscle at rest-length; the intensity depends not only on the sarcomere length but on the time that has elapsed since dissection of the muscle. The movement of cross-bridges giving rise to these intensity changes are not caused solely by the withdrawal of actin from the A-band.When a muscle contracts or passes into rigor many changes occur that are independent of the sarcomere length: the myosin layer lines decrease in intensity to about 30% of their initial value when the muscle contracts, and disappear completely when the muscle passes into rigor. Both in contracting and rigor muscles at all sarcomere lengths the spacings of the meridional reflections at 143 Å and 72 Å are 1% greater than from a live relaxed muscle at rest-length. It is deduced that the initial movement of cross-bridges from their positions in resting muscle does not depend on the interaction of each cross-bridge with actin, but on a conformational change in the backbone of the myosin filament: occurring as a result of activation. The possibility is discussed that the conformational change occurs because the myosin filament, like the actin filament, has an activation control mechanism. Finally, all the X-ray diffraction patterns are interpreted on a model in which the myosin filament can exist in one of two possible states: a relaxed state which gives a diffraction pattern with strong myosin layer lines and an axial spacing of 143.4 Å, and an activated state which gives no layer lines but a meridional spacing of 144.8 Å.     

The length–tension curve in muscle depends on lattice spacing

Classic interpretations of the striated muscle length–tension curve focus on how force varies with overlap of thin (actin) and thick (myosin) filaments. New models of sarcomere geometry and experiments with skinned synchronous insect flight muscle suggest that changes in the radial distance between the actin and myosin filaments, the filament lattice spacing, are responsible for between 20% and 50% of the change in force seen between sarcomere lengths of 1.4 and 3.4 µm. Thus, lattice spacing is a significant force regulator, increasing the slope of muscle''s force–length dependence.     

Compliance of thin filaments in skinned fibers of rabbit skeletal muscle.

The mechanical compliance (reciprocal of stiffness) of thin filaments was estimated from the relative compliance of single, skinned muscle fibers in rigor at sarcomere lengths between 1.8 and 2.4 micron. The compliance of the fibers was calculated as the ratio of sarcomere length change to tension change during imposition of repetitive cycles of small stretches and releases. Fiber compliance decreased as the sarcomere length was decreased below 2.4 micron. The compliance of the thin filaments could be estimated from this decrement because in this range of lengths overlap between the thick and thin filaments is complete and all of the myosin heads bind to the thin filament in rigor. Thus, the compliance of the overlap region of the sarcomere is constant as length is changed and the decrease in fiber compliance is due to decrease of the nonoverlap length of the thin filaments (the I band). The compliance value obtained for the thin filaments implies that at 2.4-microns sarcomere length, the thin filaments contribute approximately 55% of the total sarcomere compliance. Considering that the sarcomeres are approximately 1.25-fold more compliant in active isometric contractions than in rigor, the thin filaments contribute approximately 44% to sarcomere compliance during isometric contraction.     

On the theory of muscle contraction: filament extensibility and the development of isometric force and stiffness.

The newly discovered extensibility of actin and myosin filaments challenges the foundation of the theory of muscle mechanics. We have reformulated A. F. Huxley's sliding filament theory to explicitly take into account filament extensibility. During isometric force development, growing cross-bridge tractions transfer loads locally between filaments, causing them to extend and, therefore, to slide locally relative to one another. Even slight filament extensibility implies that 1) relative displacement between the two must be nonuniform along the region of filament overlap, 2) cross-bridge strain must vary systematically along the overlap region, and importantly, 3) the local shortening velocities, even at constant overall sarcomere length, reduce force below the level that would have developed if the filaments had been inextensible. The analysis shows that an extensible filament system with only two states (attached and detached) displays three important characteristics: 1) muscle stiffness leads force during force development; 2) cross-bridge stiffness is significantly higher than previously assessed by inextensible filament models; and 3) stiffness is prominently dissociated from the number of attached cross-bridges during force development. The analysis also implies that the local behavior of one myosin head must depend on the state of neighboring attachment sites. This coupling occurs exclusively through local sliding velocities, which can be significant, even during isometric force development. The resulting mechanical cooperativity is grounded in fiber mechanics and follows inevitably from filament extensibility.     

A structural origin of latency relaxation in frog skeletal muscle

A time-resolved x-ray diffraction study at a time resolution of 0.53 ms was made to investigate the structural origin of latency relaxation (LR) in frog skeletal muscle. Intensity and spacing measurements were made on meridional reflections from the Ca-binding protein troponin and the thick filament and on layer lines from the thin filament. At 16 degrees C, the intensity and spacing of all reflections started to change at 4 ms, simultaneously with the LR. At 0 degrees C, the intensity of the troponin reflection and the layer lines from the thin filament and the spacing of the 14.3-nm myosin meridional reflection, but not the spacing of other myosin meridional reflections, began to change at approximately 15 ms, when the LR also started. Intensity of myosin-based reflections started to change later. When the muscle was stretched to non-overlap length, the intensity and spacing changes of the myosin reflections disappeared. The simultaneous spacing change of the 14.3-nm myosin meridional reflection with the LR suggests that detachment of myosin heads that are bound to actin in the resting muscle is the cause of the LR.     

Structural changes during activation of frog muscle studied by time-resolved X-ray diffraction

The pattern given by contracting frog muscle can be followed with high time resolution using synchrotron radiation as a high-intensity X-ray source. We have studied the behaviour of the second actin layer-line (axial spacing of approximately 179 A) at an off-meridional spacing of approximately 0.023 A-1, a region of the diagram that is sensitive to the position of tropomyosin in the thin filaments. In confirmation of earlier work, we find that there is a substantial increase in the intensity of this part of the pattern during contraction. We find that the reflection reaches half its final intensity about 17 milliseconds after the stimulus at 6 degrees C. The changes in the equatorial reflections, which arise from movement of crossbridges towards the thin filaments, occur with a delay of about 12 to 17 milliseconds relative to this change in the actin pattern. In over-stretched muscle, where thick and thin filaments no longer overlap, the changes in the actin second layer-line still take place upon stimulation with a time course and intensity similar to that observed at full overlap. This indicates that tropomyosin movement, in response to calcium binding to troponin, is the first structural step in muscular contraction, and is the prerequisite for myosin binding. A change in intensity similar to that found in contracting muscle is seen in rigor, where tropomyosin is probably locked in the active position. During relaxation the earlier stages in the decrease in intensity of the second actin layer-line take place significantly sooner after the last stimulus than tension decay. In over-stretched muscles the intensity decay is appreciably faster than in the same muscles at rest length, where attached crossbridges may interfere with the return of tropomyosin to its resting position.     

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.     

X-ray diffraction patterns from mammalian heart muscle

We have obtained light and X-ray diffraction patterns from trabecular and papillary muscles of various mammalian hearts in the living resting state and in rigor. Equatorial X-ray diffraction patterns from living muscles show the 1,0 and 1,1 reflections from a hexagonal lattice of filaments. The lattice spacing varies with sarcomere length over the observable range (2·0 to 2·5 μm) in such a manner that the lattice volume remains constant. In the living resting state the 1,0 reflection is stronger than the 1,1 reflection, whereas in rigor the 1,1 reflection is almost as strong as the 1,0 reflection. These intensity changes are similar to those found in vertebrate skeletal muscle, suggesting that the mechanism of cross-bridge attachment to actin is similar in both muscles.Two types of meridional X-ray diffraction pattern were observed in muscles in different conditions. One type, obtained from dead or glycerol-extracted muscles or from muscles treated with iodoacetate, showed a strong actin-related pattern but only a weak pattern associated with myosin. This type of pattern was similar to that from vertebrate skeletal muscle in rigor. The other type, obtained from living, resting muscle, showed a weaker actin pattern but a stronger myosin pattern. The myosin pattern included layer-line reflections associated with projections from the thick filaments. This second type of pattern was similar to that from resting vertebrate skeletal muscle, but the layer lines were weaker. The weakness of the myosin layer lines may indicate that part of the high resting tension found in heart muscle arises from a small amount of actin-myosin interaction in the resting state. Such interaction could provide a mechanism for varying the diastolic length of heart muscle and thereby the diastolic volume of the heart.     

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.     

ULTRASTRUCTURE OF THE RESTING AND CONTRACTED STRIATED MUSCLE FIBER AT DIFFERENT DEGREES OF STRETCH

Passive stretch, isometric contraction, and shortening were studied in electron micrographs of striated, non-glycerinated frog muscle fibers. The artifacts due to the different steps of preparation were evaluated by comparing sarcomere length and fiber diameter before, during, and after fixation and after sectioning. Tension and length were recorded in the resting and contracted fiber before and during fixation. The I filaments could be traced to enter the A band between the A filaments on both sides of the I band, creating a zone of overlap which decreased linearly with stretch and increased with shortening. This is consistent with a sliding filament model. The decrease in the length of the A and I filaments during isometric contraction and the finding that fibers stretched to a sarcomere length of 3.7 µ still developed 30 per cent of the maximum tetanic tension could not be explained in terms of the sliding filament model. Shortening of the sarcomeres near the myotendinous junctions which still have overlap could account for only one-sixth of this tension, indicating that even those sarcomeres stretched to such a degree that there is a gap between A and I filaments are activated during isometric contraction (increase in stiffness). Shortening, too, was associated with changes in filament length. The diameter of A filaments remained unaltered with stretch and with isometric contraction. Shortening of 50 per cent was associated with a 13 per cent increase in A filament diameter. The area occupied by the fibrils and by the interfibrillar space increased with shortening, indicating a 20 per cent reduction in the volume of the fibrils when shortening amounted to 40 per cent.     

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to “breathing,” advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.     

Behaviour of the crossbridges in stretched or compressed muscle fibres

The maximum chord of the myosin heads is comparable to the closest surface-to-surface spacing between the myofilaments in a muscle at the slack length. Therefore, when the sarcomere length increases or when the fibre is compressed, the surface-to-surface myofilament spacing becomes lower than the head long axis. We conclude that, in stretched or compressed fibres, some crossbridges cannot attach, owing to steric hindrance. When the amount of compression is limited, this hindrance may be overcome by a tilting of the heads in the plane perpendicular to the filament axes; in this case, there is no consequence as concerns the crossbridge properties. In highly compressed fibres, the crossbridges become progressively hindered and all the crossbridges are hindered for an axis-to-axis spacing representing about 60% of the spacing observed under zero external osmotic pressure. In this case, both the isometric tension and the ATPase activity of the fibre are zero. In fibres stretched up to 3.77 microns (sarcomere length corresponding to the disappearance of the overlap between the thick and the thin filaments), the ratio of hindered crossbridges over the functional crossbridges may be estimated at about 55%. In stretched fibres, a noticeable proportion of crossbridges are sterically hindered and the crossbridges performance (e.g. constants of attachment and detachment) depends on filament spacing, i.e. on sarcomere length. Therefore, we think it is probably impossible to consider the crossbridges as independent force converters, since this idea requires that the crossbridge properties are independent of sarcomere length. In this connection, all the experiments performed on osmotically compressed fibres are of major importance for the understanding of the true mechanisms of muscle contraction.     

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.     

Thin filament length regulation in striated muscle sarcomeres: pointed-end dynamics go beyond a nebulin ruler

The actin (thin) filaments in striated muscle are highly regulated and precisely specified in length to optimally overlap with the myosin (thick) filaments for efficient myofibril contraction. Here, we review and critically discuss recent evidence for how thin filament lengths are controlled in vertebrate skeletal, vertebrate cardiac, and invertebrate (arthropod) sarcomeres. Regulation of actin polymerization dynamics at the slow-growing (pointed) ends by the capping protein tropomodulin provides a unified explanation for how thin filament lengths are physiologically optimized in all three muscle types. Nebulin, a large protein thought to specify thin filament lengths in vertebrate skeletal muscle through a ruler mechanism, may not control pointed-end actin dynamics directly, but instead may stabilize a large core region of the thin filament. We suggest that this stabilizing function for nebulin modifies the lengths primarily specified by pointed-end actin dynamics to generate uniform filament lengths in vertebrate skeletal muscle. We suggest that nebulette, a small homolog of nebulin, may stabilize a correspondingly shorter core region and allow individual thin filament lengths to vary according to working sarcomere lengths in vertebrate cardiac muscle. We present a unified model for thin filament length regulation where these two mechanisms cooperate to tailor thin filament lengths for specific contractile environments in diverse muscles.     

Stiffness and fraction of Myosin motors responsible for active force in permeabilized muscle fibers from rabbit psoas

The stiffness of the single myosin motor (epsilon) is determined in skinned fibers from rabbit psoas muscle by both mechanical and thermodynamic approaches. Changes in the elastic strain of the half-sarcomere (hs) are measured by fast mechanics both in rigor, when all myosin heads are attached, and during active contraction, with the isometric force (T0) modulated by changing either [Ca2+] or temperature. The hs compliance is 43.0+/-0.8 nm MPa-1 in isometric contraction at saturating [Ca2+], whereas in rigor it is 28.2+/-1.1 nm MPa-1. The equivalent compliance of myofilaments is 21.0+/-3.3 nm MPa-1. Accordingly, the stiffness of the ensemble of myosin heads attached in the hs is 45.5+/-1.7 kPa nm-1 in isometric contraction at saturating [Ca2+] (e0), and in rigor (er) it rises to 138.9+/-21.2 kPa nm-1. Epsilon, calculated from er and the lattice molecular dimensions, is 1.21+/-0.18 pN nm-1. epsilon estimated, using a thermodynamic approach, from the relation of T0 at saturating [Ca2+] versus the reciprocal of absolute temperature is 1.25+/-0.14 pN nm-1, similar to that estimated for fibers in rigor. Consequently, the ratio e0/er (0.33+/-0.05) can be used to estimate the fraction of attached heads during isometric contraction at saturating [Ca2+]. If the osmotic agent dextran T-500 (4 g/100 ml) is used to reduce the lateral filament spacing of the relaxed fiber to the value before skinning, both e0 and er increase by approximately 40%. Epsilon becomes approximately 1.7 pN nm-1 and the fraction and the force of myosin heads attached in the isometric contraction remain the same as before dextran application. The finding that the fraction of myosin heads attached to actin in an isometric contraction is 0.33 rules out the hypothesis of multiple mechanical cycles per ATP hydrolyzed.     

Filament compliance effects can explain tension overshoots during force development

Spatially explicit stochastic simulations of myosin S1 heads attaching to a single actin filament were used to investigate the process of force development in contracting muscle. Filament compliance effects were incorporated by adjusting the spacing between adjacent actin binding sites and adjacent myosin heads in response to cross-bridge attachment/detachment events. Appropriate model parameters were determined by multi-dimensional optimization and used to simulate force development records corresponding to different levels of Ca(2+) activation. Simulations in which the spacing between both adjacent actin binding sites and adjacent myosin S1 heads changed by approximately 0.06 nm after cross-bridge attachment/detachment events 1), exhibited tension overshoots with a Ca(2+) dependence similar to that measured experimentally and 2), mimicked the observed k(tr)-relative tension relationship without invoking a Ca(2+)-dependent increase in the rate of cross-bridge state transitions. Tension did not overshoot its steady-state value in control simulations modeling rigid thick and thin filaments with otherwise identical parameters. These results underline the importance of filament geometry and actin binding site availability in quantitative theories of muscle contraction.