Donnan potentials from striated muscle liquid crystals. Lattice spacing dependence.

Electrochemical potentials were measured as a function of myofilament packing density in crayfish striated muscle. The A-band striations are supramolecular smectic B1 lattice assemblies of myosin filaments and the I-band striations are nematic liquid crystals of actin filaments. Both A- and I-bands generate potentials derived from the fixed charge that is associated with structural proteins. In the reported experiments, filament packing density was varied by osmotically reducing lattice volume. The electrochemical potentials were measured from the A- and I-bands in the relaxed condition over a range of lattice volumes. From the measurements of relative cross-sectional area, unit-cell volume (obtained by low-angle x-ray diffraction) and previously determined effective linear charge densities (Aldoroty, R.A., N.B. Garty, and E.W. April, 1985, Biophys. J., 47:89-96), Donnan potentials can be predicted for any amount of compression. In the relaxed condition, the predicted Donnan potentials correspond to the measured electrochemical potentials. In the rigor condition, however, a net increase in negative charge associated with the myosin filament is observed. The predictability of the data demonstrates the applicability of Donnan equilibrium theory to the measurement of electrochemical potentials from liquid-crystalline systems. Moreover, the relationship between filament spacing and the Donnan potential is consistent with the concept that surface charge provides the necessary electrostatic force to stabilize the myofilament lattice.     

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.     

Donnan potentials from the A- and I-bands of glycerinated and chemically skinned muscles, relaxed and in rigor.

Using a combination of microelectrode measurements and high-power microscopy we have demonstrated that different Donnan potentials can be recorded from the A- and I-bands of glycerinated and chemically skinned muscles in rigor, so that the A-band fixed charge concentration exceeds the I-band fixed charge concentration in the rigor condition. In relaxation the two potentials, and therefore the two charge concentrations, are equal in the two bands. X-ray data are presented for relaxed and rigor rat semitendinosus muscle, chemically skinned, and actin and myosin filament charges are calculated under a variety of conditions. Our conclusions are that (a) the fixed (protein) charge is different in the A- and I-bands of striated muscle in the rigor state; (b) the fixed charges are equal in the A- and I-bands of relaxed muscle; (c) the largest charge change between relaxation and rigor is on the thick filament. This occurs whether or not the myosin heads are cross-linked to the thin filaments. (d) Possibly an event on the myosin molecule, the binding of ATP (or certain other ligands) causes a disseminated change that modifies the ion-binding capacity of the myosin rods, or part of them.     

The myofilament lattice: studies on isolated fibers. IV. Lattice equilibria in striated muscle.

Accounts of similarities between the thick filament lattice of striated muscle and smectic liquid-crystalline structures have focused upon an equilibrium between electrostatic (repulsive) and van der Waal's (attractive) forces. In living, intact muscle the fiber volume constitutes an additional important parameter which influences the amount of interaxial separation between the filaments. This is demonstrable by comparison of the lattice behavior of living fibers with that of fibers from which the sarcolemma has either been removed or made leaky by glycerination. These comparisons were made mainly by low-angle X-ray diffraction under conditions of changes in sarcomere length, ionic strength or osmolarity, and pH. Single fibers with the sarcolemma removed and glycerinated muscle have lattices which behave in accord with equilibrium liquid-crystalline systems in which the thick filament spacing is determined by the balance between electrostatic and van der Waal's forces. Conversely, osmotic and shortening studies demonstrate that the living, intact muscle has a lattice which behaves in accord with the so-called non-equilibrium (volume-constrained) liquid-crystalline condition in which the interaxial separation between the thick filaments is solely due to the amount of volume available as determined by the Donnan steady-state across the sarcolemma.     

A mathematical model of the sarcomere mechanics of cross-striated muscle with consideration of the stretch and twist of actin filaments

A mathematical model of sarcomere mechanics, which takes into account the elongation of actin and myosin filaments and also twisting of the actin filaments in the sarcomere of striated muscle during contraction is presented. The model accounts for the experimentally observed phenomena of the stretch and twist of the actin filaments due to strong binding of myosin heads and the pulling force. Some model parameters were estimated from published experimental data. The results of modeling show that the twist of actin filaments can play a substantial role in the mechanical responses of contracting muscle fibers to step changes of their length.     

X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction.

To clarify the extensibility of thin actin and thick myosin filaments in muscle, we examined the spacings of actin and myosin filament-based reflections in x-ray diffraction patterns at high resolution during isometric contraction of frog skeletal muscles and steady lengthening of the active muscles using synchrotron radiation as an intense x-ray source and a storage phosphor plate as a high sensitivity, high resolution area detector. Spacing of the actin meridional reflection at approximately 1/2.7 nm-1, which corresponds to the axial rise per actin subunit in the thin filament, increased about 0.25% during isometric contraction of muscles at full overlap length of thick and thin filaments. The changes in muscles stretched to approximately half overlap of the filaments, when they were scaled linearly up to the full isometric tension, gave an increase of approximately 0.3%. Conversely, the spacing decreased by approximately 0.1% upon activation of muscles at nonoverlap length. Slow stretching of a contracting muscle increased tension and increased this spacing over the isometric contraction value. Scaled up to a 100% tension increase, this corresponds to a approximately 0.26% additional change, consistent with that of the initial isometric contraction. Taken together, the extensibility of the actin filament amounts to 3-4 nm of elongation when a muscle switches from relaxation to maximum isometric contraction. Axial spacings of the layer-line reflections at approximately 1/5.1 nm-1 and approximately 1/5.9 nm-1 corresponding to the pitches of the right- and left-handed genetic helices of the actin filament, showed similar changes to that of the meridional reflection during isometric contraction of muscles at full overlap. The spacing changes of these reflections, which also depend on the mechanical load on the muscle, indicate that elongation is accompanied by slight changes of the actin helical structure possibly because of the axial force exerted by the actomyosin cross-bridges. Additional small spacing changes of the myosin meridional reflections during length changes applied to contracting muscles represented an increase of approximately 0.26% (scaled up to a 100% tension increase) in the myosin periodicity, suggesting that such spacing changes correspond to a tension-related extension of the myosin filaments. Elongation of the myosin filament backbone amounts to approximately 2.1 nm per half sarcomere. The results indicate that a large part (approximately 70%) of the sarcomere compliance of an active muscle is caused by the extensibility of the actin and myosin filaments; 42% of the compliance resides in the actin filaments, and 27% of it is in the myosin filaments.     

On the relation between filament overlap and the number of calcium-binding sites on glycerinated muscle fibers.

The formation of rigor complexes between the thick and thin filaments of glycerinated rabbit psoas muscle fibers causes the fibers to bind more calcium at any given level of free calcium. I studied the maximum amount of calcium bound as a function of filament overlap under rigor conditions. Fibers stretched to zero filament overlap (sarcomere length greater than 3.8 micron) bound exactly 75% as much calcium as fibers with maximum overlap. Between these extremes a linear relationship was found between maximum bound calcium and the length of the overlap zone. The results support the hypothesis that in the intact filament lattice one of the four calcium-binding sites of troponin depends for its existence on attachment between myosin and actin. In addition, the linear relation between maximum bound calcium and filament overlap is consistent with the assumption that the cooperative effect of rigor complex formation on calcium binding is limited to the binding site in the immediate vicinity of the rigor complex.     

The Three Filament Model of Skeletal Muscle Stability and Force Production

Ever since the 1950s, muscle force regulation has been associated with the cross-bridge interactions between the two contractile filaments, actin and myosin. This gave rise to what is referred to as the "two-filament sarcomere model". This model does not predict eccentric muscle contractions well, produces instability of myosin alignment and force production on the descending limb of the force-length relationship, and cannot account for the vastly decreased ATP requirements of actively stretched muscles. Over the past decade, we and others, identified that a third myofilament, titin, plays an important role in stabilizing the sarcomere and the myosin filament. Here, we demonstrate additionally how titin is an active participant in muscle force regulation by changing its stiffness in an activation/force dependent manner and by binding to actin, thereby adjusting its free spring length. Therefore, we propose that skeletal muscle force regulation is based on a three filament model that includes titin, rather than a two filament model consisting only of actin and myosin filaments.     

ANALYSIS OF MUSCLE CONTRACTION BY ULTRAVIOLET MICROBEAM DISRUPTION OF SARCOMERE STRUCTURE

In an effort to differentiate between the sliding filament theory for muscle contraction and alternative views which propose attachment between actin and myosin filaments at or across the H zone, rabbit psoas myofibrils were irradiated in various areas of the sarcomere with an ultraviolet microbeam. Irradiation of the I band appears to destroy the actin filaments; in vitro irradiation of F actin causes an irreversible depolymerization of the protein. Irradiation of the A band disorients the myosin but causes no apparent loss of dry mass. These effects are maximal at the wavelength of maximum absorption of the proteins involved. Actin filaments, released at the Z line of a sarcomere, are seen to slide into the A band on addition of ATP. Irradiation of a full A band prevents contraction, whereas irradiation of two-thirds of the A band, leaving a lateral edge intact, permits contraction at the non-irradiated edge. Thus contraction can occur in what is in essence only one-third of a sarcomere, eliminating any necessity for postulated H zone connections. These observations are in complete accord with the classical sliding filament theory but incompatible with either the contralateral filament hypothesis or the actin folding model for muscle contraction.     

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.     

Sarcomeric pattern formation by actin cluster coalescence

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells.     

Donnan potentials from striated muscle liquid crystals. A-band and I-band measurements.

A-band and I-band potentials are measured selectively in crayfish skinned long-tonic muscle fibers. The microelectrode tip diameters used in this study are shown to be sufficiently small to permit the discrete placement of an electrode into either an A-band or I-band. Random and directed impalements into mechanically skinned fibers with microelectrodes yields reproducible trimodal distributions of potentials where the modalities represent the A-band (-1.80 mV), the I-band (-0.76 mV), and the Z-line vicinity (-3.63 mV). In conjunction with Donnan equilibrium theory, fixed charge concentrations are calculated from the measured potentials for the A-band (25.9 mmol e-/l), I-band (10.9 mmol e-/l), and Z-line vicinity (52.3 mmol e-/l). When skinned fibers are treated with Triton X-100, the mean potentials (and charge concentrations) decrease: A-band to -1.71 mV (24.6 mmol e-/l), I-band to -0.71 mV (10.2 mmol e-/l), and the Z-line vicinity to -3.40 mV (49.0 mmol e/l). In the A-band this represents a loss of 1.3 mmol e-/l while in the I-band 0.7 mmol e-/l are lost; both decreases are attributed to the removal of internal membranous structures. In the rigor condition the A-band increases to -2.18 mV (33.1 mmol e-/l) and the I-band increases to -0.88 mV (13.3 mmol e-/l). Relative to the relaxed condition, this represents an increase of 8.5 mmol e-/l and 3.1 mmol e-/l in the A-band and I-band, respectively. The evidence shows that it is practical to measure A-band and I-band potentials selectively. Further, it is demonstrated that similar measurements can be obtained from agar, another polyelectrolyte gel system (see Appendix).     

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.     

Architecture of the sarcomere matrix of skeletal muscle: immunoelectron microscopic evidence that suggests a set of parallel inextensible nebulin filaments anchored at the Z line

Nebulin, a giant myofibrillar protein (600-800 kD) that is abundant (3%) in the sarcomere of a wide range of skeletal muscles, has been proposed as a component of a cytoskeletal matrix that coexists with actin and myosin filaments within the sarcomere. Immunoblot analysis indicates that although polypeptides of similar size are present in cardiac and smooth muscles at low abundance, those proteins show no immunological cross-reactivity with skeletal muscle nebulin. Gel analysis reveals that nebulins in various skeletal muscles of rabbit belong to at least two classes of size variants. A monospecific antibody has been used to localize nebulin by immunoelectron microscopy in a mechanically split rabbit psoas muscle fiber preparation. Labeled split fibers exhibit six pairs of stripes of antibody-imparted transverse densities spaced at 0.1-1.0 micron from the Z line within each sarcomere. These epitopes maintain a fixed distance to the Z line irrespective of sarcomere length and do not exhibit the characteristic elastic stretch-response of titin epitopes within the I band domain. It is proposed that nebulin constitutes a set of inextensible filaments attached at one end to the Z line and that nebulin filaments are in parallel, and not in series, with titin filaments. Thus the skeletal muscle sarcomere may have two sets of nonactomyosin filaments: a set of I segment-linked nebulin filaments and a set of A segment-linked titin filaments. This four-filament sarcomere model raises the possibility that nebulin and titin might act as organizing templates and length- determining factors for actin and myosin respectively.     

Saturation transfer electron paramagnetic resonance of spin-labeled muscle fibers. Dependence of myosin head rotational motion on sarcomere length

We have investigated the orientation and rotational mobility of spin-labeled myosin heads in muscle fibers as a function of the sarcomere length in the absence of ATP. An iodoacetamide spin label was used to label selectively two-thirds of the sulfhydryl-1 groups in glycerinated rabbit psoas muscle. Conventional electron paramagnetic resonance experiments were used to determine the orientation distribution of the probes relative to the fiber axis, and saturation transfer experiments were used to detect sub-millisecond rotational motion. When fibers are at sarcomere length 2.3 microns (full overlap), spin-labeled heads have a high degree of orientational order. The probes are in a single, narrow orientation distribution (full width 15 degrees), and they exhibit no detectable sub-millisecond rotational motion. When fibers are stretched (sarcomere length increased), either before or after labeling, disorder and microsecond mobility increase greatly, in proportion to the fraction of myosin heads that are no longer in the overlap zone between the thick and thin filaments. Saturation transfer difference spectra show that a fraction of myosin heads equal to the fraction outside the overlap zone have much more rotational mobility than those in fibers at full overlap, and almost as much as in synthetic myosin filaments. The most likely interpretation is that some of the probes, corresponding approximately to the fraction of heads in the overlap zone, remain oriented and immobile, while the rest are highly disordered (angular spread greater than 90 degrees) and mobile (microsecond rotational motion). Thus, it appears that myosin heads are rigidly immobilized by actin, but they rotate through large angles on the microsecond time-scale when detached from actin, even in the absence of ATP.     

Actin-myosin interaction: The role of myosin in determining the actin pattern in self-assembled ‘hybrid’ contractile units

Self-assembly of actin-myosin filamentous complexes was assayed by polymerizing rabbit G-ADP actin on formed filaments of lobster myosin. The resulting contractile units indicate a 12-member actin orbital rather than the six-member orbital obtained previously using rabbit myosin and actin. Furthermore, the pattern of actin distribution surrounding the myosin filament is similar to that of the lobster tonic muscle sarcomere rather than the trigonal actin position characteristic of vertebrate muscle. The results show that the pattern and mode of actin complexing is determined by the specific myosin and the arrangement of the cross-bridges on the organized filament.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

Titin organisation and the 3D architecture of the vertebrate-striated muscle I-band

The giant muscle protein titin (connectin) is known to serve as a cytoskeletal element in muscle sarcomeres. It elastically restrains lengthening sarcomeres, it aids the integrity and central positioning of the A-band in the sarcomere and it may act as a template upon which some sarcomeric components are laid down during myogenesis. A puzzle has been how titin molecules, arranged systematically within the hexagonal A-band lattice of myosin filaments, can redistribute through the I-band to their anchoring sites in the tetragonal Z-band lattice. Recent work by Liversage and colleagues has suggested that there are six titin molecules per half myosin filament. Since there are two actin filaments per half myosin filament in a half sarcomere, this means that there are three titin molecules interacting with each Z-band unit cell containing one actin filament in the same sarcomere and one of opposite polarity from the next sarcomere. Liversage et al. suggested that the three titins might be distributed with two on an actin filament of one polarity and one on the filament of opposite polarity. Here, we build on this suggestion and discuss the transition of titin from the A-band to the Z-band. We show that there are good structural and mechanical reasons why titin might be organised as Liversage et al., suggested and we discuss the possible relationships between A-band arrangements in successive sarcomeres along a myofibril.     

The Stepping Pattern of Myosin X Is Adapted for Processive Motility on Bundled Actin

Myosin X is a molecular motor that is adapted to select bundled actin filaments over single actin filaments for processive motility. Its unique form of motility suggests that myosin X's stepping mechanism takes advantage of the arrangement of actin filaments and the additional target binding sites found within a bundle. Here we use fluorescence imaging with one-nanometer accuracy to show that myosin X takes steps of ∼18 nm along a fascin-actin bundle. This step-size is well short of the 36-nm step-size observed in myosin V and myosin VI that corresponds to the actin pseudohelical repeat distance. Myosin X is able to walk along bundles with this step-size if it straddles two actin filaments, but would be quickly forced to spiral into the constrained interior of the bundle if it were to use only a single actin filament. We also demonstrate that myosin X takes many sideways steps as it walks along a bundle, suggesting that it can switch actin filament pairs within the bundle as it walks. Sideways steps to the left or the right occur on bundles with equal frequency, suggesting a degree of lateral flexibility such that the motor's working stroke does not bias it to the left or to the right. On single actin filaments, we find a broad mixture of 10-20-nm steps, which again falls short of the 36-nm actin repeat. Moreover, the motor leans to the right as it walks along single filaments, which may require myosin X to adopt strained configurations. As a control, we also tracked myosin V stepping along actin filaments and fascin-actin bundles. We find that myosin V follows a narrower path on both structures, walking primarily along one surface of an actin filament and following a single filament within a bundle while occasionally switching to neighboring filaments. Together, these results delineate some of the structural features of the motor and the track that allow myosin X to recognize actin filament bundles.