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.     

G146V mutation at the hinge region of actin reveals a myosin class-specific requirement of actin conformations for motility

The G146V mutation in actin is dominant lethal in yeast. G146V actin filaments bind cofilin only minimally, presumably because cofilin binding requires the large and small actin domains to twist with respect to one another around the hinge region containing Gly-146, and the mutation inhibits that twisting motion. A number of studies have suggested that force generation by myosin also requires actin filaments to undergo conformational changes. This prompted us to examine the effects of the G146V mutation on myosin motility. When compared with wild-type actin filaments, G146V filaments showed a 78% slower gliding velocity and a 70% smaller stall force on surfaces coated with skeletal heavy meromyosin. In contrast, the G146V mutation had no effect on either gliding velocity or stall force on myosin V surfaces. Kinetic analyses of actin-myosin binding and ATPase activity indicated that the weaker affinity of actin filaments for myosin heads carrying ADP, as well as reduced actin-activated ATPase activity, are the cause of the diminished motility seen with skeletal myosin. Interestingly, the G146V mutation disrupted cooperative binding of myosin II heads to actin filaments. These data suggest that myosin-induced conformational changes in the actin filaments, presumably around the hinge region, are involved in mediating the motility of skeletal myosin but not myosin V and that the specific structural requirements for the actin subunits, and thus the mechanism of motility, differ among myosin classes.     

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.     

Influence of dispersion in myosin filament orientation and anisotropic filament contractions in smooth muscle

A new constitutive model for the biomechanical behaviour of smooth muscle tissue is proposed. The active muscle contraction is accomplished by the relative sliding between actin and myosin filaments, comprising contractile units in the smooth muscle cells. The orientation of the myosin filaments, and thereby the contractile units, are taken to exhibit a statistical dispersion around a preferred direction. The number of activated cross-bridges between the actin and myosin filaments governs the contractile force generated by the muscle and also the contraction speed. A strain-energy function is used to describe the mechanical behaviour of the smooth muscle tissue. Besides the active contractile apparatus, the mechanical model also incorporates a passive elastic part. The constitutive model was compared to histological and isometric tensile test results for smooth muscle tissue from swine carotid artery. In order to be able to predict the active stress at different muscle lengths, a filament dispersion significantly larger than the one observed experimentally was required. Furthermore, a comparison of the predicted active stress for a case of uniaxially oriented myosin filaments and a case of filaments with a dispersion based on the experimental histological data shows that the difference in generated stress is noticeable but limited. Thus, the results suggest that myosin filament dispersion alone cannot explain the increase in active muscle stress with increasing muscle stretch.     

Characterization of in vitro motility assays using smooth muscle and cytoplasmic myosins

We have used two in vitro motility assays to study the relative movement of actin and myosin from turkey gizzards (smooth muscle) and human platelets. In the Nitella-based in vitro motility assay, myosin-coated polymer beads move over a fixed substratum of actin bundles derived from dissection of the alga, Nitella, whereas in the sliding actin filament assay fluorescently labeled actin filaments slide over myosin molecules adhered to a glass surface. Both assay systems yielded similar relative velocities using smooth muscle myosin and actin under our standard conditions. We have studied the effects of ATP, ionic strength, magnesium, and tropomyosin on the velocity and found that with the exception of the dependence on MgCl2, the two assays gave very similar results. Calcium over a concentration of pCa 8 to 4 had no effect on the velocity of actin filaments. Phosphorylated smooth muscle myosin propelled filaments of smooth muscle and skeletal muscle actin at the same rate. Phosphorylated smooth muscle and cytoplasmic myosin monomers also moved actin filaments, demonstrating that filament formation is not required for movement.     

The contractile apparatus of striated muscle in the course of atrophy and regeneration

Summary Changes in the contractile apparatus of denervated rat soleus muscles were investigated during the course of reinnervation.As observed earlier, in the course of denervation atrophy the ratio of myosin to actin filaments decreases because myosin filaments disappear faster than actin filaments (Jakubiec-Puka et al. 1981 a). After reinnervation the amount of myosin filaments and myosin heavy chains (myosin HC) in the muscle increased during the first few days; the increment of actin content was negligible. The proportion of myosin HC to actin remained lower than normal for about 30 days. The excess of actin filaments frequently observed in the newly-formed myofibrils reflects this disproportion.The results show a lability of myosin and suggest some cytoskeletal role for actin filaments.     

The variable twist of actin and its modulation by actin-binding proteins

Previous studies demonstrated that actin filaments have variable twist in which the intersubunit angles vary by approximately +/- 10 degrees within a filament. In this work we show that this variability was unchanged when different methods were used to prepare filaments for electron microscopy. We also show that actin-binding proteins can modulate the variability in twist. Three preparations of actin filaments were photographed in the electron microscope: negatively stained filaments, replicas of rapidly frozen, etched filaments, and frozen hydrated filaments. In addition, micrographs of actin + tropomyosin + troponin (thin filaments), of actin + myosin S1 (decorated filaments), and of filaments frayed from the acrosomal process of Limulus sperm (Limulus filaments) were obtained. We used two independent methods to measure variable twist based on Fourier transforms of single filaments. The first involved measuring layer line intensity versus filament length and the second involved measuring layer line position. We measured a variability in the intersubunit angle of actin filaments of approximately 12 degrees independent of the method of preparation or of measurement. Thin filaments have 15 degrees of variability, but the increase over pure actin is not statistically significant. Decorated filaments and Limulus filaments, however, have significantly less variability (approximately 2 and 1 degree, respectively), indicating a torsional stiffening relative to actin. The results from actin alone using different preparative methods are evidence that variable twist is a property of actin in solution. The results from actin filaments in the presence of actin-binding proteins suggest that the angular variability can be modulated, depending on the biological function.     

Super helix formation of actin filaments in an in vitro motile system.

Muscle contraction results from relative sliding of actin and myosin filaments. However, the possibility that actin filaments twist or rotate during sliding has not yet been experimentally investigated. We found that a super helix of an actin filament is formed in an in vitro motile system. This fact suggests that an actin filament twists and rotates due to a torque component of a sliding force generated at cross-bridges.     

F-actin retains a memory of angular order

Modifications can be made to F-actin that do not interfere with the binding of myosin but inhibit force generation, suggesting that actin's internal dynamics are important for muscle contraction. Observations from electron microscopy and x-ray diffraction have shown that subunits in F-actin have a relatively fixed axial rise but a variable twist. One possible explanation for this is that the actin subunits randomly exist in different discrete states of "twist, " with a significant energy barrier separating these states. This would result in very slow torsional transitions. Paracrystals impose increased order on F-actin filaments by reducing the variability in twist. By looking at filaments that have recently been dissociated from paracrystals, we find that F-actin retains a "memory" of its previous environment that persists for many seconds. This would be consistent with slow torsional transitions between discrete states of twist.     

Chick brain actin and myosin. Isolation and characterization

Brain actin extracted from an acetone powder of chick brains was purified by a cycle of polymerization-depolymerization followed by molecular sieve chromatography. The brain actin had a subunit molecular weight of 42,000 daltons as determined by co-electrophoresis with muscle actin. It underwent salt-dependent g to f transformation to form double helical actin filaments which could be "decorated" by muscle myosin subfragment 1. A critical concentration for polymerization of 1.3 microM was determined by measuring either the change in viscosity or absorbance at 232 nm. Brain actin was also capable of stimulating the ATPase activity of muscle myosin. Brain myosin was isolated from whole chick brain by a procedure involving high salt extraction, ammonium sulfate fractionation and molecular sieve chromatography. The purified myosin was composed of a 200,000-dalton heavy chain and three lower molecular weight light chains. In 0.6 M KCl the brain myosin had ATPase activity which was inhibited by Mg++, stimulated by Ca++, and maximally activated by EDTA. When dialyzed against 0.1 M KCl, the brain myosin self-assembled into short bipolar filaments. The bipolar filaments associated with each other to form long concatamers, and this association was enhanced by high concentrations of Mg++ ion. The brain myosin did not interact with chicken skeletal muscle myosin to form hybrid filaments. Furthermore, antibody recognition studies demonstrated that myosins from chicken brain, skeletal muscle, and smooth muscle were unique.     

The ghost muscle fiber with thin filaments reconstructed from nonmuscle actin--a model for studying the cytoskeleton using polarization microfluorimetry]

In muscle fibers which are free of myosin, tropomyosin and troponin thin filaments were reconstructed from muscle and non-muscle G-actin modified with 1,5-IAEDANS. Using polarized microfluorimetry it was shown that actin in such filaments maintained the ability to respond to conformational changes during actin interaction with subfragment of myosin (S1). The models of muscle fibers with reconstructed from non-muscle actin thin filaments are supposed to use for investigation of mechanisms of cell cytoskeleton functions with the help of polarized microfluorimetry.     

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.     

Study of regulatory effect of tropomyosin on actin-myosin interaction in skeletal muscle by in vitro motility assay

The interaction between myosin and actin in striated muscle tissue is regulated by Ca²⁺ via thin filament regulatory proteins. Skeletal muscle possesses a whole pattern of myosin and tropomyosin isoforms. The regulatory effect of tropomyosin on actin-myosin interaction was investigated by measuring the sliding velocity of both actin and actin-tropomyosin filaments over fast and slow skeletal myosins using the in vitro motility assay. The actin-tropomyosin filaments were reconstructed with tropomyosin isoforms from striated muscle tissue. It was found that tropomyosins with different content of α-, β-, and γ-chains added to actin filaments affect the sliding velocity of filaments in different ways. On the other hand, the sliding velocity of filaments with the same content of α-, β-, and Γ-chains depends on myosin isoforms of striated muscle. The reciprocal effects of myosin and tropomyosin on actin-myosin interaction in striated muscle may play a significant role in maintenance of effective work of striated muscle both during ontogenesis and under pathological conditions.     

Actin-facilitated assembly of smooth muscle myosin induces formation of actomyosin fibrils

To identify regulatory mechanisms potentially involved in formation of actomyosin structures in smooth muscle cells, the influence of F-actin on smooth muscle myosin assembly was examined. In physiologically relevant buffers, AMPPNP binding to myosin caused transition to the soluble 10S myosin conformation due to trapping of nucleotide at the active sites. The resulting 10S myosin-AMPPNP complex was highly stable and thick filament assembly was suppressed. However, upon addition to F-actin, myosin readily assembled to form thick filaments. Furthermore, myosin assembly caused rearrangement of actin filament networks into actomyosin fibers composed of coaligned F-actin and myosin thick filaments. Severin-induced fragmentation of actin in actomyosin fibers resulted in immediate disassembly of myosin thick filaments, demonstrating that actin filaments were indispensable for mediating myosin assembly in the presence of AMPPNP. Actomyosin fibers also formed after addition of F-actin to nonphosphorylated 10S myosin monomers containing the products of ATP hydrolysis trapped at the active site. The resulting fibers were rapidly disassembled after addition of millimolar MgATP and consequent transition of myosin to the soluble 10S state. However, reassembly of myosin filaments in the presence of MgATP and F-actin could be induced by phosphorylation of myosin P-light chains, causing regeneration of actomyosin fiber bundles. The results indicate that actomyosin fibers can be spontaneously formed by F-actin-mediated assembly of smooth muscle myosin. Moreover, induction of actomyosin fibers by myosin light chain phosphorylation in the presence of actin filament networks provides a plausible hypothesis for contractile fiber assembly in situ.     

Fine structure and contraction of isolated muscle actomyosin

Summary A modified thread model of isolated cross-striated muscle actomyosin was produced, which a priori consisted of both actin and myosin filaments forming a random network. This modified model contracts to the same extent as the normal model which lacks myosin filaments prior to contraction.The striking difference in the contraction behavior of the two models indicates 1) that in the normal model myosin filament formation occurs during contraction and 2) that the pre-existence of myosin filaments in the modified model increases the speed of contraction. Hence, the sliding mechanism involving myosin filaments is able to operate at a higher speed than the sliding mechanism which utilizes oligomeric myosin.     

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.     

Crossbridge and tropomyosin positions observed in native, interacting thick and thin filaments

Tropomyosin movements on thin filaments are thought to sterically regulate muscle contraction, but have not been visualized during active filament sliding. In addition, although 3-D visualization of myosin crossbridges has been possible in rigor, it has been difficult for thick filaments actively interacting with thin filaments. In the current study, using three-dimensional reconstruction of electron micrographs of interacting filaments, we have been able to resolve not only tropomyosin, but also the docking sites for weak and strongly bound crossbridges on thin filaments. In relaxing conditions, tropomyosin was observed on the outer domain of actin, and thin filament interactions with thick filaments were rare. In contracting conditions, tropomyosin had moved to the inner domain of actin, and extra density, reflecting weakly bound, cycling myosin heads, was also detected, on the extreme periphery of actin. In rigor conditions, tropomyosin had moved further on to the inner domain of actin, and strongly bound myosin heads were now observed over the junction of the inner and outer domains. We conclude (1) that tropomyosin movements consistent with the steric model of muscle contraction occur in interacting thick and thin filaments, (2) that myosin-induced movement of tropomyosin in activated filaments requires strongly bound crossbridges, and (3) that crossbridges are bound to the periphery of actin, at a site distinct from the strong myosin binding site, at an early stage of the crossbridge cycle.     

A filamentous cytoskeleton in vertebrate smooth muscle fibers.

There are three classes of myofilaments in vertebrate smooth muscle fibers. The thin filaments correspond to actin and the thick filaments are identified with myosin. The third class of myofilaments (100 A diam) is distinguished from both the actin and the myosin on the basis of fine structure, solubility, and pattern of localization in the muscle fibers. Direct structural evidence is presented to show that the 100A filament constitute an integrated filamentous network with the dense bodies in the sarcoplasm, and that they are not connected to either the actin or myosin filaments. Examination of (a) isolated dense bodies, (b) series of consecutive sections through the dense bodies, and (c) redistributed dense bodies in stretched muscle fibers supports this conclusion. It follows that the 100-A filaments complexes constitute a structrally distinct filamentous network. Analysis of polyacrylamide gels after electrophoresis of cell fractions that are enriched with respect to the 100-A filaments shows the presence of a new muscle protein with a molecular weight of 55,000. This protein can form filamentous segments that closely resemble in structure the native, isolated 100-A filaments. The results indicate that the filamentous network has a structure and composition that distinguish it from the actin and myosin in vertebrate smooth muscle.     

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.     

The Role of Structural Dynamics of Actin in Class-Specific Myosin Motility

The structural dynamics of actin, including the tilting motion between the small and large domains, are essential for proper interactions with actin-binding proteins. Gly146 is situated at the hinge between the two domains, and we previously showed that a G146V mutation leads to severe motility defects in skeletal myosin but has no effect on motility of myosin V. The present study tested the hypothesis that G146V mutation impaired rotation between the two domains, leading to such functional defects. First, our study showed that depolymerization of G146V filaments was slower than that of wild-type filaments. This result is consistent with the distinction of structural states of G146V filaments from those of the wild type, considering the recent report that stabilization of actin filaments involves rotation of the two domains. Next, we measured intramolecular FRET efficiencies between two fluorophores in the two domains with or without skeletal muscle heavy meromyosin or the heavy meromyosin equivalent of myosin V in the presence of ATP. Single-molecule FRET measurements showed that the conformations of actin subunits of control and G146V actin filaments were different in the presence of skeletal muscle heavy meromyosin. This altered conformation of G146V subunits may lead to motility defects in myosin II. In contrast, distributions of FRET efficiencies of control and G146V subunits were similar in the presence of myosin V, consistent with the lack of motility defects in G146V actin with myosin V. The distribution of FRET efficiencies in the presence of myosin V was different from that in the presence of skeletal muscle heavy meromyosin, implying that the roles of actin conformation in myosin motility depend on the type of myosin.