Elastic bending and active tilting of myosin heads during muscle contraction

Molecular Events of the Crossbridge Cycle Reflected in the Force–Velocity Relationship of Activated Muscle

Muscles convert chemical energy to mechanical work. Mechanical performance of a muscle is often assessed by the muscle’s ability to shorten and generate power over a range of loads or forces, characterized by the force–velocity and force–power relationships. The hyperbolic force–velocity relationship of muscle, for a long time, has been regarded as a pure empirical description of the force–velocity data. Connections between mechanical manifestation in terms of force–velocity properties and the kinetics of the crossbridge cycle have only been established recently. In this review, we describe how the model of Huxley’s crossbridge kinetics can be transformed to the hyperbolic Hill equation, and link the changes in force–velocity properties to molecular events within the crossbridge cycle driven by ATP hydrolysis. This allows us to reinterpret some findings from previous studies on experimental interventions that altered the force–velocity relationship and gain further insight into the molecular mechanisms of muscle contraction under physiological and pathophysiological conditions.

Anisotropic Elasticity of the Myosin Motor in Muscle

To define the mechanics and energetics of the myosin motor action in muscles, it is mandatory to know fundamental parameters such as the stiffness and the force of the single myosin motor, and the fraction of motors attached during contraction. These parameters can be defined in situ using sarcomere-level mechanics in single muscle fibers under the assumption that the stiffness of a myosin dimer with both motors attached (as occurs in rigor, when all motors are attached) is twice that of a single motor (as occurs in the isometric contraction). We use a mechanical/structural model to identify the constraints that underpin the stiffness of the myosin dimer with both motors attached to actin. By comparing the results of the model with the data in the literature, we conclude that the two-fold axial stiffness of the dimers with both motors attached is justified by a stiffness of the myosin motor that is anisotropic and higher along the axis of the myofilaments. A lower azimuthal stiffness of the motor plays an important role in the complex architecture of the sarcomere by allowing the motors to attach to actin filaments at different azimuthal angles relative to the thick filament.

Analysis methods and quality criteria for investigating muscle physiology using x-ray diffraction

X-ray diffraction studies of muscle have been tremendously powerful in providing fundamental insights into the structures of, for example, the myosin and actin filaments in a variety of muscles and the physiology of the cross-bridge mechanism during the contractile cycle. However, interpretation of x-ray diffraction patterns is far from trivial, and if modeling of the observed diffraction intensities is required it needs to be performed carefully with full knowledge of the possible pitfalls. Here, we discuss (1) how x-ray diffraction can be used as a tool to monitor various specific muscle properties and (2) how to get the most out of the rest of the observed muscle x-ray diffraction patterns by modeling where the reliability of the modeling conclusions can be objectively tested. In other x-ray diffraction methods, such as protein crystallography, the reliability of every step of the process is estimated and quoted in published papers. In this way, the quality of the structure determination can be properly assessed. To be honest with ourselves in the muscle field, we need to do as near to the same as we can, within the limitations of the techniques that we are using. We discuss how this can be done. We also use test cases to reveal the dos and don’ts of using x-ray diffraction to study muscle physiology.

The Sliding Filament Theory Since Andrew Huxley: Multiscale and Multidisciplinary Muscle Research

Two groundbreaking papers published in 1954 laid out the theory of the mechanism of muscle contraction based on force-generating interactions between myofilaments in the sarcomere that cause filaments to slide past one another during muscle contraction. The succeeding decades of research in muscle physiology have revealed a unifying interest: to understand the multiscale processes-from atom to organ-that govern muscle function. Such an understanding would have profound consequences for a vast array of applications, from developing new biomimetic technologies to treating heart disease. However, connecting structural and functional properties that are relevant at one spatiotemporal scale to those that are relevant at other scales remains a great challenge. Through a lens of multiscale dynamics, we review in this article current and historical research in muscle physiology sparked by the sliding filament theory.

Contracting striated muscle has a dynamic I-band spring with an undamped stiffness 100 times larger than the passive stiffness

KEY POINTS

Fast sarcomere-level mechanics in contracting intact fibres from frog skeletal muscle reveal an I-band spring with an undamped stiffness 100 times larger than the known static stiffness. This undamped stiffness remains constant in the range of sarcomere length 2.7-3.1 µm, showing the ability of the I-band spring to adapt its length to the width of the I-band. The stiffness and tunability of the I-band spring implicate titin as a force contributor that, during contraction, allows weaker half-sarcomeres to equilibrate with in-series stronger half-sarcomeres, preventing the development of sarcomere length inhomogeneity. This work opens new possibilities for the detailed in situ description of the structural-functional basis of muscle dysfunctions related to mutations or site-directed mutagenesis in titin that alter the I-band stiffness.

ABSTRACT

Force and shortening in the muscle sarcomere are due to myosin motors from thick filaments pulling nearby actin filaments toward the sarcomere centre. Thousands of serially linked sarcomeres in muscle make the shortening (and the shortening speed) macroscopic, while the intrinsic instability of in-series force generators is likely prevented by the cytoskeletal protein titin that connects the thick filament with the sarcomere end, working as an I-band spring that accounts for the rise of passive force with sarcomere length (SL). However, current estimates of titin stiffness, deduced from the passive force-SL relation and single molecule mechanics, are much smaller than what is required to avoid the development of large inhomogeneities among sarcomeres. In this work, using 4 kHz stiffness measurements on a population of sarcomeres selected along an intact fibre isolated from frog skeletal muscle contracting at different SLs (temperature 4°C), we measure the undamped stiffness of an I-band spring that at SL > 2.7 µm attains a maximum constant value of ∼6 pN nm-1 per half-thick filament, two orders of magnitude larger than expected from titin-related passive force. We conclude that a titin-like dynamic spring in the I-band, made by an undamped elastic element in-series with damped elastic elements, adapts its length to the SL with kinetics that provide force balancing among serially linked sarcomeres during contraction. In this way, the I-band spring plays a fundamental role in preventing the development of SL inhomogeneity.

The Work of Titin Protein Folding as a Major Driver in Muscle Contraction

Single-molecule atomic force microscopy and magnetic tweezers experiments have demonstrated that titin immunoglobulin (Ig) domains are capable of folding against a pulling force, generating mechanical work that exceeds that produced by a myosin motor. We hypothesize that upon muscle activation, formation of actomyosin cross bridges reduces the force on titin, causing entropic recoil of the titin polymer and triggering the folding of the titin Ig domains. In the physiological force range of 4-15 pN under which titin operates in muscle, the folding contraction of a single Ig domain can generate 200% of the work of entropic recoil and occurs at forces that exceed the maximum stalling force of single myosin motors. Thus, titin operates like a mechanical battery, storing elastic energy efficiently by unfolding Ig domains and delivering the charge back by folding when the motors are activated during a contraction. We advance the hypothesis that titin folding and myosin activation act as inextricable partners during muscle contraction.

Large and reversible myosin-dependent forces in rigidity sensing

Cells sense the rigidity of their environment through localized pinching, which occurs when myosin molecular motors generate contractions within actin filaments anchoring the cell to its surroundings. We present high-resolution experiments performed on these elementary contractile units in cells. Our experimental results challenge the current understanding of molecular motor force generation. Surprisingly, bipolar myosin filaments generate much larger forces per motor than measured in single molecule experiments. Further, contraction to a fixed distance, followed by relaxation at the same rate, is observed over a wide range of matrix rigidities. Lastly, step-wise displacements of the matrix contacts are apparent during both contraction and relaxation. Building upon a generic two-state model of molecular motor collections, we interpret these unexpected observations as spontaneously emerging features of a collective motor behavior. Our approach explains why, in the cellular context, collections of resilient and slow motors contract in a stepwise fashion while collections of weak and fast motors do not. We thus rationalize the specificity of motor contractions implied in rigidity sensing compared to previous in vitro observations.

Monitoring the myosin crossbridge cycle in contracting muscle: steps towards 'Muscle-the Movie'

Some vertebrate muscles (e.g. those in bony fish) have a simple lattice A-band which is so well ordered that low-angle X-ray diffraction patterns are sampled in a simple way amenable to crystallographic techniques. Time-resolved X-ray diffraction through the contractile cycle should provide a movie of the molecular movements involved in muscle contraction. Generation of 'Muscle-The Movie' was suggested in the 1990s and since then efforts have been made to work out how to achieve it. Here we discuss how a movie can be generated, we discuss the problems and opportunities, and present some new observations. Low angle X-ray diffraction patterns from bony fish muscles show myosin layer lines that are well sampled on row-lines expected from the simple hexagonal A-band lattice. The 1st, 2nd and 3rd myosin layer lines at d-spacings of around 42.9 nm, 21.5 nm and 14.3 nm respectively, get weaker in patterns from active muscle, but there is a well-sampled intensity remnant along the layer lines. We show here that the pattern from the tetanus plateau is not a residual resting pattern from fibres that have not been fully activated, but is a different well-sampled pattern showing the presence of a second, myosin-centred, arrangement of crossbridges within the active crossbridge population. We also show that the meridional M3 peak from active muscle has two components of different radial widths consistent with (i) active myosin-centred (probably weak-binding) heads giving a narrow peak and (ii) heads on actin in strong states giving a broad peak.

Muscle Function from Organisms to Molecules

Gaps in our understanding of muscle contraction at the molecular level limit the ability to predict in vivo muscle forces in humans and animals during natural movements. Because muscles function as motors, springs, brakes, or struts, it is not surprising that uncertainties remain as to how sarcomeres produce these different behaviors. Current theories fail to explain why a single extra stimulus, added shortly after the onset of a train of stimuli, doubles the rate of force development. When stretch and doublet stimulation are combined in a work loop, muscle force doubles and work increases by 50% per cycle, yet no theory explains why this occurs. Current theories also fail to predict persistent increases in force after stretch and decreases in force after shortening. Early studies suggested that all of the instantaneous elasticity of muscle resides in the cross-bridges. Subsequent cross-bridge models explained the increase in force during active stretch, but required ad hoc assumptions that are now thought to be unreasonable. Recent estimates suggest that cross-bridges account for only ∼12% of the energy stored by muscles during active stretch. The inability of cross-bridges to account for the increase in force that persists after active stretching led to development of the sarcomere inhomogeneity theory. Nearly all predictions of this theory fail, yet the theory persists. In stretch-shortening cycles, muscles with similar activation and contractile properties function as motors or brakes. A change in the phase of activation relative to the phase of length changes can convert a muscle from a motor into a spring or brake. Based on these considerations, it is apparent that the current paradigm of muscle mechanics is incomplete. Recent advances in our understanding of giant muscle proteins, including twitchin and titin, allow us to expand our vision beyond cross-bridges to understand how muscles contribute to the biomechanics and control of movement.

Basic science and clinical use of eccentric contractions: History and uncertainties

The peculiar attributes of muscles that are stretched when active have been noted for nearly a century. Understandably, the focus of muscle physiology has been primarily on shortening and isometric contractions, as eloquently revealed by A.V. Hill and subsequently by his students. When the sliding filament theory was introduced by A.F. Huxley and H.E. Huxley, it was a relatively simple task to link Hill's mechanical observations to the actions of the cross bridges during these shortening and isometric contractions. In contrast, lengthening or eccentric contractions have remained somewhat enigmatic. Dismissed as necessarily causing muscle damage, eccentric contractions have been much more difficult to fit into the cross-bridge theory. The relatively recent discovery of the giant elastic sarcomeric filament titin has thrust a previously missing element into any discussion of muscle function, in particular during active stretch. Indeed, the unexpected contribution of giant elastic proteins to muscle contractile function is highlighted by recent discoveries that twitchin-actin interactions are responsible for the "catch" property of invertebrate muscle. In this review, we examine several current theories that have been proposed to account for the properties of muscle during eccentric contraction. We ask how well each of these explains existing data and how an elastic filament can be incorporated into the sliding filament model. Finally, we review the increasing body of evidence for the benefits of including eccentric contractions into a program of muscle rehabilitation and strengthening.

Standard Loading Profile in Matrix Rigidity Sensing

It is important to learn features of locally applied forces by cells during matrix rigidity sensing, since the function of mechanosensing proteins would be affected by force magnitude, loading velocity, or even loading history. Here, we investigate a rigidity-sensing apparatus consisting of a contractile unit on matrices. Strikingly, our analysis indicates that the matrix rigidity is not only sensed with a fixed step size in displacement but also with a fixed apparent loading velocity. The fixed step size is shown to be correlated with the monomer size of actin filament. This work suggests that the loading profile during rigidity sensing is regulated by various aspects of the contractile unit, which then serves as the standard in sensing varied rigidity of the matrix.

Mechanical parameters of the molecular motor myosin II determined in permeabilised fibres from slow and fast skeletal muscles of the rabbit

KEY POINTS

The different performance of slow and fast muscles is mainly attributed to diversity of the myosin heavy chain (MHC) isoform expressed within them. In this study fast sarcomere-level mechanics has been applied to Ca²⁺ -activated single permeabilised fibres isolated from soleus (containing the slow myosin isoform) and psoas (containing the fast myosin isoform) muscles of rabbit for a comparative definition of the mechano-kinetics of force generation by slow and fast myosin isoforms in situ. The stiffness and the force of the slow myosin isoform are three times smaller than those of the fast isoform, suggesting that the stiffness of the myosin motor is a determinant of the isoform-dependent functional diversity between skeletal muscles. These results open the question of the mechanism that can reconcile the reduced performance of the slow MHC with the higher efficiency of the slow muscle.

ABSTRACT

The skeletal muscle exhibits large functional differences depending on the myosin heavy chain (MHC) isoform expressed in its molecular motor, myosin II. The differences in the mechanical features of force generation by myosin isoforms were investigated in situ by using fast sarcomere-level mechanical methods in permeabilised fibres (sarcomere length 2.4 μm, temperature 12°C, 4% dextran T-500) from slow (soleus, containing the MHC-1 isoform) and fast (psoas, containing the MHC-2X isoform) skeletal muscle of the rabbit. The stiffness of the half-sarcomere was determined at the plateau of Ca²⁺ -activated isometric contractions and in rigor and analysed with a model that accounted for the filament compliance to estimate the stiffness of the myosin motor (ε). ε was 0.56 ± 0.04 and 1.70 ± 0.37 pN nm^-1 for the slow and fast isoform, respectively, while the average strain per attached motor (s₀ ) was similar (∼3.3 nm) in both isoforms. Consequently the force per motor (F₀  = εs₀ ) was three times smaller in the slow isoform than in the fast isoform (1.89 ± 0.43 versus 5.35 ± 1.51 pN). The fraction of actin-attached motors responsible for maximum isometric force at saturating Ca²⁺ (T_0,4.5 ) was 0.47 ± 0.09 in soleus fibres, 70% larger than that in psoas fibres (0.29 ± 0.08), so that F₀ in slow fibres was decreased by only 53%. The lower stiffness and force of the slow myosin isoform open the question of the molecular basis of the higher efficiency of slow muscle with respect to fast muscle.

X-ray Diffraction Evidence for Low Force Actin-Attached and Rigor-Like Cross-Bridges in the Contractile Cycle

Defining the structural changes involved in the myosin cross-bridge cycle on actin in active muscle by X-ray diffraction will involve recording of the whole two dimensional (2D) X-ray diffraction pattern from active muscle in a time-resolved manner. Bony fish muscle is the most highly ordered vertebrate striated muscle to study. With partial sarcomere length (SL) control we show that changes in the fish muscle equatorial A-band (10) and (11) reflections, along with (10)/(11) intensity ratio and the tension, are much more rapid than without such control. Times to 50% change with SL control were 19.5 (±2.0) ms, 17.0 (±1.1) ms, 13.9 (±0.4) ms and 22.5 (±0.8) ms, respectively, compared to 25.0 (±3.4) ms, 20.5 (±2.6) ms, 15.4 (±0.6) ms and 33.8 (±0.6) ms without control. The (11) intensity and the (10)/(11) intensity ratio both still change ahead of tension, supporting the likelihood of the presence of a head population close to or on actin, but producing little or no force, in the early stages of the contractile cycle. Higher order equatorials (e.g., (30), (31), and (32)), more sensitive to crossbridge conformation and distribution, also change very rapidly and overshoot their tension plateau values by a factor of around two, well before the tension plateau has been reached, once again indicating an early low-force cross-bridge state in the contractile cycle. Modelling of these intensity changes suggests the presence of probably two different actin-attached myosin head structural states (mainly low-force attached and rigor-like). No more than two main attached structural states are necessary and sufficient to explain the observations. We find that 48% of the heads are off actin giving a resting diffraction pattern, 20% of heads are in the weak binding conformation and 32% of the heads are in the strong (rigor-like) state. The strong states account for 96% of the tension at the tetanus plateau.

Cardiac Myosin Binding Protein-C Phosphorylation Modulates Myofilament Length-Dependent Activation

Cardiac myosin binding protein-C (cMyBP-C) phosphorylation is an important regulator of contractile function, however, its contributions to length-dependent changes in cross-bridge (XB) kinetics is unknown. Therefore, we performed mechanical experiments to quantify contractile function in detergent-skinned ventricular preparations isolated from wild-type (WT) hearts, and hearts expressing non-phosphorylatable cMyBP-C [Ser to Ala substitutions at residues Ser273, Ser282, and Ser302 (i.e., 3SA)], at sarcomere length (SL) 1.9 μm or 2.1μm, prior and following protein kinase A (PKA) treatment. Steady-state force generation measurements revealed a blunting in the length-dependent increase in myofilament Ca(2+)-sensitivity of force generation (pCa50) following an increase in SL in 3SA skinned myocardium compared to WT skinned myocardium. Dynamic XB behavior was assessed at submaximal Ca(2+)-activations by imposing an acute rapid stretch of 2% of initial muscle length, and measuring both the magnitudes and rates of resultant phases of force decay due to strain-induced XB detachment and delayed force rise due to recruitment of additional XBs with increased SL (i.e., stretch activation). The magnitude (P2) and rate of XB detachment (k rel) following stretch was significantly reduced in 3SA skinned myocardium compared to WT skinned myocardium at short and long SL, and prior to and following PKA treatment. Furthermore, the length-dependent acceleration of k rel due to decreased SL that was observed in WT skinned myocardium was abolished in 3SA skinned myocardium. PKA treatment accelerated the rate of XB recruitment (k df) following stretch at both SL's in WT but not in 3SA skinned myocardium. The amplitude of the enhancement in force generation above initial pre-stretch steady-state levels (P3) was not different between WT and 3SA skinned myocardium at any condition measured. However, the magnitude of the entire delayed force phase which can dip below initial pre-stretch steady-state levels (Pdf) was significantly lower in 3SA skinned myocardium under all conditions, in part due to a reduced magnitude of XB detachment (P2) in 3SA skinned myocardium compared to WT skinned myocardium. These findings demonstrate that cMyBP-C phospho-ablation regulates SL- and PKA-mediated effects on XB kinetics in the myocardium, which would be expected to contribute to the regulation of the Frank-Starling mechanism.

Temperature effect on the chemomechanical regulation of substeps within the power stroke of a single Myosin II

Myosin IIs in the skeletal muscle are highly efficient nanoscale machines evolved in nature. Understanding how they function can not only bring insights into various biological processes but also provide guidelines to engineer synthetic nanoscale motors working in the vicinity of thermal noise. Though it was clearly demonstrated that the behavior of a skeletal muscle fiber, or that of a single myosin was strongly affected by the temperature, how exactly the temperature affects the kinetics of a single myosin is not fully understood. By adapting the newly developed transitional state model, which successfully explained the intriguing motor force regulation during skeletal muscle contraction, here we systematically explain how exactly the power stroke of a single myosin proceeds, with the consideration of the chemomechanical regulation of sub-steps within the stroke. The adapted theory is then utilized to investigate the temperature effect on various aspects of the power stroke. Our analysis suggests that, though swing rates, the isometric force, and the maximal stroke size all strongly vary with the temperature, the temperature can have a very small effect on the releasable elastic energy within the power stroke.

Mechanics of Vascular Smooth Muscle

Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress-development, sustained stress-maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip-catch bond, and a regulated two-step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress-strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure-function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM.

Poorly understood aspects of striated muscle contraction

Muscle contraction results from cyclic interactions between the contractile proteins myosin and actin, driven by the turnover of adenosine triphosphate (ATP). Despite intense studies, several molecular events in the contraction process are poorly understood, including the relationship between force-generation and phosphate-release in the ATP-turnover. Different aspects of the force-generating transition are reflected in the changes in tension development by muscle cells, myofibrils and single molecules upon changes in temperature, altered phosphate concentration, or length perturbations. It has been notoriously difficult to explain all these events within a given theoretical framework and to unequivocally correlate observed events with the atomic structures of the myosin motor. Other incompletely understood issues include the role of the two heads of myosin II and structural changes in the actin filaments as well as the importance of the three-dimensional order. We here review these issues in relation to controversies regarding basic physiological properties of striated muscle. We also briefly consider actomyosin mutation effects in cardiac and skeletal muscle function and the possibility to treat these defects by drugs.

Mechanism of the calcium-regulation of muscle contraction--in pursuit of its structural basis

The author reviewed the research that led to establish the structural basis for the mechanism of the calcium-regulation of the contraction of striated muscles. The target of calcium ions is troponin on the thin filaments, of which the main component is the double-stranded helix of actin. A model of thin filament was generated by adding tropomyosin and troponin. During the process to provide the structural evidence for the model, the troponin arm was found to protrude from the calcium-depleted troponin and binds to the carboxyl-terminal region of actin. As a result, the carboxyl-terminal region of tropomyosin shifts and covers the myosin-binding sites of actin to block the binding of myosin. At higher calcium concentrations, the troponin arm changes its partner from actin to the main body of calcium-loaded troponin. Then, tropomyosin shifts back to the position near the grooves of actin double helix, and the myosin-binding sites of actin becomes available to myosin resulting in force generation through actin-myosin interactions.

The contributions of filaments and cross-bridges to sarcomere compliance in skeletal muscle

Force generation in the muscle sarcomere is driven by the head domain of the myosin molecule extending from the thick filament to form cross-bridges with the actin-containing thin filament. Following attachment, a structural working stroke in the head pulls the thin filament towards the centre of the sarcomere, producing, under unloaded conditions, a filament sliding of ∼ 11 nm. The mechanism of force generation by the myosin head depends on the relationship between cross-bridge force and movement, which is determined by compliances of the cross-bridge (C(cb)) and filaments. By measuring the force dependence of the spacing of the high-order myosin- and actin-based X-ray reflections from sartorius muscles of Rana esculenta we find a combined filament compliance (Cf) of 13.1 ± 1.2 nm MPa(-1), close to recent estimates from single fibre mechanics (12.8 ± 0.5 nm MPa(-1)). C(cb) calculated using these estimates is 0.37 ± 0.12 nm pN(-1), a value fully accounted for by the compliance of the myosin head domain, 0.38 ± 0.06 nm pN(-1), obtained from the intensity changes of the 14.5 nm myosin-based X-ray reflection in response to 3 kHz oscillations imposed on single muscle fibres in rigor. Thus, a significant contribution to C(cb) from the myosin tail that joins the head to the thick filament is excluded. The low C(cb) value indicates that the myosin head generates isometric force by a small sub-step of the 11 nm stroke that drives filament sliding at low load. The implications of these results for the mechanism of force generation by myosins have general relevance for cardiac and non-muscle myosins as well as for skeletal muscle.

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.

Molecular mechanism regulating myosin and cardiac functions by ELC

The essential myosin light chain (ELC) is involved in modulation of force generation of myosin motors and cardiac contraction, while its mechanism of action remains elusive. We hypothesized that ELC could modulate myosin stiffness which subsequently determines its force production and cardiac contraction. Therefore, we generated heterologous transgenic mouse (TgM) strains with cardiomyocyte-specific expression of ELC with human ventricular ELC (hVLC-1; TgM(hVLC-1)) or E56G-mutated hVLC-1 (hVLC-1(E56G); TgM(E56G)). hVLC-1 or hVLC-1(E56G) expression in TgM was around 39% and 41%, respectively of total VLC-1. Laser trap and in vitro motility assays showed that stiffness and actin sliding velocity of myosin with hVLC-1 prepared from TgM(hVLC-1) (1.67 pN/nm and 2.3 μm/s, respectively) were significantly higher than myosin with hVLC-1(E56G) prepared from TgM(E56G) (1.25 pN/nm and 1.7 μm/s, respectively) or myosin with mouse VLC-1 (mVLC-1) prepared from C57/BL6 (1.41 pN/nm and 1.5 μm/s, respectively). Maximal left ventricular pressure development of isolated perfused hearts in vitro prepared from TgM(hVLC-1) (80.0 mmHg) were significantly higher than hearts from TgM(E56G) (66.2 mmHg) or C57/BL6 (59.3±3.9 mmHg). These findings show that ELCs decreased myosin stiffness, in vitro motility, and thereby cardiac functions in the order hVLC-1>hVLC-1(E56G)≈mVLC-1. They also suggest a molecular pathomechanism of hypertrophic cardiomyopathy caused by hVLC-1 mutations.

Sarcomere-length dependence of myosin filament structure in skeletal muscle fibres of the frog

X-ray diffraction patterns were recorded at beamline ID02 of the European Synchrotron Radiation Facility from small bundles of skeletal muscle fibres from Rana esculenta at sarcomere lengths between 2.1 and 3.5 μm at 4°C. The intensities of the X-ray reflections from resting fibres associated with the quasi-helical order of the myosin heads and myosin binding protein C (MyBP-C) decreased in the sarcomere length range 2.6-3.0 μm but were constant outside it, suggesting that an OFF conformation of the thick filament is maintained by an interaction between MyBP-C and the thin filaments. During active isometric contraction the intensity of the M3 reflection from the regular repeat of the myosin heads along the filaments decreased in proportion to the overlap between thick and thin filaments, with no change in its interference fine structure. Thus, myosin heads in the regions of the thick filaments that do not overlap with thin filaments are highly disordered during isometric contraction, in contrast to their quasi-helical order at rest. Heads in the overlap region that belong to two-headed myosin molecules that are fully detached from actin are also highly disordered, in contrast to the detached partners of actin-attached heads. These results provide strong support for the concept of a regulatory structural transition in the thick filament involving changes in both the organisation of the myosin heads on its surface and the axial periodicity of the myosin tails in its backbone, mediated by an interaction between MyBP-C and the thin filaments.

Stiffness, working stroke, and force of single-myosin molecules in skeletal muscle: elucidation of these mechanical properties via nonlinear elasticity evaluation

In muscles, the arrays of skeletal myosin molecules interact with actin filaments and continuously generate force at various contraction speeds. Therefore, it is crucial for myosin molecules to generate force collectively and minimize the interference between individual myosin molecules. Knowledge of the elasticity of myosin molecules is crucial for understanding the molecular mechanisms of muscle contractions because elasticity directly affects the working and drag (resistance) force generation when myosin molecules are positively or negatively strained. The working stroke distance is also an important mechanical property necessary for elucidation of the thermodynamic efficiency of muscle contractions at the molecular level. In this review, we focus on these mechanical properties obtained from single-fiber and single-molecule studies and discuss recent findings associated with these mechanical properties. We also discuss the potential molecular mechanisms associated with reduction of the drag effect caused by negatively strained myosin molecules.

The cross-bridge spring: can cool muscles store elastic energy?

Muscles not only generate force. They may act as springs, providing energy storage to drive locomotion. Although extensible myofilaments are implicated as sites of energy storage, we show that intramuscular temperature gradients may enable molecular motors (cross-bridges) to store elastic strain energy. By using time-resolved small-angle x-ray diffraction paired with in situ measurements of mechanical energy exchange in flight muscles of Manduca sexta, we produced high-speed movies of x-ray equatorial reflections, indicating cross-bridge association with myofilaments. A temperature gradient within the flight muscle leads to lower cross-bridge cycling in the cooler regions. Those cross-bridges could elastically return energy at the extrema of muscle lengthening and shortening, helping drive cyclic wing motions. These results suggest that cross-bridges can perform functions other than contraction, acting as molecular links for elastic energy storage.

Molecular mechanism of actin-myosin motor in muscle

The interaction of actin and myosin powers striated and smooth muscles and some other types of cell motility. Due to its highly ordered structure, skeletal muscle is a very convenient object for studying the general mechanism of the actin-myosin molecular motor. The history of investigation of the actin-myosin motor is briefly described. Modern concepts and data obtained with different techniques including protein crystallography, electron microscopy, biochemistry, and protein engineering are reviewed. Particular attention is given to X-ray diffraction studies of intact muscles and single muscle fibers with permeabilized membrane as they give insight into structural changes that underlie force generation and work production by the motor. Time-resolved low-angle X-ray diffraction on contracting muscle fibers using modern synchrotron radiation sources is used to follow movement of myosin heads with unique time and spatial resolution under near physiological conditions.

The azimuthal path of myosin V and its dependence on lever-arm length

Myosin V (myoV) is a two-headed myosin capable of taking many successive steps along actin per diffusional encounter, enabling it to transport vesicular and ribonucleoprotein cargos in the dense and complex environment within cells. To better understand how myoV navigates along actin, we used polarized total internal reflection fluorescence microscopy to examine angular changes of bifunctional rhodamine probes on the lever arms of single myoV molecules in vitro. With a newly developed analysis technique, the rotational motions of the lever arm and the local orientation of each probe relative to the lever arm were estimated from the probe’s measured orientation. This type of analysis could be applied to similar studies on other motor proteins, as well as other proteins with domains that undergo significant rotational motions. The experiments were performed on recombinant constructs of myoV that had either the native-length (six IQ motifs and calmodulins [CaMs]) or truncated (four IQ motifs and CaMs) lever arms. Native-length myoV-6IQ mainly took straight steps along actin, with occasional small azimuthal tilts around the actin filament. Truncated myoV-4IQ showed an increased frequency of azimuthal steps, but the magnitudes of these steps were nearly identical to those of myoV-6IQ. The results show that the azimuthal deflections of myoV on actin are more common for the truncated lever arm, but the range of these deflections is relatively independent of its lever-arm length.

Structural and functional aspects of the myosin essential light chain in cardiac muscle contraction

The myosin essential light chain (ELC) is a structural component of the actomyosin cross-bridge, but its function is poorly understood, especially the role of the cardiac specific N-terminal extension in modulating actomyosin interaction. Here, we generated transgenic (Tg) mice expressing the A57G (alanine to glycine) mutation in the cardiac ELC known to cause familial hypertrophic cardiomyopathy (FHC). The function of the ELC N-terminal extension was investigated with the Tg-Δ43 mouse model, whose myocardium expresses a truncated ELC. Low-angle X-ray diffraction studies on papillary muscle fibers in rigor revealed a decreased interfilament spacing (≈ 1.5 nm) and no alterations in cross-bridge mass distribution in Tg-A57G mice compared to Tg-WT, expressing the full-length nonmutated ELC. The truncation mutation showed a 1.3-fold increase in I(1,1)/I(1,0), indicating a shift of cross-bridge mass from the thick filament backbone toward the thin filaments. Mechanical studies demonstrated increased stiffness in Tg-A57G muscle fibers compared to Tg-WT or Tg-Δ43. The equilibrium constant for the cross-bridge force generation step was smallest in Tg-Δ43. These results support an important role for the N-terminal ELC extension in prepositioning the cross-bridge for optimal force production. Subtle changes in the ELC sequence were sufficient to alter cross-bridge properties and lead to pathological phenotypes.

Visualizing key hinges and a potential major source of compliance in the lever arm of myosin

We have determined the 2.3-Å-resolution crystal structure of a myosin light chain domain, corresponding to one type found in sea scallop catch ("smooth") muscle. This structure reveals hinges that may function in the "on" and "off" states of myosin. The molecule adopts two different conformations about the heavy chain "hook" and regulatory light chain (RLC) helix D. This conformational change results in extended and compressed forms of the lever arm whose lengths differ by 10 Å. The heavy chain hook and RLC helix D hinges could thus serve as a potential major and localized source of cross-bridge compliance during the contractile cycle. In addition, in one of the molecules of the crystal, part of the RLC N-terminal extension is seen in atomic detail and forms a one-turn alpha-helix that interacts with RLC helix D. This extension, whose sequence is highly variable in different myosins, may thus modulate the flexibility of the lever arm. Moreover, the relative proximity of the phosphorylation site to the helix D hinge suggests a potential role for conformational changes about this hinge in the transition between the on and off states of regulated myosins.

Crossbridge and filament compliance in muscle: implications for tension generation and lever arm swing

The stiffness of myosin heads attached to actin is a crucial parameter in determining the kinetics and mechanics of the crossbridge cycle. It has been claimed that the stiffness of myosin heads in the anterior tibialis muscle of the common frog (Rana temporaria) is as high as 3.3 pN/nm, substantially higher than its value in rabbit muscle (~1.7 pN/nm). However, the crossbridge stiffness measurement has a large error since the contribution of crossbridges to half-sarcomere compliance is obtained by subtracting from the half-sarcomere compliance the contributions of the thick and thin filaments, each with a substantial error. Calculation of its value for isometric contraction also depends on the fraction of heads that are attached, for which there is no consensus. Surprisingly, the stiffness of the myosin head from the edible frog, Rana esculenta, determined in the same manner, is only 60% of that in Rana temporaria. In our view it is unlikely that the value of such a crucial parameter could differ so substantially between two frog species. Since the means of the myosin head stiffness in these two species are not significantly different, we suggest that the best estimate of the stiffness of the myosin heads for frog muscle is the average of these data, a value similar to that for rabbit muscle. This would allow both frog and rabbit muscles to operate the same low-cooperativity mechanism for the crossbridge cycle with only one or two tension-generating steps. We review evidence that much of the compliance of the myosin head is located in the pliant region where the lever arm emerges from the converter and propose that tension generation ("tensing") caused by the rotation and movement of the converter is a separate event from the passive swinging of the lever arm in its working stroke in which the strain energy stored in the pliant region is used to do work.

Response of rigor cross-bridges to stretch detected by fluorescence lifetime imaging microscopy of myosin essential light chain in skeletal muscle fibers

We applied fluorescence lifetime imaging microscopy to map the microenvironment of the myosin essential light chain (ELC) in permeabilized skeletal muscle fibers. Four ELC mutants containing a single cysteine residue at different positions in the C-terminal half of the protein (ELC-127, ELC-142, ELC-160, and ELC-180) were generated by site-directed mutagenesis, labeled with 7-diethylamino-3-((((2-iodoacetamido)ethyl)amino)carbonyl)coumarin, and introduced into permeabilized rabbit psoas fibers. Binding to the myosin heavy chain was associated with a large conformational change in the ELC. When the fibers were moved from relaxation to rigor, the fluorescence lifetime increased for all label positions. However, when 1% stretch was applied to the rigor fibers, the lifetime decreased for ELC-127 and ELC-180 but did not change for ELC-142 and ELC-160. The differential change of fluorescence lifetime demonstrates the shift in position of the C-terminal domain of ELC with respect to the heavy chain and reveals specific locations in the lever arm region sensitive to the mechanical strain propagating from the actin-binding site to the lever arm.

Electron tomography of cryofixed, isometrically contracting insect flight muscle reveals novel actin-myosin interactions

Background

Isometric muscle contraction, where force is generated without muscle shortening, is a molecular traffic jam in which the number of actin-attached motors is maximized and all states of motor action are trapped with consequently high heterogeneity. This heterogeneity is a major limitation to deciphering myosin conformational changes in situ.

Methodology

We used multivariate data analysis to group repeat segments in electron tomograms of isometrically contracting insect flight muscle, mechanically monitored, rapidly frozen, freeze substituted, and thin sectioned. Improved resolution reveals the helical arrangement of F-actin subunits in the thin filament enabling an atomic model to be built into the thin filament density independent of the myosin. Actin-myosin attachments can now be assigned as weak or strong by their motor domain orientation relative to actin. Myosin attachments were quantified everywhere along the thin filament including troponin. Strong binding myosin attachments are found on only four F-actin subunits, the “target zone”, situated exactly midway between successive troponin complexes. They show an axial lever arm range of 77°/12.9 nm. The lever arm azimuthal range of strong binding attachments has a highly skewed, 127° range compared with X-ray crystallographic structures. Two types of weak actin attachments are described. One type, found exclusively in the target zone, appears to represent pre-working-stroke intermediates. The other, which contacts tropomyosin rather than actin, is positioned M-ward of the target zone, i.e. the position toward which thin filaments slide during shortening.

Conclusion

We present a model for the weak to strong transition in the myosin ATPase cycle that incorporates azimuthal movements of the motor domain on actin. Stress/strain in the S2 domain may explain azimuthal lever arm changes in the strong binding attachments. The results support previous conclusions that the weak attachments preceding force generation are very different from strong binding attachments.

FRET characterisation for cross-bridge dynamics in single-skinned rigor muscle fibres

In this work we demonstrate for the first time the use of Förster resonance energy transfer (FRET) as an assay to monitor the dynamics of cross-bridge conformational changes directly in single muscle fibres. The advantage of FRET imaging is its ability to measure distances in the nanometre range, relevant for structural changes in actomyosin cross-bridges. To reach this goal we have used several FRET couples to investigate different locations in the actomyosin complex. We exchanged the native essential light chain of myosin with a recombinant essential light chain labelled with various thiol-reactive chromophores. The second fluorophore of the FRET couple was introduced by three approaches: labelling actin, labelling SH1 cysteine and binding an adenosine triphosphate (ATP) analogue. We characterise FRET in rigor cross-bridges: in this condition muscle fibres are well described by a single FRET population model which allows us to evaluate the true FRET efficiency for a single couple and the consequent donor–acceptor distance. The results obtained are in good agreement with the distances expected from crystallographic data. The FRET characterisation presented herein is essential before moving onto dynamic measurements, as the FRET efficiency differences to be detected in an active muscle fibre are on the order of 10–15% of the FRET efficiencies evaluated here. This means that, to obtain reliable results to monitor the dynamics of cross-bridge conformational changes, we had to fully characterise the system in a steady-state condition, demonstrating firstly the possibility to detect FRET and secondly the viability of the present approach to distinguish small FRET variations.

The mechanism of the resistance to stretch of isometrically contracting single muscle fibres

Rapid attachment to actin of the detached motor domain of myosin dimers with one motor domain already attached has been hypothesized to explain the stretch-induced changes in X-ray interference and stiffness of active muscle. Here, using half-sarcomere mechanics in single frog muscle fibres (2.15 microm sarcomere length and 4 degrees C), we show that: (1) an increase in stiffness of the half-sarcomere under stretch is specific to isometric contraction and does not occur in rigor, indicating that the mechanism of stiffness increase is an increase in the number of attached motors; (2) 2 ms after 100 micros stretches (amplitude 2-8 nm per half-sarcomere) imposed during an isometric tetanus, the stiffness of the array of myosin motors in each half-sarcomere (e(m)) increases above the isometric value (e(m0)); (3) e(m) has a sigmoidal dependence on the distortion of the motor domains (Delta z) attached in isometric contraction, with a maximum approximately 2 e(m0) for a distortion of approximately 6 nm; e(m) is influenced by detachment of motors at z > 6 nm; (4) at the end of the 100 micros stretch the relation between e(m)/e(m0) and Delta z lies slightly but not significantly above that at 2 ms. These results support the idea that stretch-induced sliding of the actin filament distorts the actin-attached motor domain of the myosin dimers away from the centre of the sarcomere, providing the steric conditions for rapid attachment of the second motor domain. The rate of new motor attachment must be as high as 7.5 x 10(4) s(1) and explains the rapid and efficient increase of the resistance of active muscle to stretch.

Inferring crossbridge properties from skeletal muscle energetics

Work is generated in muscle by myosin crossbridges during their interaction with the actin filament. The energy from which the work is produced is the free energy change of ATP hydrolysis and efficiency quantifies the fraction of the energy supplied that is converted into work. The purpose of this review is to compare the efficiency of frog skeletal muscle determined from measurements of work output and either heat production or chemical breakdown with the work produced per crossbridge cycle predicted on the basis of the mechanical responses of contracting muscle to rapid length perturbations. We review the literature to establish the likely maximum crossbridge efficiency for frog skeletal muscle (0.4) and, using this value, calculate the maximum work a crossbridge can perform in a single attachment to actin (33 x 10(-21) J). To see whether this amount of work is consistent with our understanding of crossbridge mechanics, we examine measurements of the force responses of frog muscle to fast length perturbations and, taking account of filament compliance, determine the crossbridge force-extension relationship and the velocity dependences of the fraction of crossbridges attached and average crossbridge strain. These data are used in combination with a Huxley-Simmons-type model of the thermodynamics of the attached crossbridge to determine whether this type of model can adequately account for the observed muscle efficiency. Although it is apparent that there are still deficiencies in our understanding of how to accurately model some aspects of ensemble crossbridge behaviour, this comparison shows that crossbridge energetics are consistent with known crossbridge properties.

Cardiomyopathy mutations reveal variable region of myosin converter as major element of cross-bridge compliance

The ability of myosin to generate motile forces is based on elastic distortion of a structural element of the actomyosin complex (cross-bridge) that allows strain to develop before filament sliding. Addressing the question, which part of the actomyosin complex experiences main elastic distortion, we suggested previously that the converter domain might be the most compliant region of the myosin head domain. Here we test this proposal by studying functional effects of naturally occurring missense mutations in the beta-myosin heavy chain, 723Arg --> Gly (R723G) and 736Ile --> Thr (I736T), in comparison to 719Arg --> Trp (R719W). All three mutations are associated with hypertrophic cardiomyopathy and are located in the converter region of the myosin head domain. We determined several mechanical parameters of single skinned slow fibers isolated from Musculus soleus biopsies of hypertrophic cardiomyopathy patients and healthy controls. Major findings of this study for mutation R723G were i), a >40% increase in fiber stiffness in rigor with a 2.9-fold increase in stiffness per myosin head (S( *)(rigor R723G) = 0.84 pN/nm S( *)(rigor WT) = 0.29 pN/nm); and ii), a significant increase in force per head (F( *)(10 degrees C), 1.99 pN vs. 1.49 pN = 1.3-fold increase; F( *)(20 degrees C), 2.56 pN vs. 1.92 pN = 1.3-fold increase) as well as stiffness per head during isometric steady-state contraction (S( *)(active10 degrees C), 0.52 pN/nm vs. 0.28 pN/nm = 1.9-fold increase). Similar changes were found for mutation R719W (2.6-fold increase in S( *)(rigor); 1.8-fold increase in F( *)(10 degrees C), 1.6-fold in F( *)(20 degrees C); twofold increase in S( *)(active10 degrees C)). Changes in active cross-bridge cycling kinetics could not account for the increase in force and active stiffness. For the above estimates the previously determined fraction of mutated myosin in the biopsies was taken into account. Data for wild-type myosin of slow soleus muscle fibers support previous findings that for the slow myosin isoform S( *) and F( *) are significantly lower than for fast myosin e.g., of rabbit psoas muscle. The data indicate that two mutations, R723G and R719W, are associated with an increase in resistance to elastic distortion of the individual mutated myosin heads whereas mutation I736T has essentially no effect. The data strongly support the notion that major elastic distortion occurs within the converter itself. Apparently, the compliance depends on specific residues, e.g., R719 and R723, presumably located at strategic positions near the long alpha-helix of the light chain binding domain. Because amino acids 719 and 723 are nonconserved residues, cross-bridge stiffness may well be specifically tuned for different myosins.

Structural changes in myosin motors and filaments during relaxation of skeletal muscle

Structural changes in myosin motors and filaments during relaxation from short tetanic contractions of intact single fibres of frog tibialis anterior muscles at sarcomere length 2.14 mum, 4 degrees C were investigated by X-ray diffraction. Force declined at a steady rate for several hundred milliseconds after the last stimulus, while sarcomere lengths remained almost constant. During this isometric phase of relaxation the intensities of the equatorial and meridional M3 X-ray reflections associated with the radial and axial distributions of myosin motors also recovered at a steady rate towards their resting values, consistent with progressive net detachment of myosin motors from actin filaments. Stiffness measurements confirmed that the fraction of motors attached to actin declined at a constant rate, but also revealed a progressive increase in force per motor. The interference fine structure of the M3 reflection suggested that actin-attached myosin motors are displaced towards the start of their working stroke during isometric relaxation. There was negligible recovery of the intensities of the meridional and layer-line reflections associated with the quasi-helical distribution of myosin motors in resting muscle during isometric relaxation, and the 1.5% increase in the axial periodicity of the myosin filament associated with muscle activation was not reversed. When force had decreased to roughly half its tetanus plateau value, the isometric phase of relaxation abruptly ended, and the ensuing chaotic relaxation had an exponential half-time of ca 60 ms. Recovery of the equatorial X-ray intensities was largely complete during chaotic relaxation, but the other X-ray signals recovered more slowly than force.

Removal of the cardiac myosin regulatory light chain increases isometric force production

The myosin neck, which is supported by the interactions between light chains and the underlying alpha-helical heavy chain, is thought to act as a lever arm to amplify movements originating in the globular motor domain. Here, we studied the role of the cardiac myosin regulatory light chains (RLCs) in the capacity of myosin to produce force using a novel optical-trap-based isometric force in vitro motility assay. We measured the isometric force and actin filament velocity for native porcine cardiac (PC) myosin, RLC-depleted PC (PC(depl)) myosin, and PC myosin reconstituted with recombinant bacterially expressed human cardiac RLC (PC(recon)). RLC depletion reduced unloaded actin filament velocity by 58% and enhanced the myosin-based isometric force approximately 2-fold. No significant change between PC and PC(depl) preparations was observed in the maximal rate of actin-activated myosin ATPase activity. Reconstitution of PC(depl) myosin with human RLC partially restored the velocity and force levels to near untreated values. The reduction in unloaded velocity after RLC extraction is consistent with the myosin neck acting as a lever, while the enhancement in isometric force can be directly related to enhancement of unitary force. The force data are consistent with a model in which the neck region behaves as a cantilevered beam.

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 contribution of the elastic reaction is severely underestimated in studies on myofibril contraction

We have considered the Huxley-Simmons manoeuvre. On the assumption that the quick release is an elastic process and on the basis of the isometric tension and of the stiffness of the muscle fibre we calculated that the spontaneous release of the fibre requires approximately 43 micros, which is much faster than the observed release, approximately 180 micros. We concluded that the observed quick release is a guided process. After proper selection of the mass and of the stiffness of the system we mimicked the early recovery and noticed that most of the energy required to accomplish the early recovery is supplied by the kinetic energy accumulated during the course of the quick release. We computed that the frequency of the working strokes in the half sarcomere was between 4x10(6) and 40x10(6) s(-1). This is not to say that the ATPase rate constants are accumulative but only that the overall frequency of the working strokes in the half saromere is many orders of magnitude faster than the average ATPase rate constant. With this frequency no part of the Huxley-Simmons manoeuvre, quick release included, escapes the control of the working stroke. This means also that there is no reason to take the early recovery as an indication of the length of the working stroke.

The effect of myofilament compliance on kinetics of force generation by myosin motors in muscle

We use the inhibitor of isometric force of skeletal muscle N-benzyl-p-toluene sulfonamide (BTS) to decrease, in a dose dependent way, the number of myosin motors attached to actin during the steady isometric contraction of single fibers from frog skeletal muscle (4 degrees C, 2.1 microm sarcomere length). In this way we can reduce the strain in the myofilament compliance during the isometric tetanus (T(0)) from 3.54 nm in the control solution (T(0,NR)) to approximately 0.5 nm in 1 microM BTS, where T(0) is reduced to approximately 0.15 T(0,NR). The quick force recovery after a step release (1-3 nm per half-sarcomere) becomes faster with the increase of BTS concentration and the decrease of T(0). The simulation of quick force recovery with a multistate model of force generation, that adapts Huxley and Simmons model to account for both the high stiffness of the myosin motor (approximately 3 pN/nm) and the myofilament compliance, shows that the increase in the rate of quick force recovery by BTS is explained by the reduced strain in the myofilaments, consequent to the decrease in half-sarcomere force. The model estimates that i), for the same half-sarcomere release the state transition kinetics in the myosin motor are five times faster in the absence of filament compliance than in the control; and ii), the rate of force recovery from zero to T(0) is approximately 6000/s in the absence of filament compliance.

Force-generating cross-bridges during ramp-shaped releases: evidence for a new structural state

Mechanical and two-dimensional (2D) x-ray diffraction studies suggest that during isometric steady-state contraction, strongly bound cross-bridges mostly occupy early states in the power stroke, whereas rigor or rigor-like cross-bridges could not be detected. However, it remained unclear whether cross-bridges accumulate, at least transiently, in rigor or rigor-like states in response to rapid-length releases. We addressed this question using time-resolved recording of 2D x-ray diffraction patterns of permeabilized fibers from rabbit psoas muscles during isometric contraction and when small, ramp-shaped length-releases were applied to these fibers. This maneuver allows a transient accumulation of cross-bridges in states near the end of their power stroke. By lowering the temperature to 5 degrees C, force transients were slowed sufficiently to record diffraction patterns in several 2-4-ms time frames before and during such releases, using the RAPID detector (Refined ADC Per Input Detector) at beam line ID02 of the European Synchrotron Radiation Facility (Grenoble, France). The same sequence of frames was recorded in relaxation and rigor. Comparisons of 2D patterns recorded during isometric contraction, with patterns recorded at different [MgATPgammaS] and at 1 degrees C, showed that changes in intensity profiles along the first and sixth actin layer lines (ALL1 and ALL6, respectively) allowed for discernment of the formation of rigor or rigor-like cross-bridges. During ramp-shaped releases of activated fibers, intensity profiles along ALL1 and ALL6 did not reveal evidence for the accumulation of rigor-like cross-bridges. Instead, changes in the ALL6-profile suggest that during ramp-shaped releases, cross-bridges transiently accumulate in a structural state that, to our knowledge, was not previously seen, but that could well be a strongly bound state with the light-chain binding domain in a conformation between a near prepower-stroke (isometric) orientation and the orientation in rigor.

Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay

The force generated between actin and myosin acts predominantly along the direction of the actin filament, resulting in relative sliding of the thick and thin filaments in muscle or transport of myosin cargos along actin tracks. Previous studies have also detected lateral forces or torques that are generated between actin and myosin, but the origin and biological role of these sideways forces is not known. Here we adapt an actin gliding filament assay to measure the rotation of an actin filament about its axis ("twirling") as it is translocated by myosin. We quantify the rotation by determining the orientation of sparsely incorporated rhodamine-labeled actin monomers, using polarized total internal reflection microscopy. To determine the handedness of the filament rotation, linear incident polarizations in between the standard s- and p-polarizations were generated, decreasing the ambiguity of our probe orientation measurement fourfold. We found that whole myosin II and myosin V both twirl actin with a relatively long (approximately 1 microm), left-handed pitch that is insensitive to myosin concentration, filament length, and filament velocity.

Effect of inorganic phosphate on the force and number of myosin cross-bridges during the isometric contraction of permeabilized muscle fibers from rabbit psoas

The relation between the chemical and mechanical steps of the myosin-actin ATPase reaction that leads to generation of isometric force in fast skeletal muscle was investigated in demembranated fibers of rabbit psoas muscle by determining the effect of the concentration of inorganic phosphate (Pi) on the stiffness of the half-sarcomere (hs) during transient and steady-state conditions of the isometric contraction (temperature 12 degrees C, sarcomere length 2.5 mum). Changes in the hs strain were measured by imposing length steps or small 4 kHz oscillations on the fibers in control solution (without added Pi) and in solution with 3-20 mM added Pi. At the plateau of the isometric contraction in control solution, the hs stiffness is 22.8 +/- 1.1 kPa nm(-1). Taking the filament compliance into account, the total stiffness of the array of myosin cross-bridges in the hs (e) is 40.7 +/- 3.7 kPa nm(-1). An increase in [Pi] decreases the stiffness of the cross-bridge array in proportion to the isometric force, indicating that the force of the cross-bridge remains constant independently of [Pi]. The rate constant of isometric force development after a period of unloaded shortening (r(F)) is 23.5 +/- 1.0 s(-1) in control solution and increases monotonically with [Pi], attaining a maximum value of 48.6 +/- 0.9 s(-1) at 20 mM [Pi], in agreement with the idea that Pi release is a relatively fast step after force generation by the myosin cross-bridge. During isometric force development at any [Pi], e and thus the number of attached cross-bridges increase in proportion to the force, indicating that, independently of the speed of the process that leads to myosin attachment to actin, there is no significant (>1 ms) delay between generation of stiffness and generation of force by the cross-bridges.

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 degrees C and 30 degrees 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 approximately 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.

Orientation of the essential light chain region of myosin in relaxed, active, and rigor muscle

The orientation of the ELC region of myosin in skeletal muscle was determined by polarized fluorescence from ELC mutants in which pairs of introduced cysteines were cross-linked by BSR. The purified ELC-BSRs were exchanged for native ELC in demembranated fibers from rabbit psoas muscle using a trifluoperazine-based protocol that preserved fiber function. In the absence of MgATP (in rigor) the ELC orientation distribution was narrow; in terms of crystallographic structures of the myosin head, the LCD long axis linking heavy-chain residues 707 and 843 makes an angle (beta) of 120-125 degrees with the filament axis. This is approximately 30 degrees larger than the broader distribution determined previously from RLC probes, suggesting that, relative to crystallographic structures, the LCD is bent between its ELC and RLC regions in rigor muscle. The ELC orientation distribution in relaxed muscle had two broad peaks with beta approximately 70 degrees and approximately 110 degrees, which may correspond to the two head regions of each myosin molecule, in contrast with the single broad distribution of the RLC region in relaxed muscle. During isometric contraction the ELC orientation distribution peaked at beta approximately 105 degrees , similar to that determined previously for the RLC region.

Force transients and minimum cross-bridge models in muscular contraction

Two- and three-state cross-bridge models are considered and examined with respect to their ability to predict three distinct phases of the force transients that occur in response to step change in muscle fiber length. Particular attention is paid to satisfying the Le Châtelier-Brown Principle. This analysis shows that the two-state model can account for phases 1 and 2 of a force transient, but is barely adequate to account for phase 3 (delayed force) unless a stretch results in a sudden increase in the number of cross-bridges in the detached state. The three-state model (A-->B-->C-->A) makes it possible to account for all three phases if we assume that the A-->B transition is fast (corresponding to phase 2), the B-->A transition is of intermediate speed (corresponding to phase 3), and the C-->A transition is slow; in such a scenario, states A and C can support or generate force (high force states) but state B cannot (detached, or low-force state). This model involves at least one ratchet mechanism. In this model, force can be generated by either of two transitions: B-->A or B-->C. To determine which of these is the major force-generating step that consumes ATP and transduces energy, we examine the effects of ATP, ADP, and phosphate (Pi) on force transients. In doing so, we demonstrate that the fast transition (phase 2) is associated with the nucleotide-binding step, and that the intermediate-speed transition (phase 3) is associated with the Pi-release step. To account for all the effects of ligands, it is necessary to expand the three-state model into a six-state model that includes three ligand-bound states. The slowest phase of a force transient (phase 4) cannot be explained by any of the models described unless an additional mechanism is introduced. Here we suggest a role of series compliance to account for this phase, and propose a model that correlates the slowest step of the cross-bridge cycle (transition C-->A) to: phase 4 of step analysis, the rate constant k(tr) of the quick-release and restretch experiment, and the rate constant k(act) for force development time course following Ca(2+) activation.