Force and kinetics of fast and slow muscle myosin determined with a synthetic sarcomere-like nanomachine.

Myosin II is the muscle molecular motor that works in two bipolar arrays in each thick filament of the striated (skeletal and cardiac) muscle, converting the chemical energy into steady force and shortening by cyclic ATP-driven interactions with the nearby actin filaments. Different isoforms of the myosin motor in the skeletal muscles account for the different functional requirements of the slow muscles (primarily responsible for the posture) and fast muscles (responsible for voluntary movements). To clarify the molecular basis of the differences, here the isoform-dependent mechanokinetic parameters underpinning the force of slow and fast muscles are defined with a unidimensional synthetic nanomachine powered by pure myosin isoforms from either slow or fast rabbit skeletal muscle. Data fitting with a stochastic model provides a self-consistent estimate of all the mechanokinetic properties of the motor ensemble including the motor force, the fraction of actin-attached motors and the rate of transition through the attachment-detachment cycle. The achievements in this paper set the stage for any future study on the emergent mechanokinetic properties of an ensemble of myosin molecules either engineered or purified from mutant animal models or human biopsies.

Sarcomere level mechanics of the fast skeletal muscle of the medaka fish larva.

The medaka fish (Oryzias latipes) is a vertebrate model used in developmental biology and genetics. Here we explore its suitability as a model for investigating the molecular mechanisms of human myopathies caused by mutations in sarcomeric proteins. To this end, the relevant mechanical parameters of the intact skeletal muscle of wild-type medaka are determined using the transparent tail at larval stage 40. Tails were mounted at sarcomere length of 2.1 µm in a thermoregulated trough containing physiological solution. Tetanic contractions were elicited at physiological temperature (10°C-30°C) by electrical stimulation, and sarcomere length changes were recorded with nanometer-microsecond resolution during both isometric and isotonic contractions with a striation follower. The force output has been normalized for the actual fraction of the cross section of the tail occupied by the myofilament lattice, as established with transmission electron microscopy (TEM), and then for the actual density of myofilaments, as established with X-ray diffraction. Under these conditions, the mechanical performance of the contracting muscle of the wild-type larva can be defined at the level of the half-thick filament, where ∼300 myosin motors work in parallel as a collective motor, allowing a detailed comparison with the established performance of the skeletal muscle of different vertebrates. The results of this study point out that the medaka fish larva is a suitable model for the investigation of the genotype/phenotype correlations and therapeutic possibilities in skeletal muscle diseases caused by mutations in sarcomeric proteins.NEW & NOTEWORTHY The suitability of the medaka fish as a model for investigating the molecular mechanisms of human myopathies caused by mutations of sarcomeric proteins is tested by combining structural analysis and sarcomere-level mechanics of the skeletal muscle of the tail of medaka larva. The mechanical performance of the medaka muscle, scaled at the level of the myosin-containing thick filament, together with its reduced genome duplication makes this model unique for investigations of the genotype/phenotype correlations in human myopathies.

Dependence of myosin filament structure on intracellular calcium concentration in skeletal muscle.

Contraction of skeletal muscle is triggered by an increase in intracellular calcium concentration that relieves the structural block on actin-binding sites in resting muscle, potentially allowing myosin motors to bind and generate force. However, most myosin motors are not available for actin binding because they are stabilized in folded helical tracks on the surface of myosin-containing thick filaments. High-force contraction depends on the release of the folded motors, which can be triggered by stress in the thick filament backbone, but additional mechanisms may link the activation of the thick filaments to that of the thin filaments or to intracellular calcium concentration. Here, we used x-ray diffraction in combination with temperature-jump activation to determine the steady-state calcium dependence of thick filament structure and myosin motor conformation in near-physiological conditions. We found that x-ray signals associated with the perpendicular motors characteristic of isometric force generation had almost the same calcium sensitivity as force, but x-ray signals associated with perturbations in the folded myosin helix had a much higher calcium sensitivity. Moreover, a new population of myosin motors with a longer axial periodicity became prominent at low levels of calcium activation and may represent an intermediate regulatory state of the myosin motors in the physiological pathway of filament activation.

Titin activates myosin filaments in skeletal muscle by switching from an extensible spring to a mechanical rectifier.

Titin is a molecular spring in parallel with myosin motors in each muscle half-sarcomere, responsible for passive force development at sarcomere length (SL) above the physiological range (>2.7 µm). The role of titin at physiological SL is unclear and is investigated here in single intact muscle cells of the frog (Rana esculenta), by combining half-sarcomere mechanics and synchrotron X-ray diffraction in the presence of 20 µM para-nitro-blebbistatin, which abolishes the activity of myosin motors and maintains them in the resting state even during activation of the cell by electrical stimulation. We show that, during cell activation at physiological SL, titin in the I-band switches from an SL-dependent extensible spring (OFF-state) to an SL-independent rectifier (ON-state) that allows free shortening while resisting stretch with an effective stiffness of ~3 pN nm-1 per half-thick filament. In this way, I-band titin efficiently transmits any load increase to the myosin filament in the A-band. Small-angle X-ray diffraction signals reveal that, with I-band titin ON, the periodic interactions of A-band titin with myosin motors alter their resting disposition in a load-dependent manner, biasing the azimuthal orientation of the motors toward actin. This work sets the stage for future investigations on scaffold and mechanosensing-based signaling functions of titin in health and disease.

The force of the myosin motor sets cooperativity in thin filament activation of skeletal muscles.

Contraction of striated muscle is regulated by a dual mechanism involving both thin, actin-containing filament and thick, myosin-containing filament. Thin filament is activated by Ca2+ binding to troponin, leading to tropomyosin displacement that exposes actin sites for interaction with myosin motors, extending from the neighbouring stress-activated thick filaments. Motor attachment to actin contributes to spreading activation along the thin filament, through a cooperative mechanism, still unclear, that determines the slope of the sigmoidal relation between isometric force and pCa (-log[Ca2+]), estimated by Hill coefficient nH. We use sarcomere-level mechanics in demembranated fibres of rabbit skeletal muscle activated by Ca2+ at different temperatures (12-35 °C) to show that nH depends on the motor force at constant number of attached motors. The definition of the role of motor force provides fundamental constraints for modelling the dynamics of thin filament activation and defining the action of small molecules as possible therapeutic tools.

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.

Allosteric modulation of cardiac myosin mechanics and kinetics by the conjugated omega-7,9 trans-fat rumenic acid.

KEY POINTS: Direct binding of rumenic acid to the cardiac myosin-2 motor domain increases the release rate for orthophosphate and increases the Ca2+ responsiveness of cardiac muscle at low load. Physiological cellular concentrations of rumenic acid affect the ATP turnover rates of the super-relaxed and disordered relaxed states of ß-cardiac myosin, leading to a net increase in myocardial metabolic load. In Ca2+ -activated trabeculae, rumenic acid exerts a direct inhibitory effect on the force-generating mechanism without affecting the number of force-generating motors. In the presence of saturating actin concentrations rumenic acid binds to the ß-cardiac myosin-2 motor domain with an EC50 of 200 nM. Molecular docking studies provide information about the binding site, the mode of binding, and associated allosteric communication pathways. Free rumenic acid may exceed thresholds in cardiomyocytes above which contractile efficiency is reduced and interference with small molecule therapeutics, targeting cardiac myosin, occurs. ABSTRACT: Based on experiments using purified myosin motor domains, reconstituted actomyosin complexes and rat heart ventricular trabeculae, we demonstrate direct binding of rumenic acid, the cis-delta-9-trans-delta-11 isomer of conjugated linoleic acid, to an allosteric site located in motor domain of mammalian cardiac myosin-2 isoforms. In the case of porcine ß-cardiac myosin, the EC50 for rumenic acid varies from 10.5 µM in the absence of actin to 200 nM in the presence of saturating concentrations of actin. Saturating concentrations of rumenic acid increase the maximum turnover of basal and actin-activated ATPase activity of ß-cardiac myosin approximately 2-fold but decrease the force output per motor by 23% during isometric contraction. The increase in ATP turnover is linked to an acceleration of the release of the hydrolysis product orthophosphate. In the presence of 5 µM rumenic acid, the difference in the rate of ATP turnover by the super-relaxed and disordered relaxed states of cardiac myosin increases from 4-fold to 20-fold. The equilibrium between the two functional myosin states is not affected by rumenic acid. Calcium responsiveness is increased under zero-load conditions but unchanged under load. Molecular docking studies provide information about the rumenic acid binding site, the mode of binding, and associated allosteric communication pathways. They show how the isoform-specific replacement of residues in the binding cleft induces a different mode of rumenic acid binding in the case of non-muscle myosin-2C and blocks binding to skeletal muscle and smooth muscle myosin-2 isoforms.

Dependence of thick filament structure in relaxed mammalian skeletal muscle on temperature and interfilament spacing.

Contraction of skeletal muscle is regulated by structural changes in both actin-containing thin filaments and myosin-containing thick filaments, but myosin-based regulation is unlikely to be preserved after thick filament isolation, and its structural basis remains poorly characterized. Here, we describe the periodic features of the thick filament structure in situ by high-resolution small-angle x-ray diffraction and interference. We used both relaxed demembranated fibers and resting intact muscle preparations to assess whether thick filament regulation is preserved in demembranated fibers, which have been widely used for previous studies. We show that the thick filaments in both preparations exhibit two closely spaced axial periodicities, 43.1 nm and 45.5 nm, at near-physiological temperature. The shorter periodicity matches that of the myosin helix, and x-ray interference between the two arrays of myosin in the bipolar filament shows that all zones of the filament follow this periodicity. The 45.5-nm repeat has no helical component and originates from myosin layers closer to the filament midpoint associated with the titin super-repeat in that region. Cooling relaxed or resting muscle, which partially mimics the effects of calcium activation on thick filament structure, disrupts the helical order of the myosin motors, and they move out from the filament backbone. Compression of the filament lattice of demembranated fibers by 5% Dextran, which restores interfilament spacing to that in intact muscle, stabilizes the higher-temperature structure. The axial periodicity of the filament backbone increases on cooling, but in lattice-compressed fibers the periodicity of the myosin heads does not follow the extension of the backbone. Thick filament structure in lattice-compressed demembranated fibers at near-physiological temperature is similar to that in intact resting muscle, suggesting that the native structure of the thick filament is largely preserved after demembranation in these conditions, although not in the conditions used for most previous studies with this preparation.

Orthophosphate increases the efficiency of slow muscle-myosin isoform in the presence of omecamtiv mecarbil.

Omecamtiv mecarbil (OM) is a putative positive inotropic tool for treatment of systolic heart dysfunction, based on the finding that in vivo it increases the ejection fraction and in vitro it prolongs the actin-bond life time of the cardiac and slow-skeletal muscle isoforms of myosin. OM action in situ, however, is still poorly understood as the enhanced Ca2+-sensitivity of the myofilaments is at odds with the reduction of force and rate of force development observed at saturating Ca2+. Here we show, by combining fast sarcomere-level mechanics and ATPase measurements in single slow demembranated fibres from rabbit soleus, that the depressant effect of OM on the force per attached motor is reversed, without effect on the ATPase rate, by physiological concentrations of inorganic phosphate (Pi) (1-10 mM). This mechanism could underpin an energetically efficient reduction of systolic tension cost in OM-treated patients, whenever [Pi] increases with heart-beat frequency.

Myopalladin promotes muscle growth through modulation of the serum response factor pathway.

BACKGROUND: Myopalladin (MYPN) is a striated muscle-specific, immunoglobulin-containing protein located in the Z-line and I-band of the sarcomere as well as the nucleus. Heterozygous MYPN gene mutations are associated with hypertrophic, dilated, and restrictive cardiomyopathy, and homozygous loss-of-function truncating mutations have recently been identified in patients with cap myopathy, nemaline myopathy, and congenital myopathy with hanging big toe. METHODS: Constitutive MYPN knockout (MKO) mice were generated, and the role of MYPN in skeletal muscle was studied through molecular, cellular, biochemical, structural, biomechanical, and physiological studies in vivo and in vitro. RESULTS: MKO mice were 13% smaller compared with wild-type controls and exhibited a 48% reduction in myofibre cross-sectional area (CSA) and significantly increased fibre number. Similarly, reduced myotube width was observed in MKO primary myoblast cultures. Biomechanical studies showed reduced isometric force and power output in MKO mice as a result of the reduced CSA, whereas the force developed by each myosin molecular motor was unaffected. While the performance by treadmill running was similar in MKO and wild-type mice, MKO mice showed progressively decreased exercise capability, Z-line damage, and signs of muscle regeneration following consecutive days of downhill running. Additionally, MKO muscle exhibited progressive Z-line widening starting from 8 months of age. RNA-sequencing analysis revealed down-regulation of serum response factor (SRF)-target genes in muscles from postnatal MKO mice, important for muscle growth and differentiation. The SRF pathway is regulated by actin dynamics as binding of globular actin to the SRF-cofactor myocardin-related transcription factor A (MRTF-A) prevents its translocation to the nucleus where it binds and activates SRF. MYPN was found to bind and bundle filamentous actin as well as interact with MRTF-A. In particular, while MYPN reduced actin polymerization, it strongly inhibited actin depolymerization and consequently increased MRTF-A-mediated activation of SRF signalling in myogenic cells. Reduced myotube width in MKO primary myoblast cultures was rescued by transduction with constitutive active SRF, demonstrating that MYPN promotes skeletal muscle growth through activation of the SRF pathway. CONCLUSIONS: Myopalladin plays a critical role in the control of skeletal muscle growth through its effect on actin dynamics and consequently the SRF pathway. In addition, MYPN is important for the maintenance of Z-line integrity during exercise and aging. These results suggest that muscle weakness in patients with biallelic MYPN mutations may be associated with reduced myofibre CSA and SRF signalling and that the disease phenotype may be aggravated by exercise.

Low temperature traps myosin motors of mammalian muscle in a refractory state that prevents activation.

Myosin motors in the thick filament of resting striated (skeletal and cardiac) muscle are trapped in an OFF state, in which the motors are packed in helical tracks on the filament surface, inhibiting their interactions with actin and utilization of ATP. To investigate the structural changes induced in the thick filament of mammalian skeletal muscle by changes in temperature, we collected x-ray diffraction patterns from the fast skeletal muscle extensor digitorum longus of the mouse in the temperature range from near physiological (35°C) to 10°C, in which the maximal isometric force (T 0) shows a threefold decrease. In resting muscle, x-ray reflections signaling the OFF state of the thick filament indicate that cooling produces a progressive disruption of the OFF state with motors moving away from the ordered helical tracks on the surface of the thick filament. We find that the number of myosin motors in the OFF state at 10°C is half of that at 35°C. At T 0, changes in the x-ray signals that report the fraction and conformation of actin-attached motors can be explained if the threefold decrease in force associated with lowering temperature is due not only to a decrease in the force-generating transition in the actin-attached motors but also to a twofold decrease in the number of such motors. Thus, lowering the temperature reduces to the same extent the fraction of motors in the OFF state at rest and the fraction of motors attached to actin at T 0, suggesting that motors that leave the OFF state accumulate in a disordered refractory state that makes them unavailable for interaction with actin upon stimulation. This regulatory effect of temperature on the thick filament of mammalian skeletal muscle could represent an energetically convenient mechanism for hibernating animals.

Inotropic interventions do not change the resting state of myosin motors during cardiac diastole.

When striated (skeletal and cardiac) muscle is in its relaxed state, myosin motors are packed in helical tracks on the surface of the thick filament, folded toward the center of the sarcomere, and unable to bind actin or hydrolyze ATP (OFF state). This raises the question of whatthe mechanism is that integrates the Ca2+-dependent thin filament activation, making myosin heads available for interaction with actin. Here we test the interdependency of the thin and thick filament regulatory mechanisms in intact trabeculae from the rat heart. We record the x-ray diffraction signals that mark the state of the thick filament during inotropic interventions (increase in sarcomere length from 1.95 to 2.25 µm and addition of 10-7 M isoprenaline), which potentiate the twitch force developed by an electrically paced trabecula by up to twofold. During diastole, none of the signals related to the OFF state of the thick filament are significantly affected by these interventions, except the intensity of both myosin-binding protein C- and troponin-related meridional reflections, which reduce by 20% in the presence of isoprenaline. These results indicate that recruitment of myosin motors from their OFF state occurs independently and downstream from thin filament activation. This is in agreement with the recently discovered mechanism based on thick filament mechanosensing in which the number of motors available for interaction with actin rapidly adapts to the stress on the thick filament and thus to the loading conditions of the contraction. The gain of this positive feedback may be modulated by both sarcomere length and the degree of phosphorylation of myosin-binding protein C.

The force and stiffness of myosin motors in the isometric twitch of a cardiac trabecula and the effect of the extracellular calcium concentration.

KEY POINTS: Fast sarcomere-level mechanics in intact trabeculae, which allows the definition of the mechano-kinetic properties of cardiac myosin in situ, is a fundamental tool not only for understanding the molecular mechanisms of heart performance and regulation, but also for investigating the mechanisms of the cardiomyopathy-causing mutations in the myosin and testing small molecules for therapeutic interventions. The approach has been applied to measure the stiffness and force of the myosin motor and the fraction of motors attached during isometric twitches of electrically paced trabeculae under different extracellular Ca2+ concentrations. Although the average force of the cardiac myosin motor (∼6 pN) is similar to that of the fast myosin isoform of skeletal muscle, the stiffness (1.07 pN nm-1 ) is 2- to 3-fold smaller. The increase in the twitch force developed in the presence of larger extracellular Ca2+ concentrations is fully accounted for by a proportional increase in the number of attached motors. ABSTRACT: The mechano-kinetic properties of the cardiac myosin were studied in situ, in trabeculae dissected from the right ventricle of the rat heart, by measuring the stiffness of the half-sarcomere both at the twitch force peak (Tp ) of an electrically paced intact trabecula at different extracellular Ca2+ concentrations ([Ca2+ ]o ), and in the same trabecula after skinning and induction of rigor. Taking into account the contribution of filament compliance to half-sarcomere compliance and the lattice geometry, we found that the stiffness of the cardiac myosin motor is 1.07 ± 0.09 pN nm-1 , which is slightly larger than that of the slow myosin isoform of skeletal muscle (0.6-0.8 pN nm-1 ) and 2- to 3-fold smaller than that of the fast skeletal muscle isoform. The increase in Tp from 61 ± 4 kPa to 93 ± 9 kPa, induced by raising [Ca2+ ]o from 1 to 2.5 mm at sarcomere length ∼2.2 µm, is accompanied by an increase of the half-sarcomere stiffness that is explained by an increase of the fraction of actin-attached motors from 0.08 ± 0.01 to 0.12 ± 0.02, proportional to Tp . Consequently, each myosin motor bears an average force of 6.14 ± 0.52 pN independently of Tp and [Ca2+ ]o . The application of fast sarcomere-level mechanics to intact trabeculae to define the mechano-kinetic properties of the cardiac myosin in situ represents a powerful tool for investigating cardiomyopathy-causing mutations in the myosin motor and testing specific therapeutic interventions.

Myosin filament activation in the heart is tuned to the mechanical task.

The mammalian heart pumps blood through the vessels, maintaining the dynamic equilibrium in a circulatory system driven by two pumps in series. This vital function is based on the fine-tuning of cardiac performance by the Frank-Starling mechanism that relates the pressure exerted by the contracting ventricle (end systolic pressure) to its volume (end systolic volume). At the level of the sarcomere, the structural unit of the cardiac myocytes, the Frank-Starling mechanism consists of the increase in active force with the increase of sarcomere length (length-dependent activation). We combine sarcomere mechanics and micrometer-nanometer-scale X-ray diffraction from synchrotron light in intact ventricular trabeculae from the rat to measure the axial movement of the myosin motors during the diastole-systole cycle under sarcomere length control. We find that the number of myosin motors leaving the off, ATP hydrolysis-unavailable state characteristic of the diastole is adjusted to the sarcomere length-dependent systolic force. This mechanosensing-based regulation of the thick filament makes the energetic cost of the systole rapidly tuned to the mechanical task, revealing a prime aspect of the Frank-Starling mechanism. The regulation is putatively impaired by cardiomyopathy-causing mutations that affect the intramolecular and intermolecular interactions controlling the off state of the motors.

Minimum number of myosin motors accounting for shortening velocity under zero load in skeletal muscle.

KEY POINTS: Myosin filament mechanosensing determines the efficiency of the contraction by adapting the number of switched ON motors to the load. Accordingly, the unloaded shortening velocity (V0 ) is already set at the end of latency relaxation (LR), ∼10 ms after the start of stimulation, when the myosin filament is still in the OFF state. Here the number of actin-attached motors per half-myosin filament (n) during V0 shortening imposed either at the end of LR or at the plateau of the isometric contraction is estimated from the relation between half-sarcomere compliance and force during the force redevelopment after shortening. The value of n decreases progressively with shortening and, during V0 shortening starting at the end of LR, is 1-4. Reduction of n is accounted for by a constant duty ratio of 0.05 and a parallel switching OFF of motors, explaining the very low rate of ATP utilization found during unloaded shortening. ABSTRACT: The maximum velocity at which a skeletal muscle can shorten (i.e. the velocity of sliding between the myosin filament and the actin filament under zero load, V0 ) is already set at the end of the latency relaxation (LR) preceding isometric force generation, ∼10 ms after the start of electrical stimulation in frog muscle fibres at 4°C. At this time, Ca2+ -induced activation of the actin filament is maximal, while the myosin filament is in the OFF state characterized by most of the myosin motors lying on helical tracks on the filament surface, making them unavailable for actin binding and ATP hydrolysis. Here, the number of actin-attached motors per half-thick filament during V0 shortening (n) is estimated by imposing, on tetanized single fibres from Rana esculenta (at 4°C and sarcomere length 2.15 µm), small 4 kHz oscillations and determining the relation between half-sarcomere (hs) compliance and force during the force development following V0 shortening. When V0 shortening is superimposed on the maximum isometric force T0 , n decreases progressively with the increase of shortening (range 30-80 nm per hs) and, when V0 shortening is imposed at the end of LR, n can be as low as 1-4. Reduction of n is accounted for by a constant duty ratio of the myosin motor of ∼0.05 and a parallel switching OFF of the thick filament, providing an explanation for the very low rate of ATP utilization during extended V0 shortening.

Force generation by skeletal muscle is controlled by mechanosensing in myosin filaments.

Contraction of both skeletal muscle and the heart is thought to be controlled by a calcium-dependent structural change in the actin-containing thin filaments, which permits the binding of myosin motors from the neighbouring thick filaments to drive filament sliding. Here we show by synchrotron small-angle X-ray diffraction of frog (Rana temporaria) single skeletal muscle cells that, although the well-known thin-filament mechanism is sufficient for regulation of muscle shortening against low load, force generation against high load requires a second permissive step linked to a change in the structure of the thick filament. The resting (switched 'OFF') structure of the thick filament is characterized by helical tracks of myosin motors on the filament surface and a short backbone periodicity. This OFF structure is almost completely preserved during low-load shortening, which is driven by a small fraction of constitutively active (switched 'ON') myosin motors outside thick-filament control. At higher load, these motors generate sufficient thick-filament stress to trigger the transition to its long-periodicity ON structure, unlocking the major population of motors required for high-load contraction. This concept of the thick filament as a regulatory mechanosensor provides a novel explanation for the dynamic and energetic properties of skeletal muscle. A similar mechanism probably operates in the heart.

Force and number of myosin motors during muscle shortening and the coupling with the release of the ATP hydrolysis products.

KEY POINTS: Muscle contraction is due to cyclical ATP-driven working strokes in the myosin motors while attached to the actin filament. Each working stroke is accompanied by the release of the hydrolysis products, orthophosphate and ADP. The rate of myosin-actin interactions increases with the increase in shortening velocity. We used fast half-sarcomere mechanics on skinned muscle fibres to determine the relation between shortening velocity and the number and strain of myosin motors and the effect of orthophosphate concentration. A model simulation of the myosin-actin reaction explains the results assuming that orthophosphate and then ADP are released with rates that increase as the motor progresses through the working stroke. The ADP release rate further increases by one order of magnitude with the rise of negative strain in the final motor conformation. These results provide the molecular explanation of the relation between the rate of energy liberation and shortening velocity during muscle contraction. The chemo-mechanical cycle of the myosin II--actin reaction in situ has been investigated in Ca(2+)-activated skinned fibres from rabbit psoas, by determining the number and strain (s) of myosin motors interacting during steady shortening at different velocities (V) and the effect of raising inorganic phosphate (Pi) concentration. It was found that in control conditions (no added Pi ), shortening at V ≤ 350 nm s(-1) per half-sarcomere, corresponding to force (T) greater than half the isometric force (T0 ), decreases the number of myosin motors in proportion to the reduction of T, so that s remains practically constant and similar to the T0 value independent of V. At higher V the number of motors decreases less than in proportion to T, so that s progressively decreases. Raising Pi concentration by 10 mM, which reduces T0 and the number of motors by 40-50%, does not influence the dependence on V of number and strain. A model simulation of the myosin-actin reaction in which the structural transitions responsible for the myosin working stroke and the release of the hydrolysis products are orthogonal explains the results assuming that Pi and then ADP are released with rates that increase as the motor progresses through the working stroke. The rate of ADP release from the conformation at the end of the working stroke is also strain-sensitive, further increasing by one order of magnitude within a few nanometres of negative strain. These results provide the molecular explanation of the relation between the rate of energy liberation and the load during muscle contraction.

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.

Orthovanadate and orthophosphate inhibit muscle force via two different pathways of the myosin ATPase cycle.

Measurements of the half-sarcomere stiffness during activation of skinned fibers from rabbit psoas (sarcomere length 2.5 µm, temperature 12°C) indicate that addition of 0.1 mM orthovanadate (Vi) to the solution produces a drop to ∼1/2 in number of force-generating myosin motors, proportional to the drop in steady isometric force (T(0)), an effect similar to that produced by the addition of 10 mM phosphate (Pi). However, in contrast to Pi, Vi does not change the rate of isometric force development. The depression of T(0) in a series of activations in presence of Vi is consistent with an apparent second-order rate constant of ∼1 × 10(3) M(-1) s(-1). The rate constant of T(0) recovery in a series of activations after removal of Vi is 3.5 × 10(-2) s(-1). These results, together with the finding in the literature that the ATPase rate is reduced by Vi in proportion to isometric force, are reproduced with a kinetic model of the acto-myosin cross-bridge cycle where binding of Vi to the force-generating actomyosin-ADP state induces detachment from actin to form a stable myosin-ADP-Vi complex that is not able to complete the hydrolysis cycle and reenters the cycle only via reattachment to actin upon activation in Vi-free solution.

A kinetic model that explains the effect of inorganic phosphate on the mechanics and energetics of isometric contraction of fast skeletal muscle.

A conventional five-step chemo-mechanical cycle of the myosin-actin ATPase reaction, which implies myosin detachment from actin upon release of hydrolysis products (ADP and phosphate, Pi) and binding of a new ATP molecule, is able to fit the [Pi] dependence of the force and number of myosin motors during isometric contraction of skeletal muscle. However, this scheme is not able to explain why the isometric ATPase rate of fast skeletal muscle is decreased by an increase in [Pi] much less than the number of motors. The question can be solved assuming the presence of a branch in the cycle: in isometric contraction, when the force generation process by the myosin motor is biased at the start of the working stroke, the motor can detach at an early stage of the ATPase cycle, with Pi still bound to its catalytic site, and then rapidly release the hydrolysis products and bind another ATP. In this way, the model predicts that in fast skeletal muscle the energetic cost of isometric contraction increases with [Pi]. The large dissociation constant of the product release in the branched pathway allows the isometric myosin-actin reaction to fit the equilibrium constant of the ATPase.