The non-linear elasticity of the muscle sarcomere and the compliance of myosin motors

Design Principles and Benefits of Spatially Explicit Models of Myofilament Function

Spatially explicit models of muscle contraction include fine-scale details about the spatial, kinetic, and/or mechanical properties of the biological processes being represented within the model network. Over the past 25 years, this has primarily consisted of a set of mathematical and computational algorithms representing myosin cross-bridge activity, Ca2+-activation of contraction, and ensemble force production within a half-sarcomere representation of the myofilament network. Herein we discuss basic design principles associated with creating spatially explicit models of myofilament function, as well as model assumptions underlying model development. A brief overview of computational approaches is introduced. Opportunities for new model directions that could investigate coupled regulatory pathways between the thick-filament and thin-filaments are also presented. Given the modular design and flexibility associated with spatially explicit models, we highlight some advantages of this approach compared to other model formulations.

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.

Cross-bridge mechanics estimated from skeletal muscles' work-loop responses to impacts in legged locomotion

Legged locomotion has evolved as the most common form of terrestrial locomotion. When the leg makes contact with a solid surface, muscles absorb some of the shock-wave accelerations (impacts) that propagate through the body. We built a custom-made frame to which we fixated a rat (Rattus norvegicus, Wistar) muscle (m. gastrocnemius medialis and lateralis: GAS) for emulating an impact. We found that the fibre material of the muscle dissipates between 3.5 and [Formula: see text] ranging from fresh, fully active to passive muscle material, respectively. Accordingly, the corresponding dissipated energy in a half-sarcomere ranges between 10.4 and [Formula: see text], respectively. At maximum activity, a single cross-bridge would, thus, dissipate 0.6% of the mechanical work available per ATP split per impact, and up to 16% energy in common, submaximal, activities. We also found the cross-bridge stiffness as low as [Formula: see text], which can be explained by the Coulomb-actuating cross-bridge part dominating the sarcomere stiffness. Results of the study provide a deeper understanding of contractile dynamics during early ground contact in bouncy gait.

Myosin-based regulation of twitch and tetanic contractions in mammalian skeletal muscle

Time-resolved X-ray diffraction of isolated fast-twitch muscles of mice was used to show how structural changes in the myosin-containing thick filaments contribute to the regulation of muscle contraction, extending the previous focus on regulation by the actin-containing thin filaments. This study shows that muscle activation involves the following sequence of structural changes: thin filament activation, disruption of the helical array of myosin motors characteristic of resting muscle, release of myosin motor domains from the folded conformation on the filament backbone, and actin attachment. Physiological force generation in the 'twitch' response of skeletal muscle to single action potential stimulation is limited by incomplete activation of the thick filament and the rapid inactivation of both filaments. Muscle relaxation after repetitive stimulation is accompanied by a complete recovery of the folded motor conformation on the filament backbone but by incomplete reformation of the helical array, revealing a structural basis for post-tetanic potentiation in isolated muscles.

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 β-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 β-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 β-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 β-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.

Evolution of mechanical cooperativity among myosin II motors

Myosin II is a biomolecular machine that is responsible for muscle contraction. Myosin II motors act cooperatively: during muscle contraction, multiple motors bind to a single actin filament and pull it against an external load, like people pulling on a rope in a tug-of-war. We model the dynamics of actomyosin filaments in order to study the evolution of motor-motor cooperativity. We find that filament backsliding-the distance an actin slides backward when a motor at the end of its cycle releases-is central to the speed and efficiency of muscle contraction. Our model predicts that this backsliding has been reduced through evolutionary adaptations to the motor's binding propensity, the strength of the motor's power stroke, and the force dependence of the motor's release from actin. These properties optimize the collective action of myosin II motors, which is not a simple sum of individual motor actions. The model also shows that these evolutionary variables can explain the speed-efficiency trade-off observed across different muscle tissues. This is an example of how evolution can tune the microscopic properties of individual proteins in order to optimize complex biological functions.

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.

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.

Omecamtiv mecarbil is a small molecule effector under clinical trial for the treatment of systolic heart failure. Here the authors define the molecular mechanisms of its inotropic action and find it can increase the efficiency of contraction in muscle fibres when the orthophosphate concentration rises with the beat frequency.

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 effects of inorganic phosphate on muscle force development and energetics: challenges in modelling related to experimental uncertainties

Muscle force and power are developed by myosin cross-bridges, which cyclically attach to actin, undergo a force-generating transition and detach under turnover of ATP. The force-generating transition is intimately associated with release of inorganic phosphate (Pi) but the exact sequence of events in relation to the actual Pi release step is controversial. Details of this process are reflected in the relationships between [Pi] and the developed force and shortening velocity. In order to account for these relationships, models have proposed branched kinetic pathways or loose coupling between biochemical and force-generating transitions. A key hypothesis underlying the present study is that such complexities are not required to explain changes in the force–velocity relationship and ATP turnover rate with altered [Pi]. We therefore set out to test if models without branched kinetic paths and Pi-release occurring before the main force-generating transition can account for effects of varied [Pi] (0.1–25 mM). The models tested, one assuming either linear or non-linear cross-bridge elasticity, account well for critical aspects of muscle contraction at 0.5 mM Pi but their capacity to account for the maximum power output vary. We find that the models, within experimental uncertainties, account for the relationship between [Pi] and isometric force as well as between [Pi] and the velocity of shortening at low loads. However, in apparent contradiction with available experimental findings, the tested models produce an anomalous force–velocity relationship at elevated [Pi] and high loads with more than one possible velocity for a given load. Nevertheless, considering experimental uncertainties and effects of sarcomere non-uniformities, these discrepancies are insufficient to refute the tested models in favour of more complex alternatives.

Nonlinear Actomyosin Elasticity in Muscle?

Cyclic interactions between myosin II motor domains and actin filaments that are powered by turnover of ATP underlie muscle contraction and have key roles in motility of nonmuscle cells. The elastic characteristics of actin-myosin cross-bridges are central in the force-generating process, and disturbances in these properties may lead to disease. Although the prevailing paradigm is that the cross-bridge elasticity is linear (Hookean), recent single-molecule studies suggest otherwise. Despite convincing evidence for substantial nonlinearity of the cross-bridge elasticity in the single-molecule work, this finding has had limited influence on muscle physiology and physiology of other ordered cellular actin-myosin ensembles. Here, we use a biophysical modeling approach to close the gap between single molecules and physiology. The model is used for analysis of available experimental results in the light of possible nonlinearity of the cross-bridge elasticity. We consider results obtained both under rigor conditions (in the absence of ATP) and during active muscle contraction. Our results suggest that a wide range of experimental findings from mechanical experiments on muscle cells are consistent with nonlinear actin-myosin elasticity similar to that previously found in single molecules. Indeed, the introduction of nonlinear cross-bridge elasticity into the model improves the reproduction of key experimental results and eliminates the need for force dependence of the ATP-induced detachment rate, consistent with observations in other single-molecule studies. The findings have significant implications for the understanding of key features of actin-myosin-based production of force and motion in living cells, particularly in muscle, and for the interpretation of experimental results that rely on stiffness measurements on cells or myofibrils.

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.

Do Actomyosin Single-Molecule Mechanics Data Predict Mechanics of Contracting Muscle?

In muscle, but not in single-molecule mechanics studies, actin, myosin and accessory proteins are incorporated into a highly ordered myofilament lattice. In view of this difference we compare results from single-molecule studies and muscle mechanics and analyze to what degree data from the two types of studies agree with each other. There is reasonable correspondence in estimates of the cross-bridge power-stroke distance (7–13 nm), cross-bridge stiffness (~2 pN/nm) and average isometric force per cross-bridge (6–9 pN). Furthermore, models defined on the basis of single-molecule mechanics and solution biochemistry give good fits to experimental data from muscle. This suggests that the ordered myofilament lattice, accessory proteins and emergent effects of the sarcomere organization have only minor modulatory roles. However, such factors may be of greater importance under e.g., disease conditions. We also identify areas where single-molecule and muscle data are conflicting: (1) whether force generation is an Eyring or Kramers process with just one major power-stroke or several sub-strokes; (2) whether the myofilaments and the cross-bridges have Hookean or non-linear elasticity; (3) if individual myosin heads slip between actin sites under certain conditions, e.g., in lengthening; or (4) if the two heads of myosin cooperate.

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.

Strain in shock-loaded skeletal muscle and the time scale of muscular wobbling mass dynamics

In terrestrial locomotion, muscles undergo damped oscillations in response to limb impacts with the ground. Muscles are also actuators that generate mechanical power to allow locomotion. The corresponding elementary contractile process is the work stroke of an actin-myosin cross-bridge, which may be forcibly detached by superposed oscillations. By experimentally emulating rat leg impacts, we found that full activity and non-fatigue must meet to possibly prevent forcible cross-bridge detachment. Because submaximal muscle force represents the ordinary locomotor condition, our results show that forcible, eccentric cross-bridge detachment is a common, physiological process even during isometric muscle contractions. We also calculated the stiffnesses of the whole muscle-tendon complex and the fibre material separately, as well as Young's modulus of the latter: 1.8 MPa and 0.75 MPa for fresh, fully active and passive fibres, respectively. Our inferred Young's modulus of the tendon-aponeurosis complex suggests that stiffness in series to the fibre material is determined by the elastic properties of the aponeurosis region, rather than the tendon material. Knowing these stiffnesses and the muscle mass, the complex' eigenfrequency for responses to impacts can be quantified, as well as the size-dependency of this time scale of muscular wobbling mass dynamics.

Coordinated force generation of skeletal myosins in myofilaments through motor coupling

In contrast to processive molecular motors, skeletal myosins form a large motor ensemble for contraction of muscles against high loads. Despite numerous information on the molecular properties of skeletal myosin, its ensemble effects on collective force generation have not been rigorously clarified. Here we show 4 nm stepwise actin displacements generated by synthetic myofilaments beyond a load of 30 pN, implying that steps cannot be driven exclusively by single myosins, but potentially by coordinated force generations among multiple myosins. The simulation model shows that stepwise actin displacements are primarily caused by coordinated force generation among myosin molecules. Moreover, the probability of coordinated force generation can be enhanced against high loads by utilizing three factors: strain-dependent kinetics between force-generating states; multiple power stroke steps; and high ATP concentrations. Compared with other molecular motors, our findings reveal how the properties of skeletal myosin are tuned to perform cooperative force generation for efficient muscle contraction.

Skeletal muscle myosin forms large ensembles to generate force against high loads. Using optical tweezers and simulation Kaya et al. provide experimental evidence for cooperative force generation, and describe how the molecular properties of skeletal myosins are tuned for coordinated power strokes.

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.

Thick filament mechano-sensing is a calcium-independent regulatory mechanism in skeletal muscle

Recent X-ray diffraction studies on actively contracting fibres from skeletal muscle showed that the number of myosin motors available to interact with actin-containing thin filaments is controlled by the stress in the myosin-containing thick filaments. Those results suggested that thick filament mechano-sensing might constitute a novel regulatory mechanism in striated muscles that acts independently of the well-known thin filament-mediated calcium signalling pathway. Here we test that hypothesis using probes attached to the myosin regulatory light chain in demembranated muscle fibres. We show that both the extent and kinetics of thick filament activation depend on thick filament stress but are independent of intracellular calcium concentration in the physiological range. These results establish direct control of myosin motors by thick filament mechano-sensing as a general regulatory mechanism in skeletal muscle that is independent of the canonical calcium signalling pathway.

Recent data suggest that muscle contraction is regulated by thick filament mechano-sensing in addition to the well-known thin filament-mediated calcium signalling pathway. Here the authors provide direct evidence that myosin activation in skeletal muscle is controlled by thick filament stress independently of calcium.

Tropomyosin controls sarcomere-like contractions for rigidity sensing and suppressing growth on soft matrices

Cells test the rigidity of the extracellular matrix by applying forces to it through integrin adhesions. Recent measurements show that these forces are applied by local micrometre-scale contractions, but how contraction force is regulated by rigidity is unknown. Here we performed high temporal- and spatial-resolution tracking of contractile forces by plating cells on sub-micrometre elastomeric pillars. We found that actomyosin-based sarcomere-like contractile units (CUs) simultaneously moved opposing pillars in net steps of ∼2.5 nm, independent of rigidity. What correlated with rigidity was the number of steps taken to reach a force level that activated recruitment of α-actinin to the CUs. When we removed actomyosin restriction by depleting tropomyosin 2.1, we observed larger steps and higher forces that resulted in aberrant rigidity sensing and growth of non-transformed cells on soft matrices. Thus, we conclude that tropomyosin 2.1 acts as a suppressor of growth on soft matrices by supporting proper rigidity sensing.

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.

Physical principles demonstrate that the biceps femoris muscle relative to the other hamstring muscles exerts the most force: implications for hamstring muscle strain injuries

Of the hamstring muscle group the biceps femoris muscle is the most commonly injured muscle in sports requiring interval sprinting. The reason for this observation is unknown. The objective of this study was to calculate the forces of all three hamstring muscles, relative to each other, during a lengthening contraction to assess for any differences that may help explain the biceps femoris predilection for injury during interval sprinting. To calculate the displacement of each individual hamstring muscle previously performed studies on cadaveric anatomical data and hamstring kinematics during sprinting were used. From these displacement calculations for each individual hamstring muscle physical principles were then used to deduce the proportion of force exerted by each individual hamstring muscle during a lengthening muscle contraction. These deductions demonstrate that the biceps femoris muscle is required to exert proportionally more force in a lengthening muscle contraction relative to the semimembranosus and semitendinosus muscles primarily as a consequence of having to lengthen over a greater distance within the same time frame. It is hypothesized that this property maybe a factor in the known observation of the increased susceptibility of the biceps femoris muscle to injury during repeated sprints where recurrent higher force is required.