RECENT IMPROVEMENTS IN SMALL ANGLE X-RAY DIFFRACTION FOR THE STUDY OF MUSCLE PHYSIOLOGY

An integrated picture of the structural pathways controlling the heart performance

The regulation of heart function is attributed to a dual filament mechanism: i) the Ca2+-dependent structural changes in the regulatory proteins of the thin, actin-containing filament making actin available for myosin motor attachment, and ii) the release of motors from their folded (OFF) state on the surface of the thick filament allowing them to attach and pull the actin filament. Thick filament mechanosensing is thought to control the number of motors switching ON in relation to the systolic performance, but its molecular basis is still controversial. Here, we use high spatial resolution X-ray diffraction data from electrically paced rat trabeculae and papillary muscles to provide a molecular explanation of the modulation of heart performance that calls for a revision of the mechanosensing hypothesis. We find that upon stimulation, titin-mediated structural changes in the thick filament switch motors ON throughout the filament within ~½ the maximum systolic force. These structural changes also drive Myosin Binding Protein-C (MyBP-C) to promote first motor attachments to actin from the central 1/3 of the half-thick filament. Progression of attachments toward the periphery of half-thick filament with increase in systolic force is carried on by near-neighbor cooperative thin filament activation by attached motors. The identification of the roles of MyBP-C, titin, thin and thick filaments in heart regulation enables their targeting for potential therapeutic interventions.

Functional role of myosin-binding protein H in thick filaments of developing vertebrate fast-twitch skeletal muscle

Myosin-binding protein H (MyBP-H) is a component of the vertebrate skeletal muscle sarcomere with sequence and domain homology to myosin-binding protein C (MyBP-C). Whereas skeletal muscle isoforms of MyBP-C (fMyBP-C, sMyBP-C) modulate muscle contractility via interactions with actin thin filaments and myosin motors within the muscle sarcomere "C-zone," MyBP-H has no known function. This is in part due to MyBP-H having limited expression in adult fast-twitch muscle and no known involvement in muscle disease. Quantitative proteomics reported here reveal that MyBP-H is highly expressed in prenatal rat fast-twitch muscles and larval zebrafish, suggesting a conserved role in muscle development and prompting studies to define its function. We take advantage of the genetic control of the zebrafish model and a combination of structural, functional, and biophysical techniques to interrogate the role of MyBP-H. Transgenic, FLAG-tagged MyBP-H or fMyBP-C both localize to the C-zones in larval myofibers, whereas genetic depletion of endogenous MyBP-H or fMyBP-C leads to increased accumulation of the other, suggesting competition for C-zone binding sites. Does MyBP-H modulate contractility in the C-zone? Globular domains critical to MyBP-C's modulatory functions are absent from MyBP-H, suggesting that MyBP-H may be functionally silent. However, our results suggest an active role. In vitro motility experiments indicate MyBP-H shares MyBP-C's capacity as a molecular "brake." These results provide new insights and raise questions about the role of the C-zone during muscle development.

Load-dependence of the activation of myosin filaments in heart muscle

Contraction of heart muscle requires activation of both the actin and myosin filaments. The mechanism of myosin filament activation is unknown, but the leading candidate hypothesis is direct mechano-sensing by the filaments. Here, we tested this hypothesis by activating intact trabeculae from rat heart by electrical stimulation under different loads and measuring myosin filament activation by X-ray diffraction. Unexpectedly, we found that the distinct structural changes in the myosin filament associated with activation had different dependences on the load. In early activation, all the structural changes indicated faster activation at higher load, as expected from the mechano-sensing hypothesis, but, at later times, the helical order of the myosin motors characteristic of the inactivated state was lost even at very low load. We conclude that mechano-sensing does operate in heart muscle, but it is supplemented by a previously undescribed mechanism that links myosin filament activation to actin filament activation. KEY POINTS: Myosin filament activation controls the strength and speed of contraction in heart muscle. Early activation of the myosin filament is determined by the filament load. At later times, myosin filament activation is controlled by a load independent pathway. This load independent pathway provides new targets and assays for drug development.

Calcium has a direct effect on thick filament activation in porcine myocardium

Sarcomere activation in striated muscle requires both thin filament-based and thick filament-based activation mechanisms. Recent studies have shown that myosin heads on the thick filaments undergo OFF to ON structural transitions in response to calcium (Ca2+) in permeabilized porcine myocardium in the presence of a small molecule inhibitor that eliminated active force. The changes in X-ray diffraction signatures of OFF to ON transitions were interpreted as Ca2+ acting to activate the thick filaments. Alternatively, Ca2+ binding to troponin could initiate a Ca2+-dependent crosstalk from the thin filament to the thick filament via interfilament connections such as the myosin binding protein-C. Here, we exchanged native troponin in permeabilized porcine myocardium for troponin containing the cTnC D65A mutation, which disallows the activation of troponin through Ca2+ binding to determine if Ca2+-dependent thick filament activation persists in the absence of thin filament activation. After the exchange protocol, over 95% of the Ca2+-activated force was eliminated. Equatorial intensity ratio increased significantly in both WT and D65A exchanged myocardium with increasing Ca2+ concentration. The degree of helical ordering of the myosin heads decreased by the same amount in WT and D65A myocardium when Ca2+ concentration increased. These results are consistent with a direct effect of Ca2+ in activating the thick filament rather than an indirect effect due to Ca2+-mediated crosstalk between the thick and thin filaments.

Differences in thick filament activation in fast rodent skeletal muscle and slow porcine cardiac muscle

There is a growing appreciation that regulation of muscle contraction requires both thin filament and thick filament activation in order to fully activate the sarcomere. The prevailing mechano-sensing model for thick filament activation was derived from experiments on fast-twitch muscle. We address the question whether, or to what extent, this mechanism can be extrapolated to the slow muscle in the hearts of large mammals, including humans. We investigated the similarities and differences in structural signatures of thick filament activation in porcine myocardium as compared to fast rat extensor digitorum longus (EDL) skeletal muscle under relaxed conditions and sub-maximal contraction using small angle X-ray diffraction. Thick and thin filaments were found to adopt different structural configurations under relaxing conditions, and myosin heads showed different changes in configuration upon sub-maximal activation, when comparing the two muscle types. Titin was found to have an X-ray diffraction signature distinct from those of the overall thick filament backbone, and its spacing change appeared to be positively correlated to the force exerted on the thick filament. Structural changes in fast EDL muscle were found to be consistent with the mechano-sensing model. In porcine myocardium, however, the structural basis of mechano-sensing is blunted suggesting the need for additional activation mechanism(s) in slow cardiac muscle. These differences in thick filament regulation can be related to their different physiological roles where fast muscle is optimized for rapid, burst-like, contractions, and the slow cardiac muscle in large mammalian hearts adopts a more finely tuned, graded response to allow for their substantial functional reserve. KEY POINTS: Both thin filament and thick filament activation are required to fully activate the sarcomere. Thick and thin filaments adopt different structural configurations under relaxing conditions, and myosin heads show different changes in configuration upon sub-maximal activation in fast extensor digitorum longus muscle and slow porcine cardiac muscle. Titin has an X-ray diffraction signature distinct from those of the overall thick filament backbone and this titin reflection spacing change appeared to be directly proportional to the force exerted on the thick filament. Mechano-sensing is blunted in porcine myocardium suggesting the need for additional activation mechanism(s) in slow cardiac muscle. Fast skeletal muscle is optimized for rapid, burst-like contractions, and the slow cardiac muscle in large mammalian hearts adopts a more finely tuned graded response to allow for their substantial functional reserve.

Fast myosin binding protein C knockout in skeletal muscle alters length-dependent activation and myofilament structure

In striated muscle, the sarcomeric protein myosin-binding protein-C (MyBP-C) is bound to the myosin thick filament and is predicted to stabilize myosin heads in a docked position against the thick filament, which limits crossbridge formation. Here, we use the homozygous Mybpc2 knockout (C2-/-) mouse line to remove the fast-isoform MyBP-C from fast skeletal muscle and then conduct mechanical functional studies in parallel with small-angle X-ray diffraction to evaluate the myofilament structure. We report that C2-/- fibers present deficits in force production and calcium sensitivity. Structurally, passive C2-/- fibers present altered sarcomere length-independent and -dependent regulation of myosin head conformations, with a shift of myosin heads towards actin. At shorter sarcomere lengths, the thin filament is axially extended in C2-/-, which we hypothesize is due to increased numbers of low-level crossbridges. These findings provide testable mechanisms to explain the etiology of debilitating diseases associated with MyBP-C.

Functional role of myosin-binding protein H in thick filaments of developing vertebrate fast-twitch skeletal muscle

Myosin-binding protein H (MyBP-H) is a component of the vertebrate skeletal muscle sarcomere with sequence and domain homology to myosin-binding protein C (MyBP-C). Whereas skeletal muscle isoforms of MyBP-C (fMyBP-C, sMyBP-C) modulate muscle contractility via interactions with actin thin filaments and myosin motors within the muscle sarcomere "C-zone," MyBP-H has no known function. This is in part due to MyBP-H having limited expression in adult fast-twitch muscle and no known involvement in muscle disease. Quantitative proteomics reported here reveal MyBP-H is highly expressed in prenatal rat fast-twitch muscles and larval zebrafish, suggesting a conserved role in muscle development, and promoting studies to define its function. We take advantage of the genetic control of the zebrafish model and a combination of structural, functional, and biophysical techniques to interrogate the role of MyBP-H. Transgenic, FLAG-tagged MyBP-H or fMyBP-C both localize to the C-zones in larval myofibers, whereas genetic depletion of endogenous MyBP-H or fMyBP-C leads to increased accumulation of the other, suggesting competition for C-zone binding sites. Does MyBP-H modulate contractility from the C-zone? Globular domains critical to MyBP-C's modulatory functions are absent from MyBP-H, suggesting MyBP-H may be functionally silent. However, our results suggest an active role. Small angle x-ray diffraction of intact larval tails revealed MyBP-H contributes to the compression of the myofilament lattice accompanying stretch or contraction, while in vitro motility experiments indicate MyBP-H shares MyBP-C's capacity as a molecular "brake". These results provide new insights and raise questions about the role of the C-zone during muscle development.

Myosin-binding protein C regulates the sarcomere lattice and stabilizes the OFF states of myosin heads

Muscle contraction is produced via the interaction of myofilaments and is regulated so that muscle performance matches demand. Myosin-binding protein C (MyBP-C) is a long and flexible protein that is tightly bound to the thick filament at its C-terminal end (MyBP-CC8C10), but may be loosely bound at its middle- and N-terminal end (MyBP-CC1C7) to myosin heads and/or the thin filament. MyBP-C is thought to control muscle contraction via the regulation of myosin motors, as mutations lead to debilitating disease. We use a combination of mechanics and small-angle X-ray diffraction to study the immediate and selective removal of the MyBP-CC1C7 domains of fast MyBP-C in permeabilized skeletal muscle. We show that cleavage leads to alterations in crossbridge kinetics and passive structural signatures of myofilaments that are indicative of a shift of myosin heads towards the ON state, highlighting the importance of MyBP-CC1C7 to myofilament force production and regulation.

Fast myosin binding protein C knockout in skeletal muscle alters length-dependent activation and myofilament structure

In striated muscle, some sarcomere proteins regulate crossbridge cycling by varying the propensity of myosin heads to interact with actin. Myosin-binding protein C (MyBP-C) is bound to the myosin thick filament and is predicted to interact and stabilize myosin heads in a docked position against the thick filament and limit crossbridge formation, the so-called OFF state. Via an unknown mechanism, MyBP-C is thought to release heads into the so-called ON state, where they are more likely to form crossbridges. To study this proposed mechanism, we used the C2-/- mouse line to knock down fast-isoform MyBP-C completely and total MyBP-C by ~24%, and conducted mechanical functional studies in parallel with small-angle X-ray diffraction to evaluate the myofilament structure. We report that C2-/- fibers presented deficits in force production and reduced calcium sensitivity. Structurally, passive C2-/- fibers presented altered SL-independent and SL-dependent regulation of myosin head ON/OFF states, with a shift of myosin heads towards the ON state. Unexpectedly, at shorter sarcomere lengths, the thin filament was axially extended in C2-/- vs. non-transgenic controls, which we postulate is due to increased low-level crossbridge formation arising from relatively more ON myosins in the passive muscle that elongates the thin filament. The downstream effect of increasing crossbridge formation in a passive muscle on contraction performance is not known. Such widespread structural changes to sarcomere proteins provide testable mechanisms to explain the etiology of debilitating MyBP-C-associated diseases.

Disruption of Z-Disc Function Promotes Mechanical Dysfunction in Human Myocardium: Evidence for a Dual Myofilament Modulatory Role by Alpha-Actinin 2

The ACTN2 gene encodes α-actinin 2, located in the Z-disc of the sarcomeres in striated muscle. In this study, we sought to investigate the effects of an ACTN2 missense variant of unknown significance (p.A868T) on cardiac muscle structure and function. Left ventricular free wall samples were obtained at the time of cardiac transplantation from a heart failure patient with the ACTN2 A868T heterozygous variant. This variant is in the EF 3-4 domain known to interact with titin and α-actinin. At the ultrastructural level, ACTN2 A868T cardiac samples presented small structural changes in cardiomyocytes when compared to healthy donor samples. However, contractile mechanics of permeabilized ACTN2 A868T variant cardiac tissue displayed higher myofilament Ca2+ sensitivity of isometric force, reduced sinusoidal stiffness, and faster rates of tension redevelopment at all Ca2+ levels. Small-angle X-ray diffraction indicated increased separation between thick and thin filaments, possibly contributing to changes in muscle kinetics. Molecular dynamics simulations indicated that while the mutation does not significantly impact the structure of α-actinin on its own, it likely alters the conformation associated with titin binding. Our results can be explained by two Z-disc mediated communication pathways: one pathway that involves α-actinin's interaction with actin, affecting thin filament regulation, and the other pathway that involves α-actinin's interaction with titin, affecting thick filament activation. This work establishes the role of α-actinin 2 in modulating cross-bridge kinetics and force development in the human myocardium as well as how it can be involved in the development of cardiac disease.

Myosin-binding protein C forms C-links and stabilizes OFF states of myosin

Contraction force in muscle is produced by the interaction of myosin motors in the thick filaments and actin in the thin filaments and is fine-tuned by other proteins such as myosin-binding protein C (MyBP-C). One form of control is through the regulation of myosin heads between an ON and OFF state in passive sarcomeres, which leads to their ability or inability to interact with the thin filaments during contraction, respectively. MyBP-C is a flexible and long protein that is tightly bound to the thick filament at its C-terminal end but may be loosely bound at its middle- and N-terminal end (MyBP-CC1C7). Under considerable debate is whether the MyBP-CC1C7 domains directly regulate myosin head ON/OFF states, and/or link thin filaments ("C-links"). Here, we used a combination of mechanics and small-angle X-ray diffraction to study the immediate and selective removal of the MyBP-CC1C7 domains of fast MyBP-C in permeabilized skeletal muscle. After cleavage, the thin filaments were significantly shorter, a result consistent with direct interactions of MyBP-C with thin filaments thus confirming C-links. Ca2+ sensitivity was reduced at shorter sarcomere lengths, and crossbridge kinetics were increased across sarcomere lengths at submaximal activation levels, demonstrating a role in crossbridge kinetics. Structural signatures of the thick filaments suggest that cleavage also shifted myosin heads towards the ON state - a marker that typically indicates increased Ca2+ sensitivity but that may account for increased crossbridge kinetics at submaximal Ca2+ and/or a change in the force transmission pathway. Taken together, we conclude that MyBP-CC1C7 domains play an important role in contractile performance which helps explain why mutations in these domains often lead to debilitating diseases.

The structural and functional integrities of porcine myocardium are mostly preserved by cryopreservation

Structural and functional studies of heart muscle are important to gain insights into the physiological bases of cardiac muscle contraction and the pathological bases of heart disease. While fresh muscle tissue works best for these kinds of studies, this is not always practical to obtain, especially for heart tissue from large animal models and humans. Conversely, tissue banks of frozen human hearts are available and could be a tremendous resource for translational research. It is not well understood, however, how liquid nitrogen freezing and cryostorage may impact the structural integrity of myocardium from large mammals. In this study, we directly compared the structural and functional integrity of never-frozen to previously frozen porcine myocardium to investigate the consequences of freezing and cryostorage. X-ray diffraction measurements from hydrated tissue under near-physiological conditions and electron microscope images from chemically fixed porcine myocardium showed that prior freezing has only minor effects on structural integrity of the muscle. Furthermore, mechanical studies similarly showed no significant differences in contractile capabilities of porcine myocardium with and without freezing and cryostorage. These results demonstrate that liquid nitrogen preservation is a practical approach for structural and functional studies of myocardium.

Danicamtiv increases myosin recruitment and alters the chemomechanical cross bridge cycle in cardiac muscle

Modulating myosin function is a novel therapeutic approach in patients with cardiomyopathy. Detailed mechanism of action of these agents can help predict potential unwanted affects and identify patient populations that can benefit most from them. Danicamtiv is a novel myosin activator with promising preclinical data that is currently in clinical trials. While it is known danicamtiv increases force and cardiomyocyte contractility without affecting calcium levels, detailed mechanistic studies regarding its mode of action are lacking. Using porcine cardiac tissue and myofibrils we demonstrate that Danicamtiv increases force and calcium sensitivity via increasing the number of myosin in the "on" state and slowing cross bridge turnover. Our detailed analysis shows that inhibition of ADP release results in decreased cross bridge turnover with cross bridges staying on longer and prolonging myofibril relaxation. Using a mouse model of genetic dilated cardiomyopathy, we demonstrated that Danicamtiv corrected calcium sensitivity in demembranated and abnormal twitch magnitude and kinetics in intact cardiac tissue.

Significance Statement

Directly augmenting sarcomere function has potential to overcome limitations of currently used inotropic agents to improve cardiac contractility. Myosin modulation is a novel mechanism for increased contraction in cardiomyopathies. Danicamtiv is a myosin activator that is currently under investigation for use in cardiomyopathy patients. Our study is the first detailed mechanism of how Danicamtiv increases force and alters kinetics of cardiac activation and relaxation. This new understanding of the mechanism of action of Danicamtiv can be used to help identify patients that could benefit most from this treatment.

Cardiac myosin filaments are directly regulated by calcium

Classically, striated muscle contraction is initiated by calcium (Ca2+)-dependent structural changes in regulatory proteins on actin-containing thin filaments, which allow the binding of myosin motors to generate force. Additionally, dynamic switching between resting off and active on myosin states has been shown to regulate muscle contractility, a recently validated mechanism by novel myosin-targeted therapeutics. The molecular nature of this switching, however, is not understood. Here, using a combination of small-angle x-ray fiber diffraction and biochemical assays with reconstituted systems, we show that cardiac thick filaments are directly Ca2+-regulated. We find that Ca2+ induces a structural transition of myosin heads from ordered off states close to the thick filament to disordered on states closer to the thin filaments. Biochemical assays show a Ca2+-induced transition from an inactive super-relaxed (SRX) state(s) to an active disordered-relaxed (DRX) state(s) in synthetic thick filaments. We show that these transitions are an intrinsic property of cardiac myosin only when assembled into thick filaments and provide a fresh perspective on nature's two orthogonal mechanisms to regulate muscle contraction through the thin and the thick filaments.

Thick filament activation is different in fast- and slow-twitch skeletal muscle

The contractile properties of fast-twitch and slow-twitch skeletal muscles are primarily determined by the myosin isoform content and modulated by a variety of sarcomere proteins. X-ray diffraction studies of regulatory mechanisms in muscle contraction have focused predominately on fast- or mixed-fibre muscle with slow muscle being much less studied. Here, we used time-resolved X-ray diffraction to investigate the dynamic behaviour of the myofilament proteins in relatively pure slow-twitch-fibre rat soleus (SOL) and pure fast-twitch-fibre rat extensor digitorum longus (EDL) muscle during twitch and tetanic contractions at optimal length. During twitch contractions the diffraction signatures indicating a transition in the myosin heads from ordered OFF states, where heads are held close to the thick filament backbone, to disordered ON states, where heads are free to bind to thin filaments, were found in EDL and not in SOL muscle. During tetanic contraction, changes in the disposition of myosin heads as active tension develops is a quasi-stepwise process in EDL muscle whereas in SOL muscle this relationship appears to be linear. The observed reduced extensibility of the thick filaments in SOL muscle as compared to EDL muscles indicates a molecular basis for this behaviour. These data indicate that for the EDL, thick filament activation is a cooperative strain-induced mechano-sensing mechanism, whereas for the SOL, thick filament activation has a more graded response. These different approaches to thick filament regulation in fast- and slow-twitch muscles may be adaptations for short-duration, strong contractions versus sustained, finely controlled contractions, respectively. KEY POINTS: Fast-twitch muscle and slow-twitch muscle are optimized for strong, short-duration contractions and for tonic postural activity, respectively. Structural events (OFF to ON transitions) in the myosin-containing thick filaments in fast muscle help determine the timing and strength of contractions, but these have not been studied in slow-twitch muscle. The X-ray diffraction signatures of structural OFF to ON transitions are different in fast extensor digitorum longus (EDL) and slow soleus (SOL) muscle, being completely absent during twitches in soleus muscle and blunted during tetanic contractions SOL as compared to EDL Quasi-stepwise thick filament structural OFF to ON transitions in fast twitch muscle may be an adaptation for rapid, ballistic movements, whereas more graded OFF to ON structural transitions in slow-twitch muscle may be an adaptation for slower, finer motions.

EMD-57033 Augments the Contractility in Porcine Myocardium by Promoting the Activation of Myosin in Thick Filaments

Sufficient cardiac contractility is necessary to ensure the sufficient cardiac output to provide an adequate end-organ perfusion. Inadequate cardiac output and the diminished perfusion of vital organs from depressed myocardium contractility is a hallmark end-stage of heart failure. There are no available therapeutics that directly target contractile proteins to improve the myocardium contractility and reduce mortality. The purpose of this study is to present a proof of concept to aid in the development of muscle activators (myotropes) for augmenting the contractility in clinical heart failure. Here we use a combination of cardiomyocyte mechanics, the biochemical quantification of the ATP turnover, and small angle X-ray diffraction on a permeabilized porcine myocardium to study the mechanisms of EMD-57033 (EMD) for activating myosin. We show that EMD increases the contractility in a porcine myocardium at submaximal and systolic calcium concentrations. Biochemical assays show that EMD decreases the proportion of myosin heads in the energy sparing super-relaxed (SRX) state under relaxing conditions, which are less likely to interact with actin during contraction. Structural assays show that EMD moves the myosin heads in relaxed muscles from a structurally ordered state close to the thick filament backbone, to a disordered state closer to the actin filament, while simultaneously inducing structural changes in the troponin complex on the actin filament. The dual effects of EMD on activating myosin heads and the troponin complex provides a proof of concept for the use of small molecule muscle activators for augmenting the contractility in heart failure.

Activation of the myosin motors in fast-twitch muscle of the mouse is controlled by mechano-sensing in the myosin filaments

Myosin motors in resting muscle are inactivated by folding against the backbone of the myosin filament in an ordered helical array and must be released from that conformation to engage in force generation. Time-resolved X-ray diffraction from single fibres of amphibian muscle showed that myosin filament activation could be inhibited by imposing unloaded shortening at the start of stimulation, suggesting that filaments were activated by mechanical stress. Here we improved the signal-to-noise ratio of that approach using whole extensor digitorum longus muscles of the mouse contracting tetanically at 28°C. Changes in X-ray signals associated with myosin filament activation, including the decrease in the first-order myosin layer line associated with the helical motor array, increase in the spacing of a myosin-based reflection associated with packing of myosin tails in the filament backbone, and increase in the ratio of the 1,1 and 1,0 equatorial reflections associated with movement of motors away from the backbone, were delayed by imposing 10-ms unloaded shortening at the start of stimulation. These results show that myosin filaments are predominantly activated by filament stress, as in amphibian muscle. However, a small component of filament activation at zero load was detected, implying an independent mechanism of partial filament activation. X-ray interference measurements indicated a switch-like change in myosin motor conformation at the start of force development, accompanied by transient disordering of motors in the regions of the myosin filament near its midpoint, suggesting that filament zonal dynamics also play a role in its activation. KEY POINTS: Activation of myosin filaments in extensor digitorum longus muscles of the mouse is delayed by imposing rapid shortening from the start of stimulation. Stress is the major mechanism of myosin filament activation in these muscles, but there is a small component of filament activation during electrical stimulation at zero stress. Myosin motors switch rapidly from the folded inhibited conformation to the actin-attached force-generating conformation early in force development.

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.

Small Angle X-ray Diffraction as a Tool for Structural Characterization of Muscle Disease

Small angle X-ray fiber diffraction is the method of choice for obtaining molecular level structural information from striated muscle fibers under hydrated physiological conditions. For many decades this technique had been used primarily for investigating basic biophysical questions regarding muscle contraction and regulation and its use confined to a relatively small group of expert practitioners. Over the last 20 years, however, X-ray diffraction has emerged as an important tool for investigating the structural consequences of cardiac and skeletal myopathies. In this review we show how simple and straightforward measurements, accessible to non-experts, can be used to extract biophysical parameters that can help explain and characterize the physiology and pathology of a given experimental system. We provide a comprehensive guide to the range of the kinds of measurements that can be made and illustrate how they have been used to provide insights into the structural basis of pathology in a comprehensive review of the literature. We also show how these kinds of measurements can inform current controversies and indicate some future directions.

Cooling intact and demembranated trabeculae from rat heart releases myosin motors from their inhibited conformation

Myosin filament–based regulation supplements actin filament–based regulation to control the strength and speed of contraction in heart muscle. In diastole, myosin motors form a folded helical array that inhibits actin interaction; during contraction, they are released from that array. A similar structural transition has been observed in mammalian skeletal muscle, in which cooling below physiological temperature has been shown to reproduce some of the structural features of the activation of myosin filaments during active contraction. Here, we used small-angle x-ray diffraction to characterize the structural changes in the myosin filaments associated with cooling of resting and relaxed trabeculae from the right ventricle of rat hearts from 39°C to 7°C. In intact quiescent trabeculae, cooling disrupted the folded helical conformation of the myosin motors and induced extension of the filament backbone, as observed in the transition from diastole to peak systolic force at 27°C. Demembranation of trabeculae in relaxing conditions induced expansion of the filament lattice, but the structure of the myosin filaments was mostly preserved at 39°C. Cooling of relaxed demembranated trabeculae induced changes in motor conformation and filament structure similar to those observed in intact quiescent trabeculae. Osmotic compression of the filament lattice to restore its spacing to that of intact trabeculae at 39°C stabilized the helical folded state against disruption by cooling. The myosin filament structure and motor conformation of intact trabeculae at 39°C were largely preserved in demembranated trabeculae at 27°C or above in the presence of Dextran, allowing the physiological mechanisms of myosin filament–based regulation to be studied in those conditions.

Subcellular Remodeling in Filamin C Deficient Mouse Hearts Impairs Myocyte Tension Development during Progression of Dilated Cardiomyopathy

Dilated cardiomyopathy (DCM) is a life-threatening form of heart disease that is typically characterized by progressive thinning of the ventricular walls, chamber dilation, and systolic dysfunction. Multiple mutations in the gene encoding filamin C (FLNC), an actin-binding cytoskeletal protein in cardiomyocytes, have been found in patients with DCM. However, the mechanisms that lead to contractile impairment and DCM in patients with FLNC variants are poorly understood. To determine how FLNC regulates systolic force transmission and DCM remodeling, we used an inducible, cardiac-specific FLNC-knockout (icKO) model to produce a rapid onset of DCM in adult mice. Loss of FLNC reduced systolic force development in single cardiomyocytes and isolated papillary muscles but did not affect twitch kinetics or calcium transients. Electron and immunofluorescence microscopy showed significant defects in Z-disk alignment in icKO mice and altered myofilament lattice geometry. Moreover, a loss of FLNC induces a softening myocyte cortex and structural adaptations at the subcellular level that contribute to disrupted longitudinal force production during contraction. Spatially explicit computational models showed that these structural defects could be explained by a loss of inter-myofibril elastic coupling at the Z-disk. Our work identifies FLNC as a key regulator of the multiscale ultrastructure of cardiomyocytes and therefore plays an important role in maintaining systolic mechanotransmission pathways, the dysfunction of which may be key in driving progressive DCM.

Myosin motors that cannot bind actin leave their folded OFF state on activation of skeletal muscle

The myosin motors in resting skeletal muscle are folded back against their tails in the thick filament in a conformation that makes them unavailable for binding to actin. When muscles are activated, calcium binding to troponin leads to a rapid change in the structure of the actin-containing thin filaments that uncovers the myosin binding sites on actin. Almost as quickly, myosin motors leave the folded state and move away from the surface of the thick filament. To test whether motor unfolding is triggered by the availability of nearby actin binding sites, we measured changes in the x-ray reflections that report motor conformation when muscles are activated at longer sarcomere length, so that part of the thick filaments no longer overlaps with thin filaments. We found that the intensity of the M3 reflection from the axial repeat of the motors along the thick filaments declines almost linearly with increasing sarcomere length up to 2.8 µm, as expected if motors in the nonoverlap zone had left the folded state and become relatively disordered. In a recent article in JGP, Squire and Knupp challenged this interpretation of the data. We show here that their analysis is based on an incorrect assumption about how the interference subpeaks of the M3 reflection were reported in our previous paper. We extend previous models of mass distribution along the filaments to show that the sarcomere length dependence of the M3 reflection is consistent with <10% of no-overlap motors remaining in the folded conformation during active contraction, confirming our previous conclusion that unfolding of myosin motors on muscle activation is not due to the availability of local actin binding sites.

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.

Adjusting Rotational Behavior of Molecular Rotors by a Rational Tuning of Molecular Structure

Many crystalline molecular rotors have been developed in the past decades. However, manipulating the rotational gesture that intrinsically controls the physical performance of materials remains a challenge. Herein, we report a series of crystalline rotors whose rotational gestures can be modulated by modifying the structures of molecular stators. In these dynamic crystals, the ox^2- (ox^2- = oxalate anion) behave as molecular rotators performing axial-free rotation in cavities composed of five complex cations, [M^II(en)₃]²⁺ (en = ethylenediamine). The structure of [M^II(en)₃]²⁺ that serves as a molecular stator can be tuned by varying the metal center with different ionic radii, consequently altering the chemical environment around the molecular rotator. Owing to the quasi-transverse isotropy of ox^2- and multiple hydrogen-bond interactions around it, the molecular rotator exhibits unusual motional malleability, i.e., it can rotate either longitudinally in the compound of Zn^II, or with a tilt angle of 42° in the compound of Fe^II, or even laterally in the compound of Cd^II. The atypical dynamic behavior demonstrated here provides a new chance for the development of exquisite crystalline molecular rotors with advanced tunable functionalities.

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.

Rules of nature's Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed

The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.

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.

Myosin dynamics during relaxation in mouse soleus muscle and modulation by 2'-deoxy-ATP

KEY POINTS

Skeletal muscle relaxation has been primarily studied by assessing the kinetics of force decay. Little is known about the resultant dynamics of structural changes in myosin heads during relaxation. The naturally occurring nucleotide 2-deoxy-ATP (dATP) is a myosin activator that enhances cross-bridge binding and kinetics. X-ray diffraction data indicate that with elevated dATP, myosin heads were extended closer to actin in relaxed muscle and myosin heads return to an ordered, resting state after contraction more quickly. Molecular dynamics simulations of post-powerstroke myosin suggest that dATP induces structural changes in myosin heads that increase the surface area of the actin-binding regions promoting myosin interaction with actin, which could explain the observed delays in the onset of relaxation. This study of the dATP-induced changes in myosin may be instructive for determining the structural changes desired for other potential myosin-targeted molecular compounds to treat muscle diseases.

ABSTRACT

Here we used time-resolved small-angle X-ray diffraction coupled with force measurements to study the structural changes in FVB mouse skeletal muscle sarcomeres during relaxation after tetanus contraction. To estimate the rate of myosin deactivation, we followed the rate of the intensity recovery of the first-order myosin layer line (MLL1) and restoration of the resting spacing of the third and sixth order of meridional reflection (SM3 and SM6 ) following tetanic contraction. A transgenic mouse model with elevated skeletal muscle 2-deoxy-ATP (dATP) was used to study how myosin activators may affect soleus muscle relaxation. X-ray diffraction evidence indicates that with elevated dATP, myosin heads were extended closer to actin in resting muscle. Following contraction, there is a slight but significant delay in the decay of force relative to WT muscle while the return of myosin heads to an ordered resting state was initially slower, then became more rapid than in WT muscle. Molecular dynamics simulations of post-powerstroke myosin suggest that dATP induces structural changes in myosin that increase the surface area of the actin-binding regions, promoting myosin interaction with actin. With dATP, myosin heads may remain in an activated state near the thin filaments following relaxation, accounting for the delay in force decay and the initial delay in recovery of resting head configuration, and this could facilitate subsequent contractions.

Hierarchical modeling of force generation in cardiac muscle

Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models, however, may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models-from the more refined to the more simplified-that are rigorously and systematically related to each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three model families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

Myosin filament-based regulation of the dynamics of contraction in heart muscle

Cardiovascular disease continues to be the leading cause of death worldwide, and is frequently associated with heart failure. Efforts to develop better therapeutics for heart failure have been held back by limited understanding of the normal control of contraction on the timescale of the heartbeat. We used synchrotron X-ray diffraction to determine the dynamic structural changes in the myosin motors that drive contraction in the heart muscle, and show that myosin filament-based control mechanisms determine the time course and strength of contraction, allowing those mechanisms to be targeted for developing new therapies for heart disease.

Myosin-based mechanisms are increasingly recognized as supplementing their better-known actin-based counterparts to control the strength and time course of contraction in both skeletal and heart muscle. Here we use synchrotron small-angle X-ray diffraction to determine the structural dynamics of local domains of the myosin filament during contraction of heart muscle. We show that, although myosin motors throughout the filament contribute to force development, only about 10% of the motors in each filament bear the peak force, and these are confined to the filament domain containing myosin binding protein-C, the “C-zone.” Myosin motors in domains further from the filament midpoint are likely to be activated and inactivated first in each contraction. Inactivated myosin motors are folded against the filament core, and a subset of folded motors lie on the helical tracks described previously. These helically ordered motors are also likely to be confined to the C-zone, and the associated motor conformation reforms only slowly during relaxation. Myosin filament stress-sensing determines the strength and time course of contraction in conjunction with actin-based regulation. These results establish the fundamental roles of myosin filament domains and the associated motor conformations in controlling the strength and dynamics of contraction in heart muscle, enabling those structures to be targeted to develop new therapies for heart disease.

Lattice arrangement of myosin filaments correlates with fiber type in rat skeletal muscle

The thick (myosin-containing) filaments of vertebrate skeletal muscle are arranged in a hexagonal lattice, interleaved with an array of thin (actin-containing) filaments with which they interact to produce contraction. X-ray diffraction and EM have shown that there are two types of thick filament lattice. In the simple lattice, all filaments have the same orientation about their long axis, while in the superlattice, nearest neighbors have rotations differing by 0° or 60°. Tetrapods (amphibians, reptiles, birds, and mammals) typically have only a superlattice, while the simple lattice is confined to fish. We have performed x-ray diffraction and electron microscopy of the soleus (SOL) and extensor digitorum longus (EDL) muscles of the rat and found that while the EDL has a superlattice as expected, the SOL has a simple lattice. The EDL and SOL of the rat are unusual in being essentially pure fast and slow muscles, respectively. The mixed fiber content of most tetrapod muscles and/or lattice disorder may explain why the simple lattice has not been apparent in these vertebrates before. This is supported by only weak simple lattice diffraction in the x-ray pattern of mouse SOL, which has a greater mix of fiber types than rat SOL. We conclude that the simple lattice might be common in tetrapods. The correlation between fiber type and filament lattice arrangement suggests that the lattice arrangement may contribute to the functional properties of a muscle.

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

The active force of mammalian skeletal muscle is reduced at low temperatures. Caremani et al. reveal that this is due to the rise of a population of myosin motors captured in a refractory state insensitive to muscle 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 (T₀) 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 T₀, 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 T₀, 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.

X-ray scanning microscopies of microcalcifications in abdominal aortic and popliteal artery aneurysms

Abdominal aortic and popliteal artery aneurysms are vascular diseases which show massive degeneration, weakening of the vascular wall and loss of the vascular tissue functionality. They are driven by inflammatory, hemodynamical factors and biological alterations that may lead, in the case of an abdominal aortic aneurysm, to sudden and dangerous ruptures of the arteries. Here, human aortic and popliteal aneurysm tissues were obtained during surgical repair, and studied by synchrotron radiation X-ray scanning microdiffraction and small-angle scattering, to investigate the microcalcifications present in the tissues. Data collected during the experiments were transformed into quantitative microscopy images through the combination of statistical approaches and crystallographic methods. As a result of this multi-step analysis, microcalcifications, which are markers of the pathology, were classified in terms of chemical and structural content. This analysis helped to identify the presence of nanocrystalline hy-droxy-apatite and microcrystalline cholesterol, embedded in myofilament, and elastin-containing tissue with low collagen content in predominantly nanocrystalline areas. The generality of the approach allows it to be transferred to other types of tissue and other pathologies affected by microcalcifications, such as thyroid carcinoma, breast cancer, testicular microli-thia-sis or glioblastoma.

Thick-Filament Extensibility in Intact Skeletal Muscle

Myofilament extensibility is a key structural parameter for interpreting myosin cross-bridge kinetics in striated muscle. Previous studies reported much higher thick-filament extensibility at low tension than the better-known and commonly used values at high tension, but in interpreting mechanical studies of muscle, a single value for thick-filament extensibility has usually been assumed. Here, we established the complete thick-filament force-extension curve from actively contracting, intact vertebrate skeletal muscle. To access a wide range of tetanic forces, the myosin inhibitor blebbistatin was used to induce low tetanic forces in addition to the higher tensions obtained from tetanic contractions of the untreated muscle. We show that the force/extensibility curve of the thick filament is nonlinear, so assuming a single value for thick-filament extensibility at all force levels is not justified. We also show that independent of whether tension is generated passively by sarcomere stretch or actively by cross-bridges, the thick-filament extensibility is nonlinear. Myosin head periodicity, however, only changes when active tension is generated under calcium-activated conditions. The nonlinear thick-filament force-extension curve in skeletal muscle, therefore, reflects a purely passive response to either titin-based force or actomyosin-based force, and it does not include a thick-filament activation mechanism. In contrast, the transition of myosin head periodicity to an active configuration appears to only occur in response to increased active force when calcium is present.

Myosin Head Configurations in Resting and Contracting Murine Skeletal Muscle

Transgenic mouse models have been important tools for studying the relationship of genotype to phenotype for human diseases, including those of skeletal muscle. We show that mouse skeletal muscle can produce high quality X-ray diffraction patterns establishing the mouse intact skeletal muscle X-ray preparation as a potentially powerful tool to test structural hypotheses in health and disease. A notable feature of the mouse model system is the presence of residual myosin layer line intensities in contracting mouse muscle patterns. This provides an additional tool, along with the I1,1/I1,0 intensity ratio, for estimating the proportions of active versus relaxed myosin heads under a given set of conditions that can be used to characterize a given physiological condition or mutant muscle type. We also show that analysis of the myosin layer line intensity distribution, including derivation of the myosin head radius, Rm, may be used to study the role of the super-relaxed state in myosin regulation. When the myosin inhibitor blebbistatin is used to inhibit force production, there is a shift towards a highly quasi-helically ordered configuration that is distinct from the normal resting state, indicating there are more than one helically ordered configuration for resting crossbridges.

Synchrotron Radiation X-ray Diffraction Techniques Applied to Insect Flight Muscle

X-ray fiber diffraction is a powerful tool used for investigating the molecular structure of muscle and its dynamics during contraction. This technique has been successfully applied not only to skeletal and cardiac muscles of vertebrates but also to insect flight muscle. Generally, insect flight muscle has a highly ordered structure and is often capable of high-frequency oscillations. The X-ray diffraction studies on muscle have been accelerated by the advent of 3rd-generation synchrotron radiation facilities, which can generate brilliant and highly oriented X-ray beams. This review focuses on some of the novel experiments done on insect flight muscle by using synchrotron radiation X-rays. These include diffraction recordings from single myofibrils within a flight muscle fiber by using X-ray microbeams and high-speed diffraction recordings from the flight muscle during the wing-beat of live insects. These experiments have provided information about the molecular structure and dynamic function of flight muscle in unprecedented detail. Future directions of X-ray diffraction studies on muscle are also discussed.

Statistical mechanics of the Huxley-Simmons model

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

The cross-bridge of skeletal muscle is not synchronized either by length or force step

Force and length steps, applied to a muscle fiber in the isometric state, are believed to synchronize attached cross-bridges. This alleged synchronization facilitates the interpretation of the experiments. A rapid force step elicits an elastic response of the attached cross-bridges, followed by an isotonic phase. The decay of this second isotonic phase is of the first order. This excludes that the attached cross-bridges may decay all at the same time. The change of the X-ray interference distance during the second phase measures the stroke size only in the unrealistic case that the cross-bridges are and remain all attached. A rapid force step does not synchronize attached cross-bridges. The change of X-ray interference during the second phase does not measure the stroke size. These conclusions significantly change the picture of the mechanism of skeletal muscle contraction.

Rat-tail tendon fiber SAXS high-order diffraction peaks recovered by a superbright laboratory source and a novel restoration algorithm

The nanoscale structural order of air-dried rat-tail tendon is investigated using small-angle X-ray scattering (SAXS). SAXS fiber diffraction patterns were collected with a superbright laboratory microsource at XMI-LAB [Altamura, Lassandro, Vittoria, De Caro, Siliqi, Ladisa & Giannini (2012).J. Appl. Cryst.45, 869–873] for increasing integration times (up to 10 h) and a novel algorithm was used to estimate and subtract background, and to deconvolve the beam-divergence effects. Once the algorithm is applied, the peak visibility improves considerably and reciprocal space information up to the 22nd diffraction order is retrieved (q= 0.21 Å−1,d= 29 Å) for an 8–10 h integration time. The gain in the visibility is already significant for patterns collected for 0.5 h, at least on the more intense peaks. This demonstrates the viability of detecting structural changes on a molecular/nanoscale level in tissues with state-of-the-art laboratory sources and also the technical feasibility to adopt SAXS fiber diffraction as a future potential clinical indicator for disease.

Thick-filament strain and interfilament spacing in passive muscle: effect of titin-based passive tension

We studied the effect of titin-based passive tension on sarcomere structure by simultaneously measuring passive tension and low-angle x-ray diffraction patterns on passive fiber bundles from rabbit skinned psoas muscle. We used a stretch-hold-release protocol with measurement of x-ray diffraction patterns at various passive tension levels during the hold phase before and after passive stress relaxation. Measurements were performed in relaxing solution without and with dextran T-500 to compress the lattice toward physiological levels. The myofilament lattice spacing was measured in the A-band (d(1,0)) and Z-disk (d(Z)) regions of the sarcomere. The axial spacing of the thick-filament backbone was determined from the sixth myosin meridional reflection (M6) and the equilibrium positions of myosin heads from the fourth myosin layer line peak position and the I(1,1)/I(1,0) intensity ratio. Total passive tension was measured during the x-ray experiments, and a differential extraction technique was used to determine the relations between collagen- and titin-based passive tension and sarcomere length. Within the employed range of sarcomere lengths (∼2.2-3.4 μm), titin accounted for >80% of passive tension. X-ray results indicate that titin compresses both the A-band and Z-disk lattice spacing with viscoelastic behavior when fibers are swollen after skinning, and elastic behavior when the lattice is reduced with dextran. Titin also increases the axial thick-filament spacing, M6, in an elastic manner in both the presence and absence of dextran. No changes were detected in either I(1,1)/I(1,0) or the position of peaks on the fourth myosin layer line during passive stress relaxation. Passive tension and M6 measurements were converted to thick-filament compliance, yielding a value of ∼85 m/N, which is several-fold larger than the thick-filament compliance determined by others during the tetanic tension plateau of activated intact muscle. This difference can be explained by the fact that thick filaments are more compliant at low tension (passive muscle) than at high tension (tetanic tension). The implications of our findings are discussed.

Deduction of the single-myosin-filament transforms from partially sampled layer lines in the X-ray diffraction pattern from vertebrate striated muscle

A novel method to correct a partial sampling effect, due to the hexagonal filament array of a statistical superlattice form, on the thick (myosin)-filament-based layer lines in X-ray diffraction patterns from higher-vertebrate striated muscle has been developed using the cylindrically averaged difference Patterson function [ΔQ(r, z)]. The method involves cutting off the inter-filament vector peaks that appear in the radial region beyond ∼32 nm on the ΔQ(r, z) map calculated from the observed layer-line intensities, and then deducing the single-myosin-filament transforms by inverse Fourier transformation of the truncated ΔQ(r, z). The accuracy of the cut-off method was tested using a single-myosin-filament model and a hexagonal filament-array model with a size of one superlattice unit cell. The layer-line intensities calculated from the truncated ΔQ(r, z) of the hexagonal filament-array model showed few sampling peaks, the layer lines being effectively coincident with those from the single-filament model except for the intensities close to the meridian. Some residual differences were caused by the face-to-face inter-crossbridge vectors between closest neighboring filaments, which correspond to ∼27.5% of the total number of crossbridge vectors in the truncated ΔQ(r, z) map, but the face-to-face inter-crossbridge vectors contributed mainly to the intensities close to the meridian. Their remnant off-meridional layer-line intensity components did not significantly affect a search for the optimum azimuthal orientation of myosin crossbridges in the resting state of muscle.

Experimental approaches for solution X-ray scattering and fiber diffraction

X-ray scattering and diffraction from non-crystalline systems have gained renewed interest in recent years, as focus shifts from the structural chemistry information gained by high-resolution studies to the context of structural physiology at larger length scales. Such techniques permit the study of isolated macromolecules as well as highly organized macromolecular assemblies as a whole under near-physiological conditions. Time-resolved approaches, made possible by advanced synchrotron instrumentation, add a crucial dimension to many of these investigations. This article reviews experimental approaches in non-crystalline X-ray scattering and diffraction that may be used to illuminate important scientific questions such as protein/nucleic acid folding and structure-function relationships in large macromolecular assemblies.

Skeletal muscle performance determined by modulation of number of myosin motors rather than motor force or stroke size

Skeletal muscle can bear a high load at constant length, or shorten rapidly when the load is low. This force-velocity relationship is the primary determinant of muscle performance in vivo. Here we exploited the quasi-crystalline order of myosin II motors in muscle filaments to determine the molecular basis of this relationship by X-ray interference and mechanical measurements on intact single cells. We found that, during muscle shortening at a wide range of velocities, individual myosin motors maintain a force of about 6 pN while pulling an actin filament through a 6 nm stroke, then quickly detach when the motor reaches a critical conformation. Thus we show that the force-velocity relationship is primarily a result of a reduction in the number of motors attached to actin in each filament in proportion to the filament load. These results explain muscle performance and efficiency in terms of the molecular mechanism of the myosin motor.