X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction

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.

Identifying mechanisms and therapeutic targets in muscle using Bayesian parameter estimation with conditional variational autoencoders

Cardiomyopathies, often caused by mutations in genes encoding muscle proteins, are traditionally treated by phenotyping hearts and addressing symptoms post irreversible damage. With advancements in genotyping, early diagnosis is now possible, potentially preventing such damage. However, the intricate structure of muscle and its myriad proteins make treatment predictions challenging. Here we approach the problem of estimating therapeutic targets for a mutation in mouse muscle using a spatially explicit half sarcomere muscle model. We selected 9 rate parameters in our model linked to both small molecules and cardiomyopathy-causing mutations. We then randomly varied these rate parameters and simulated an isometric twitch for each combination to generate a large training dataset. We used this dataset to train a Conditional Variational Autoencoder (CVAE), a technique used in Bayesian parameter estimation. Given simulated or experimental isometric twitches, this machine learning model is able to then predict the set of rate parameters which are most likely to yield that result. We then predict the set of rate parameters associated with both control and the cardiac Troponin C (cTnC) I61Q variant in mouse trabeculae and and model parameters that recover the abnormal 61Q cTnC twitches.

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.

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.

Evidence for multi-scale power amplification in skeletal muscle

Many animals use a combination of skeletal muscle and elastic structures to amplify power output for fast motions. Among vertebrates, tendons in series with skeletal muscle are often implicated as the primary power-amplifying spring, but muscles contain elastic structures at all levels of organization, from the muscle tendon to the extracellular matrix to elastic proteins within sarcomeres. The present study used ex vivo muscle preparations in combination with high-speed video to quantify power output, as the product of force and velocity, at several levels of muscle organization to determine where power amplification occurs. Dynamic ramp-shortening contractions in isolated frog flexor digitorum superficialis brevis were compared with isotonic power output to identify power amplification within muscle fibers, the muscle belly, free tendon and elements external to the muscle tendon. Energy accounting revealed that artifacts from compliant structures outside of the muscle-tendon unit contributed significant peak instantaneous power. This compliance included deflection of clamped bone that stored and released energy contributing 195.22±33.19 W kg-1 (mean±s.e.m.) to the peak power output. In addition, we found that power detected from within the muscle fascicles for dynamic shortening ramps was 338.78±16.03 W kg-1, or approximately 1.75 times the maximum isotonic power output of 195.23±8.82 W kg-1. Measurements of muscle belly and muscle-tendon unit also demonstrated significant power amplification. These data suggest that intramuscular tissues, as well as bone, have the capacity to store and release energy to amplify whole-muscle power output.

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.

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 force-length relation of the young adult human tibialis anterior

Background

Knowledge of the muscle's lengths at which maximum active isometric force is attained is important for predicting forces during movement. However, there is limited information about the in vivo force-length properties of a human muscle that plays crucial roles during locomotion; the tibialis anterior (TA). We therefore aimed to estimate TA's force-length relation from dorsiflexor torque-angle curves constructed from eight women and eight men.

Methods

Participants performed maximal voluntary fixed-end contractions with their right ankle dorsiflexors from 0° to 30° plantar flexion. Muscle fascicle lengths were estimated from B-mode ultrasound images, and net ankle joint torques were measured using dynamometry. Fascicle forces were estimated by dividing maximal active torques by literature-derived, angle-specific tendon moment arm lengths while assuming a fixed 50% force contribution of TA to the total dorsiflexor force and accounting for fascicle angles.

Results

Maximal active torques were higher at 15° than 20° and 30° plantar flexion (2.4-6.4 Nm, p ≤ 0.012), whereas maximal active TA fascicle forces were higher at 15° than 0°, 20° and 30° plantar flexion (25-61 N, p ≤ 0.042), but not different between 15° and 10° plantar flexion (15 N, p = 0.277). TA fascicle shortening magnitudes during fixed-end contractions were larger at 15° than 30° plantar flexion (3.9 mm, p = 0.012), but less at 15° than 0° plantar flexion (-2.4 mm, p = 0.001), with no significant differences (≤0.7 mm, p = 0.871) between TA's superficial and deep muscle compartments. Series elastic element stiffness was lowest and highest at lengths 5% shorter and 5% longer than optimum fascicle length, respectively (-30 and 15 N/mm, p ≤ 0.003).

Discussion

TA produced its maximum active force at 10-15° plantar flexion, and its normalized force-length relation had ascending and descending limbs that agreed with a simple scaled sarcomere model when active fascicle lengths from within TA's superficial or deep muscle compartment were considered. These findings can be used to inform the properties of the contractile and series elastic elements of Hill-type muscle models.

Molecular Dynamics Assessment of Mechanical Properties of the Thin Filaments in Cardiac Muscle

Contraction of cardiac muscle is regulated by Ca2+ ions via regulatory proteins, troponin (Tn), and tropomyosin (Tpm) associated with the thin (actin) filaments in myocardial sarcomeres. The binding of Ca2+ to a Tn subunit causes mechanical and structural changes in the multiprotein regulatory complex. Recent cryo-electron microscopy (cryo-EM) models of the complex allow one to study the dynamic and mechanical properties of the complex using molecular dynamics (MD). Here we describe two refined models of the thin filament in the calcium-free state that include protein fragments unresolved by cryo-EM and reconstructed using structure prediction software. The parameters of the actin helix and the bending, longitudinal, and torsional stiffness of the filaments estimated from the MD simulations performed with these models were close to those found experimentally. However, problems revealed from the MD simulation suggest that the models require further refinement by improving the protein-protein interaction in some regions of the complex. The use of relatively long refined models of the regulatory complex of the thin filament allows one to perform MD simulation of the molecular mechanism of Ca2+ regulation of contraction without additional constraints and study the effects of cardiomyopathy-associated mutation of the thin filament proteins of cardiac muscle.

The distinctive mechanical and structural signatures of residual force enhancement in myofibers

In muscle, titin proteins connect myofilaments together and are thought to be critical for contraction, especially during residual force enhancement (RFE) when force is elevated after an active stretch. We investigated titin's function during contraction using small-angle X-ray diffraction to track structural changes before and after 50% titin cleavage and in the RFE-deficient, mdm titin mutant. We report that the RFE state is structurally distinct from pure isometric contractions, with increased thick filament strain and decreased lattice spacing, most likely caused by elevated titin-based forces. Furthermore, no RFE structural state was detected in mdm muscle. We posit that decreased lattice spacing, increased thick filament stiffness, and increased non-crossbridge forces are the major contributors to RFE. We conclude that titin directly contributes to RFE.

Effects of shortening velocity on the stiffness to force ratio during isometric force redevelopment suggest mechanisms of residual force depression

Although the phenomenon of residual force depression has been known for decades, the mechanisms remain elusive. In the present study, we investigated mechanisms of residual force depression by measuring the stiffness to force ratio during force redevelopment after shortening at different velocities. The results showed that the slope of the relationship between muscle stiffness and force decreased with decreasing shortening velocity, and the y-intercept increased with decreasing shortening velocity. The differing slopes and y-intercepts indicate that the stiffness to force ratio during isometric force redevelopment depends on the active shortening velocity at a given muscle length and activation level. The greater stiffness to force ratio after active shortening can potentially be explained by weakly-bound cross bridges in the new overlap zone. However, weakly-bound cross bridges are insufficient to explain the reduced slope at the slowest shortening velocity because the reduced velocity should increase the proportion of weakly- to strongly-bound cross bridges, thereby increasing the slope. In addition, if actin distortion caused by active shortening recovers during the force redevelopment period, then the resulting slope should be similar to the non-linear slope of force redevelopment over time. Alternatively, we suggest that a tunable elastic element, such as titin, could potentially explain the results.

Structure of the Flight Muscle Thick Filament from the Bumble Bee, Bombus ignitus, at 6 Å Resolution

Four insect orders have flight muscles that are both asynchronous and indirect; they are asynchronous in that the wingbeat frequency is decoupled from the frequency of nervous stimulation and indirect in that the muscles attach to the thoracic exoskeleton instead of directly to the wing. Flight muscle thick filaments from two orders, Hemiptera and Diptera, have been imaged at a subnanometer resolution, both of which revealed a myosin tail arrangement referred to as “curved molecular crystalline layers”. Here, we report a thick filament structure from the indirect flight muscles of a third insect order, Hymenoptera, the Asian bumble bee Bombus ignitus. The myosin tails are in general agreement with previous determinations from Lethocerus indicus and Drosophila melanogaster. The Skip 2 region has the same unusual structure as found in Lethocerus indicus thick filaments, an α-helix discontinuity is also seen at Skip 4, but the orientation of the Skip 1 region on the surface of the backbone is less angled with respect to the filament axis than in the other two species. The heads are disordered as in Drosophila, but we observe no non-myosin proteins on the backbone surface that might prohibit the ordering of myosin heads onto the thick filament backbone. There are strong structural similarities among the three species in their non-myosin proteins within the backbone that suggest how one previously unassigned density in Lethocerus might be assigned. Overall, the structure conforms to the previously observed pattern of high similarity in the myosin tail arrangement, but differences in the non-myosin proteins.

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.

Passive viscoelastic response of striated muscles

Muscle cells with sarcomeric structure exhibit highly non trivial passive mechanical response. The difficulty of its continuum modeling is due to the presence of long-range interactions transmitted by extended protein skeleton. To build a rheological model for muscle 'material', we use a stochastic micromodel, and derive a linear response theory for a half-sarcomere, which can be extended to the whole fibre. Instead of the first order rheological equation, anticipated by Hill on the phenomenological grounds, we obtain a novel second order equation which shows that tension depends not only on its current length and the velocity of stretching, but also on its acceleration. Expressing the model in terms of elementary rheological elements, we show that one contribution to the visco-elastic properties of the fibre originates in cross-bridges, while the other can be linked to inert elements which move in the sarcoplasm. We apply this model to explain the striking qualitative difference between the relaxation in experiments involving perturbation of length vs. those involving perturbation of force, and we use the values of the microscopic parameters for frog muscles to show that the model is in excellent quantitative agreement with physiological experiments.

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.

Effect of Myosin Isoforms on Cardiac Muscle Twitch of Mice, Rats and Humans

To understand how pathology-induced changes in contractile protein isoforms modulate cardiac muscle function, it is necessary to quantify the temporal-mechanical properties of contractions that occur under various conditions. Pathological responses are much easier to study in animal model systems than in humans, but extrapolation between species presents numerous challenges. Employing computational approaches can help elucidate relationships that are difficult to test experimentally by translating the observations from rats and mice, as model organisms, to the human heart. Here, we use the spatially explicit MUSICO platform to model twitch contractions from rodent and human trabeculae collected in a single laboratory. This approach allowed us to identify the variations in kinetic characteristics of α- and β-myosin isoforms across species and to quantify their effect on cardiac muscle contractile responses. The simulations showed how the twitch transient varied with the ratio of the two myosin isoforms. Particularly, the rate of tension rise was proportional to the fraction of α-myosin present, while the β-isoform dominated the rate of relaxation unless α-myosin was >50%. Moreover, both the myosin isoform and the Ca2+ transient contributed to the twitch tension transient, allowing two levels of regulation of twitch contraction.

Structural Information on Bacterial Amyloid and Amyloid-DNA Complex Obtained by Small-Angle Neutron or X-Ray Scattering

Small-angle scattering is a powerful technique to obtain structural information on biomacromolecules in aqueous solution at the sub-nanometer and nanometer length scales. It provides the sizes and overall shapes of the scattering particles. While small-angle X-ray scattering (SAXS) has often been used for structural analysis of a single-component system, small-angle neutron scattering (SANS) has been used to reveal the internal organization of a multicomponent system such as protein-protein and protein-DNA complexes. This is due to the fact that the neutron scattering length is largely different between hydrogen and deuterium, and thus it allows to make a specific component in complexes "invisible" to neutrons by changing the H₂O/D₂O ratio in the solvent with or without molecular deuteration. In this chapter, we describe a method to characterize the biomolecular structures using SANS and SAXS, in particular, focusing on fibrillar proteins such as bacterial amyloids and their complexes with nucleic acids.

Interrater Reliability among Novice Raters in the Assessment of Pelvic Floor Muscle Tone Using the Reissing Tone Scale

Purpose: The authors sought to determine the interrater reliability among novice raters of intra-vaginal manual assessment of pubococcygeus muscle tone in women using the Reissing tone scale (RTS). Method: Three graduating physiotherapy students (novice raters) and one experienced pelvic floor physiotherapist assessed 31 female participants (aged 20-66 y). Assessors gave RTS scores for pubococcygeus tone at three intra-vaginal locations (6:00, 9:00, and 3:00). Interrater reliability was determined for the novice raters using a two-way random single-measures absolute agreement intra-class correlation coefficient (ICC). Spearman rank correlation (SRC) analysis determined the correlation between the novice and expert scores. Results: The ICC values for the novice raters were 0.523, 0.274, and 0.336 at 6:00, 9:00, and 3:00, and the SRC values between the novice and expert raters were 0.580, 0.320, and 0.340. Conclusions: The novice raters demonstrated low to moderate interrater reliability for intra-vaginal manual assessment of pubococcygeus tone. This result indicates that manual assessment of pelvic floor muscle tone is not reliable enough to use as a stand-alone test to guide treatment, at least for physiotherapists with limited clinical experience.

Effect of Strain Rate on Single Tau, Dimerized Tau and Tau-Microtubule Interface: A Molecular Dynamics Simulation Study

Microtubule-associated protein (MAP) tau is a cross-linking molecule that provides structural stability to axonal microtubules (MT). It is considered a potential biomarker for Alzheimer's disease (AD), dementia, and other neurological disorders. It is also a signature protein for Traumatic Brain Injury (TBI) assessment. In the case of TBI, extreme dynamic mechanical energies can be felt by the axonal cytoskeletal members. As such, fundamental understandings of the responses of single tau protein, polymerized tau protein, and tau-microtubule interfaces under high-rate mechanical forces are important. This study attempts to determine the high-strain rate mechanical behavior of single tau, dimerized tau, and tau-MT interface using molecular dynamics (MD) simulation. The results show that a single tau protein is a highly stretchable soft polymer. During deformation, first, it significantly unfolds against van der Waals and electrostatic bonds. Then it stretches against strong covalent bonds. We found that tau acts as a viscoelastic material, and its stiffness increases with the strain rate. The unfolding stiffness can be ~50-500 MPa, while pure stretching stiffness can be >2 GPa. The dimerized tau model exhibits similar behavior under similar strain rates, and tau sliding from another tau is not observed until it is stretched to >7 times of original length, depending on the strain rate. The tau-MT interface simulations show that very high strain and strain rates are required to separate tau from MT suggesting Tau-MT bonding is stronger than MT subunit bonding between themselves. The dimerized tau-MT interface simulations suggest that tau-tau bonding is stronger than tau-MT bonding. In summary, this study focuses on the structural response of individual cytoskeletal components, namely microtubule (MT) and tau protein. Furthermore, we consider not only the individual response of a component, but also their interaction with each other (such as tau with tau or tau with MT). This study will eventually pave the way to build a bottom-up multiscale brain model and analyze TBI more comprehensively.

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

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

Myosin cross-bridge kinetics slow at longer muscle lengths during isometric contractions in intact soleus from mice

Muscle contraction results from force-generating cross-bridge interactions between myosin and actin. Cross-bridge cycling kinetics underlie fundamental contractile properties, such as active force production and energy utilization. Factors that influence cross-bridge kinetics at the molecular level propagate through the sarcomeres, cells and tissue to modulate whole-muscle function. Conversely, movement and changes in the muscle length can influence cross-bridge kinetics on the molecular level. Reduced, single-molecule and single-fibre experiments have shown that increasing the strain on cross-bridges may slow their cycling rate and prolong their attachment duration. However, whether these strain-dependent cycling mechanisms persist in the intact muscle tissue, which encompasses more complex organization and passive elements, remains unclear. To investigate this multi-scale relationship, we adapted traditional step-stretch protocols for use with mouse soleus muscle during isometric tetanic contractions, enabling novel estimates of length-dependent cross-bridge kinetics in the intact skeletal muscle. Compared to rates at the optimal muscle length (L_o), we found that cross-bridge detachment rates increased by approximately 20% at 90% of L_o (shorter) and decreased by approximately 20% at 110% of L_o (longer). These data indicate that cross-bridge kinetics vary with whole-muscle length during intact, isometric contraction, which could intrinsically modulate force generation and energetics, and suggests a multi-scale feedback pathway between whole-muscle function and cross-bridge activity.

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.

Pathogenic variants in TNNC2 cause congenital myopathy due to an impaired force response to calcium

Troponin C (TnC) is a critical regulator of skeletal muscle contraction; it binds Ca2+ to activate muscle contraction. Surprisingly, the gene encoding fast skeletal TnC (TNNC2) has not yet been implicated in muscle disease. Here, we report 2 families with pathogenic variants in TNNC2. Patients present with a distinct, dominantly inherited congenital muscle disease. Molecular dynamics simulations suggested that the pathomechanisms by which the variants cause muscle disease include disruption of the binding sites for Ca2+ and for troponin I. In line with these findings, physiological studies in myofibers isolated from patients' biopsies revealed a markedly reduced force response of the sarcomeres to [Ca2+]. This pathomechanism was further confirmed in experiments in which contractile dysfunction was evoked by replacing TnC in myofibers from healthy control subjects with recombinant, mutant TnC. Conversely, the contractile dysfunction of myofibers from patients was repaired by replacing endogenous, mutant TnC with recombinant, wild-type TnC. Finally, we tested the therapeutic potential of the fast skeletal muscle troponin activator tirasemtiv in patients' myofibers and showed that the contractile dysfunction was repaired. Thus, our data reveal that pathogenic variants in TNNC2 cause congenital muscle disease, and they provide therapeutic angles to repair muscle contractility.

The myosin II coiled-coil domain atomic structure in its native environment

The atomic structure of the complete myosin tail within thick filaments isolated from Lethocerus indicus flight muscle is described and compared to crystal structures of recombinant, human cardiac myosin tail segments. Overall, the agreement is good with three exceptions: the proximal S2, in which the filament has heads attached but the crystal structure doesn't, and skip regions 2 and 4. At the head-tail junction, the tail α-helices are asymmetrically structured encompassing well-defined unfolding of 12 residues for one myosin tail, ∼4 residues of the other, and different degrees of α-helix unwinding for both tail α-helices, thereby providing an atomic resolution description of coiled-coil "uncoiling" at the head-tail junction. Asymmetry is observed in the nonhelical C termini; one C-terminal segment is intercalated between ribbons of myosin tails, the other apparently terminating at Skip 4 of another myosin tail. Between skip residues, crystal and filament structures agree well. Skips 1 and 3 also agree well and show the expected α-helix unwinding and coiled-coil untwisting in response to skip residue insertion. Skips 2 and 4 are different. Skip 2 is accommodated in an unusual manner through an increase in α-helix radius and corresponding reduction in rise/residue. Skip 4 remains helical in one chain, with the other chain unfolded, apparently influenced by the acidic myosin C terminus. The atomic model may shed some light on thick filament mechanosensing and is a step in understanding the complex roles that thick filaments of all species undergo during muscle contraction.

Power Amplification Increases With Contraction Velocity During Stretch-Shortening Cycles of Skinned Muscle Fibers

Muscle force, work, and power output during concentric contractions (active muscle shortening) are increased immediately following an eccentric contraction (active muscle lengthening). This increase in performance is known as the stretch-shortening cycle (SSC)-effect. Recent findings demonstrate that the SSC-effect is present in the sarcomere itself. More recently, it has been suggested that cross-bridge (XB) kinetics and non-cross-bridge (non-XB) structures (e.g., titin and nebulin) contribute to the SSC-effect. As XBs and non-XB structures are characterized by a velocity dependence, we investigated the impact of stretch-shortening velocity on the SSC-effect. Accordingly, we performed in vitro isovelocity ramp experiments with varying ramp velocities (30, 60, and 85% of maximum contraction velocity for both stretch and shortening) and constant stretch-shortening magnitudes (17% of the optimum sarcomere length) using single skinned fibers of rat soleus muscles. The different contributions of XB and non-XB structures to force production were identified using the XB-inhibitor Blebbistatin. We show that (i) the SSC-effect is velocity-dependent-since the power output increases with increasing SSC-velocity. (ii) The energy recovery (ratio of elastic energy storage and release in the SSC) is higher in the Blebbistatin condition compared with the control condition. The stored and released energy in the Blebbistatin condition can be explained by the viscoelastic properties of the non-XB structure titin. Consequently, our experimental findings suggest that the energy stored in titin during the eccentric phase contributes to the SSC-effect in a velocity-dependent manner.

Mechanical behavior of actin and spectrin subjected to high strain rate: A molecular dynamics simulation study

Recent nanoscopy and super-resolution microscopy studies have substantiated the structural contribution of periodic actin-spectrin lattice to the axonal cytoskeleton of neuron. However, sufficient mechanical insight is not present for spectrin and actin-spectrin network, especially in high strain rate scenario. To quantify the mechanical behavior of actin-spectrin cytoskeleton in such conditions, this study determines individual stretching characteristics of actin and spectrin at high strain rate by molecular dynamics (MD) simulation. The actin-spectrin separation criteria are also determined. It is found that both actin and spectrin have high stiffness when susceptible to high strain rate and show strong dependence on applied strain rate. The stretching stiffness of actin and forced unfolding mechanism of spectrin are in harmony with the current literature. Actin-spectrin model provides novel insight into their interaction and separation stretch. It is shown that the region vulnerable to failure is the actin-spectrin interface at lower strain rate, while it is the inter-repeat region of spectrin at higher strain rate.

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.

Phosphate has dual roles in cross-bridge kinetics in rabbit psoas single myofibrils

In this study, we aimed to study the role of inorganic phosphate (P_i) in the production of oscillatory work and cross-bridge (CB) kinetics of striated muscle. We applied small-amplitude sinusoidal length oscillations to rabbit psoas single myofibrils and muscle fibers, and the resulting force responses were analyzed during maximal Ca²⁺ activation (pCa 4.65) at 15°C. Three exponential processes, A, B, and C, were identified from the tension transients, which were studied as functions of P_i concentration ([P_i]). In myofibrils, we found that process C, corresponding to phase 2 of step analysis during isometric contraction, is almost a perfect single exponential function compared with skinned fibers, which exhibit distributed rate constants, as described previously. The [P_i] dependence of the apparent rate constants 2πb and 2πc, and that of isometric tension, was studied to characterize the force generation and P_i release steps in the CB cycle, as well as the inhibitory effect of P_i. In contrast to skinned fibers, P_i does not accumulate in the core of myofibrils, allowing sinusoidal analysis to be performed nearly at [P_i] = 0. Process B disappeared as [P_i] approached 0 mM in myofibrils, indicating the significance of the role of P_i rebinding to CBs in the production of oscillatory work (process B). Our results also suggest that P_i competitively inhibits ATP binding to CBs, with an inhibitory dissociation constant of ∼2.6 mM. Finally, we found that the sinusoidal waveform of tension is mostly distorted by second harmonics and that this distortion is closely correlated with production of oscillatory work, indicating that the mechanism of generating force is intrinsically nonlinear. A nonlinear force generation mechanism suggests that the length-dependent intrinsic rate constant is asymmetric upon stretch and release and that there may be a ratchet mechanism involved in the CB cycle.

The effect of variable troponin C mutation thin filament incorporation on cardiac muscle twitch contractions

One of the complexities of understanding the pathology of familial forms of cardiac diseases is the level of mutation incorporation in sarcomeres. Computational models of the sarcomere that are spatially explicit offer an approach to study aspects of mutational incorporation into myofilaments that are more challenging to get at experimentally. We studied two well characterized mutations of cardiac TnC, L48Q and I61Q, that decrease or increase the release rate of Ca²⁺ from cTnC, k_-Ca, resulting in HCM and DCM respectively [1]. Expression of these mutations in transgenic mice was used to provide experimental data for incorporation of 30 and 50% (respectively) into sarcomeres. Here we demonstrate that fixed length twitch contractions of trabeculae from mice containing mutant differ from WT; L48Q trabeculae have slower relaxation while I61Q trabeculae have markedly reduced peak tension. Using our multiscale modelling approach [2] we were able to describe the tension transients of WT mouse myocardium. Tension transients for the mutant cTnCs were simulated with changes in k_-Ca, measured experimentally for each cTnC mutant in whole troponin complex, a change in the affinity of cTnC for cTnI, and a reduction in the number of detached crossbridges available for binding. A major advantage of the multiscale explicit 3-D model is that it predicts the effects of variable mutation incorporation, and the effects of variations in mutation distribution within thin filaments in sarcomeres. Such effects are currently impossible to explore experimentally. We explored random and clustered distributions of mutant cTnCs in thin filaments, as well as distributions of individual thin filaments with only WT or mutant cTnCs present. The effects of variable amounts of incorporation and non-random distribution of mutant cTnCs are more marked for I61Q than L48Q cTnC. We conclude that this approach can be effective for study on mutations in multiple proteins of the sarcomere. SUMMARY: A challenge in experimental studies of diseases is accounting for the effect of variable mutation incorporation into myofilaments. Here we use a spatially explicit computational approach, informed by experimental data from transgenic mice expressing one of two mutations in cardiac Troponin C that increase or decrease calcium sensitivity. We demonstrate that the model can accurately describe twitch contractions for the data and go on to explore the effect of variable mutant incorporation and localization on simulated cardiac muscle twitches.

Evidence for Muscle Cell-Based Mechanisms of Enhanced Performance in Stretch-Shortening Cycle in Skeletal Muscle

Force attained during concentric contraction (active shortening) is transiently enhanced following eccentric contraction (active stretch) in skeletal muscle. This phenomenon is called stretch-shortening cycle (SSC) effect. Since many human movements contain combinations of eccentric and concentric contractions, a better understanding of the mechanisms underlying the SSC effect would be useful for improving physical performance, optimizing human movement efficiency, and providing an understanding of fundamental mechanism of muscle force control. Currently, the most common mechanisms proposed for the SSC effect are (i) stretch-reflex activation and (ii) storage of energy in tendons. However, abundant SSC effects have been observed in single fiber preparations where stretch-reflex activation is eliminated and storage of energy in tendons is minimal at best. Therefore, it seems prudent to hypothesize that factor(s) other than stretch-reflex activation and energy storage in tendons contribute to the SSC effect. In this brief review, we focus on possible candidate mechanisms for the SSC effect, that is, pre-activation, cross-bridge kinetics, and residual force enhancement (RFE) obtained in experimental preparations that exclude/control the influence of stretch-reflex activation and energy storage in tendons. Recent evidence supports the contribution of these factors to the mechanism of SSCs, and suggests that the extent of their contribution varies depending on the contractile conditions. Evidence for and against alternative mechanisms are introduced and discussed, and unresolved problems are mentioned for inspiring future studies in this field of research.

The Transient Mechanics of Muscle Require Only a Single Force-Producing Cross-Bridge State and a 100 Å Working Stroke

Simple Summary

With modern increased computational power, newly developed computer programs can be used to simulate how muscle contracts. Here, we created, in silico, a “virtual” muscle that includes modelled myosin cross-bridges, and, using statistical mechanical methods, we calculated the macroscopic response of the muscle during contraction and as a result of applied transients. Good fits to many experimental observations were obtained with this simple model with one attached force-producing state and using a single cross-bridge step size of 100 Å.

Abstract

An informative probe of myosin cross-bridge behaviour in active muscle is a mechanical transient experiment where, for example, a fully active muscle initially held at constant length is suddenly shortened to a new fixed length, providing a force transient, or has its load suddenly reduced, providing a length transient. We describe the simplest cross-bridge mechanical cycle we could find to model these transients. We show using the statistical mechanics of 50,000 cross-bridges that a simple cycle with two actin-attached cross-bridge states, one producing no force and the other producing force, will explain much of what has been observed experimentally, and we discuss the implications of this modelling for our understanding of how muscle works. We show that this same simple model will explain, reasonably well, the isotonic mechanical and X-ray transients under different loads observed by Reconditi et al. (2004, Nature 428, 578) and that there is no need to invoke different cross-bridge step sizes under these different conditions; a step size of 100 Å works well for all loads. We do not claim that this model provides a total mechanical explanation of how muscle works. However, we do suggest that only if there are other observations that cannot be explained by this simple model should something more complicated be considered.

Mechanical contribution to muscle thin filament activation

Vertebrate striated muscle thin filaments are thought to be thermodynamically activated in response to an increase in Ca²⁺ concentration. We tested this hypothesis by measuring time intervals for gliding runs and pauses of individual skeletal muscle thin filaments in cycling myosin motility assays. A classic thermodynamic mechanism predicts that if chemical potential is constant, transitions between runs and pauses of gliding thin filaments will occur at constant rate as given by a Poisson distribution. In this scenario, rate is given by the odds of a pause, and hence, run times between pauses fit an exponential distribution that slopes negatively for all observable run times. However, we determined that relative density of observed run times fits an exponential only at low Ca²⁺ levels that activate filament gliding. Further titration with Ca²⁺, or adding excess regulatory proteins tropomyosin and troponin, shifted the relative density of short run times to fit the positive slope of a gamma distribution, which derives from waiting times between Poisson events. Events that arise during a run and prevent the chance of ending a run for a random interval of time account for the observed run time distributions, suggesting that the events originate with cycling myosin. We propose that regulatory proteins of the thin filament require the mechanical force of cycling myosin to achieve the transition state for activation. During activation, combinations of cycling myosin that contribute insufficient activation energy delay deactivation.

In vivo X-ray diffraction and simultaneous EMG reveal the time course of myofilament lattice dilation and filament stretch

Muscle function within an organism depends on the feedback between molecular and meter-scale processes. Although the motions of muscle's contractile machinery are well described in isolated preparations, only a handful of experiments have documented the kinematics of the lattice occurring when multi-scale interactions are fully intact. We used time-resolved X-ray diffraction to record the kinematics of the myofilament lattice within a normal operating context: the tethered flight of Manduca sexta As the primary flight muscles of M.sexta are synchronous, we used these results to reveal the timing of in vivo cross-bridge recruitment, which occurred 24 ms (s.d. 26) following activation. In addition, the thick filaments stretched an average of 0.75% (s.d. 0.32) and thin filaments stretched 1.11% (s.d. 0.65). In contrast to other in vivo preparations, lattice spacing changed an average of 2.72% (s.d. 1.47). Lattice dilation of this magnitude significantly affects shortening velocity and force generation, and filament stretching tunes force generation. While the kinematics were consistent within individual trials, there was extensive variation between trials. Using a mechanism-free machine learning model we searched for patterns within and across trials. Although lattice kinematics were predictable within trials, the model could not create predictions across trials. This indicates that the variability we see across trials may be explained by latent variables occurring in this naturally functioning system. The diverse kinematic combinations we documented mirror muscle's adaptability and may facilitate its robust function in unpredictable conditions.

Cross-Bridges and Sarcomeric Non-cross-bridge Structures Contribute to Increased Work in Stretch-Shortening Cycles

Stretch-shortening cycles (SSCs) refer to the muscle action when an active muscle stretch is immediately followed by active muscle shortening. This combination of eccentric and concentric contractions is the most important type of daily muscle action and plays a significant role in natural locomotion such as walking, running or jumping. SSCs are used in human and animal movements especially when a high movement speed or economy is required. A key feature of SSCs is the increase in muscular force and work during the concentric phase of a SSC by more than 50% compared with concentric muscle actions without prior stretch (SSC-effect). This improved muscle capability is related to various mechanisms, including pre-activation, stretch-reflex responses and elastic recoil from serial elastic tissues. Moreover, it is assumed that a significant contribution to enhanced muscle capability lies in the sarcomeres itself. Thus, we investigated the force output and work produced by single skinned fibers of rat soleus muscles during and after ramp contractions at a constant velocity. Shortening, lengthening, and SSCs were performed under physiological boundary conditions with 85% of the maximum shortening velocity and stretch-shortening magnitudes of 18% of the optimum muscle length. The different contributions of cross-bridge (XB) and non-cross-bridge (non-XB) structures to the total muscle force were identified by using Blebbistatin. The experiments revealed three main results: (i) partial detachment of XBs during the eccentric phase of a SSC, (ii) significantly enhanced forces and mechanical work during the concentric phase of SSCs compared with shortening contractions with and without XB-inhibition, and (iii) no residual force depression after SSCs. The results obtained by administering Blebbistatin propose a titin-actin interaction that depends on XB-binding or active XB-based force production. The findings of this study further suggest that enhanced forces generated during the active lengthening phase of SSCs persist during the subsequent shortening phase, thereby contributing to enhanced work. Accordingly, our data support the hypothesis that sarcomeric mechanisms related to residual force enhancement also contribute to the SSC-effect. The preload of the titin molecule, acting as molecular spring, might be part of that mechanism by increasing the mechanical efficiency of work during physiological SSCs.

Triggering typical nemaline myopathy with compound heterozygous nebulin mutations reveals myofilament structural changes as pathomechanism

Nebulin is a giant protein that winds around the actin filaments in the skeletal muscle sarcomere. Compound-heterozygous mutations in the nebulin gene (NEB) cause typical nemaline myopathy (NM), a muscle disorder characterized by muscle weakness with limited treatment options. We created a mouse model with a missense mutation p.Ser6366Ile and a deletion of NEB exon 55, the Compound-Het model that resembles typical NM. We show that Compound-Het mice are growth-retarded and have muscle weakness. Muscles have a reduced myofibrillar fractional-area and sarcomeres are disorganized, contain rod bodies, and have longer thin filaments. In contrast to nebulin-based severe NM where haplo-insufficiency is the disease driver, Compound-Het mice express normal amounts of nebulin. X-ray diffraction revealed that the actin filament is twisted with a larger radius, that tropomyosin and troponin behavior is altered, and that the myofilament spacing is increased. The unique disease mechanism of nebulin-based typical NM reveals novel therapeutic targets.

Nebulin-based nemaline myopathy is a heterogenous disease with unclear pathological mechanisms. Here, the authors generate a mouse model that mimics the most common genetic cause of the disease and demonstrate that muscle weakness in this model is associated with twisted actin filaments and altered tropomyosin and troponin behaviour.

Straightening Out the Elasticity of Myosin Cross-Bridges

In a contracting muscle, myosin cross-bridges extending from thick filaments pull the interdigitating thin (actin-containing) filaments during cyclical ATP-driven interactions toward the center of the sarcomere, the structural unit of striated muscle. Cross-bridge attachments in the sarcomere have been reported to exhibit a similar stiffness under both positive and negative forces. However, in vitro measurements on filaments with a sparse complement of heads detected a decrease of the cross-bridge stiffness at negative forces attributed to the buckling of the subfragment 2 tail portion. Here, we review some old and new data that confirm that cross-bridge stiffness is nearly linear in the muscle filament lattice. The implications of high myosin stiffness at positive and negative strains are considered in muscle fibers and in nonmuscle intracellular cargo transport.

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.

Estimation of Forces on Actin Filaments in Living Muscle from X-ray Diffraction Patterns and Mechanical Data

Many biological processes are triggered or driven by mechanical forces in the cytoskeletal network, but these transducing forces have rarely been assessed. Striated muscle, with its well-organized structure provides an opportunity to assess intracellular forces using small-angle X-ray fiber diffraction. We present a new methodology using Monte Carlo simulations of muscle contraction in an explicit 3D sarcomere lattice to predict the fiber deformations and length changes along thin filaments during contraction. Comparison of predicted diffraction patterns to experimental meridional X-ray reflection profiles allows assessment of the stepwise changes in intermonomer spacings and forces in the myofilaments within living muscle cells. These changes along the filament length reflect the effect of forces from randomly attached crossbridges. This approach enables correlation of the molecular events, such as the current number of attached crossbridges and the distributions of crossbridge forces to macroscopic measurements of force and length changes during muscle contraction. In addition, assessments of fluctuations in local forces in the myofilaments may reveal how variations in the filament forces acting on signaling proteins in the sarcomere M-bands and Z-discs modulate gene expression, protein synthesis and degradation, and as well to mechanisms of adaptation of muscle in response to changes in mechanical loading.

Special Issue: The Actin-Myosin Interaction in Muscle: Background and Overview

Muscular contraction is a fundamental phenomenon in all animals; without it life as we know it would be impossible. The basic mechanism in muscle, including heart muscle, involves the interaction of the protein filaments myosin and actin. Motility in all cells is also partly based on similar interactions of actin filaments with non-muscle myosins. Early studies of muscle contraction have informed later studies of these cellular actin-myosin systems. In muscles, projections on the myosin filaments, the so-called myosin heads or cross-bridges, interact with the nearby actin filaments and, in a mechanism powered by ATP-hydrolysis, they move the actin filaments past them in a kind of cyclic rowing action to produce the macroscopic muscular movements of which we are all aware. In this special issue the papers and reviews address different aspects of the actin-myosin interaction in muscle as studied by a plethora of complementary techniques. The present overview provides a brief and elementary introduction to muscle structure and function and the techniques used to study it. It goes on to give more detailed descriptions of what is known about muscle components and the cross-bridge cycle using structural biology techniques, particularly protein crystallography, electron microscopy and X-ray diffraction. It then has a quick look at muscle mechanics and it summarises what can be learnt about how muscle works based on the other studies covered in the different papers in the special issue. A picture emerges of the main molecular steps involved in the force-producing process; steps that are also likely to be seen in non-muscle myosin interactions with cellular actin filaments. Finally, the remarkable advances made in studying the effects of mutations in the contractile assembly in causing specific muscle diseases, particularly those in heart muscle, are outlined and discussed.

Myosin Cross-Bridge Behaviour in Contracting Muscle-The T1 Curve of Huxley and Simmons (1971) Revisited

The stiffness of the myosin cross-bridges is a key factor in analysing possible scenarios to explain myosin head changes during force generation in active muscles. The seminal study of Huxley and Simmons (1971: Nature233: 533) suggested that most of the observed half-sarcomere instantaneous compliance (=1/stiffness) resides in the myosin heads. They showed with a so-called T₁ plot that, after a very fast release, the half-sarcomere tension reduced to zero after a step size of about 60Å (later with improved experiments reduced to 40Å). However, later X-ray diffraction studies showed that myosin and actin filaments themselves stretch slightly under tension, which means that most (at least two-thirds) of the half sarcomere compliance comes from the filaments and not from cross-bridges. Here we have used a different approach, namely to model the compliances in a virtual half sarcomere structure in silico. We confirm that the T₁ curve comes almost entirely from length changes in the myosin and actin filaments, because the calculated cross-bridge stiffness (probably greater than 0.4 pN/Å) is higher than previous studies have suggested. Our model demonstrates that the formulations produced by previous authors give very similar results to our model if the same starting parameters are used. However, we find that it is necessary to model the X-ray diffraction data as well as mechanics data to get a reliable estimate of the cross-bridge stiffness. In the light of the high cross-bridge stiffness found in the present study, we present a plausible modified scenario to describe aspects of the myosin cross-bridge cycle in active muscle. In particular, we suggest that, apart from the filament compliances, most of the cross-bridge contribution to the instantaneous T₁ response may come from weakly-bound myosin heads, not myosin heads in strongly attached states. The strongly attached heads would still contribute to the T₁ curve, but only in a very minor way, with a stiffness that we postulate could be around 0.1 pN/Å, a value which would generate a working stroke close to 100 Å from the hydrolysis of one ATP molecule. The new model can serve as a tool to calculate sarcomere elastic properties for any vertebrate striated muscle once various parameters have been determined (e.g., tension, T₁ intercept, temperature, X-ray diffraction spacing results).

X-ray Diffraction of Intact Murine Skeletal Muscle as a Tool for Studying the Structural Basis of Muscle Disease

Transgenic mouse models have been important tools for studying the relationship of genotype to phenotype for human diseases including those of skeletal muscle. Mouse skeletal muscle has been shown to produce high quality X-ray diffraction patterns on third generation synchrotron beamlines providing an opportunity to link changes at the level of the genotype to functional phenotypes in health and disease by determining the structural consequences of genetic changes. We present detailed protocols for preparation of specimens, collecting the X-ray patterns and extracting relevant structural parameters from the X-ray patterns that may help guide experimenters wishing to perform such experiments for themselves.

Calcium-dependent titin-thin filament interactions in muscle: observations and theory

Gaps in our understanding of muscle mechanics demonstrate that the current model is incomplete. Increasingly, it appears that a role for titin in active muscle contraction might help to fill these gaps. While such a role for titin is increasingly accepted, the underlying molecular mechanisms remain unclear. The goals of this paper are to review recent studies demonstrating Ca²⁺-dependent interactions between N2A titin and actin in vitro, to explore theoretical predictions of muscle behavior based on this interaction, and to review experimental data related to the predictions. In a recent study, we demonstrated that Ca²⁺ increases the association constant between N2A titin and F-actin; that Ca²⁺ increases rupture forces between N2A titin and F-actin; and that Ca²⁺ and N2A titin reduce sliding velocity of F-actin and reconstituted thin filaments in motility assays. Preliminary data support a role for Ig83, but other Ig domains in the N2A region may also be involved. Two mechanical consequences are inescapable if N2A titin binds to thin filaments in active muscle sarcomeres: (1) the length of titin's freely extensible I-band should decrease upon muscle activation; and (2) binding between N2A titin and thin filaments should increase titin stiffness in active muscle. Experimental observations demonstrate that these properties characterize wild type muscles, but not muscles from mdm mice with a small deletion in N2A titin, including part of Ig83. Given the new in vitro evidence for Ca²⁺-dependent binding between N2A titin and actin, it is time for skepticism to give way to further investigation.

Changes in the crystallographic structures of cardiac myosin filaments detected by polarization-dependent second harmonic generation microscopy

Detecting the structural changes caused by volume and pressure overload is critical to comprehending the mechanisms of physiologic and pathologic hypertrophy. This study explores the structural changes at the crystallographic level in myosin filaments in volume- and pressure-overloaded myocardia through polarization-dependent second harmonic generation microscopy. Here, for the first time, we report that the ratio of nonlinear susceptibility tensor components d₃₃/d₁₅ increased significantly in volume- and pressure-overloaded myocardial tissues compared with the ratio in normal mouse myocardial tissues. Through cell stretch experiments, we demonstrated that mechanical tension plays an important role in the increase of d₃₃/d₁₅ in volume- and pressure-overloaded myocardial tissues.

Synchrotron radiation X-ray diffraction studies on muscle: past, present, and future

X-ray diffraction is a technique to study the structure of materials at spatial resolutions up to an atomic scale. In the field of life science, the X-ray diffraction technique is especially suited to study materials having periodical structures, such as protein crystals, nucleic acids, and muscle. Among others, muscle is a dynamic structure and the molecular events occurring during muscle contraction have been the main interest among muscle researchers. In early days, the laboratory X-ray generators were unable to deliver X-ray flux strong enough to resolve the dynamic molecular events in muscle. This situation has dramatically been changed by the advent of intense synchrotron radiation X-rays and advanced detectors, and today X-ray diffraction patterns can be recorded from muscle at sub-millisecond time resolutions. In this review, we shed light mainly on the technical aspects of the history and the current status of the X-ray diffraction studies on muscle and discuss what will be made possible for muscle studies by the advance of new techniques.

Actin-binding domains mediate the distinct distribution of two Dictyostelium Talins through different affinities to specific subsets of actin filaments during directed cell migration

Although the distinct distribution of certain molecules along the anterior or posterior edge is essential for directed cell migration, the mechanisms to maintain asymmetric protein localization have not yet been fully elucidated. Here, we studied a mechanism for the distinct localizations of two Dictyostelium talin homologues, talin A and talin B, both of which play important roles in cell migration and adhesion. Using GFP fusion, we found that talin B, as well as its C-terminal actin-binding region, which consists of an I/LWEQ domain and a villin headpiece domain, was restricted to the leading edge of migrating cells. This is in sharp contrast to talin A and its C-terminal actin-binding domain, which co-localized with myosin II along the cell posterior cortex, as reported previously. Intriguingly, even in myosin II-null cells, talin A and its actin-binding domain displayed a specific distribution, co-localizing with stretched actin filaments. In contrast, talin B was excluded from regions rich in stretched actin filaments, although a certain amount of its actin-binding region alone was present in those areas. When cells were sucked by a micro-pipette, talin B was not detected in the retracting aspirated lobe where acto-myosin, talin A, and the actin-binding regions of talin A and talin B accumulated. Based on these results, we suggest that talin A predominantly interacts with actin filaments stretched by myosin II through its C-terminal actin-binding region, while the actin-binding region of talin B does not make such distinctions. Furthermore, talin B appears to have an additional, unidentified mechanism that excludes it from the region rich in stretched actin filaments. We propose that these actin-binding properties play important roles in the anterior and posterior enrichment of talin B and talin A, respectively, during directed cell migration.

Insights into Actin-Myosin Interactions within Muscle from 3D Electron Microscopy

Much has been learned about the interaction between myosin and actin through biochemistry, in vitro motility assays and cryo-electron microscopy (cryoEM) of F-actin, decorated with myosin heads. Comparatively less is known about actin-myosin interactions within the filament lattice of muscle, where myosin heads function as independent force generators and thus most measurements report an average signal from multiple biochemical and mechanical states. All of the 3D imaging by electron microscopy (EM) that has revealed the interplay of the regular array of actin subunits and myosin heads within the filament lattice has been accomplished using the flight muscle of the large water bug Lethocerus sp. The Lethocerus flight muscle possesses a particularly favorable filament arrangement that enables all the myosin cross-bridges contacting the actin filament to be visualized in a thin section. This review covers the history of this effort and the progress toward visualizing the complex set of conformational changes that myosin heads make when binding to actin in several static states, as well as the fast frozen actively contracting muscle. The efforts have revealed a consistent pattern of changes to the myosin head structures as determined by X-ray crystallography needed to explain the structure of the different actomyosin interactions observed in situ.

Nebulin and titin modulate cross-bridge cycling and length-dependent calcium sensitivity

Various mutations in the structural proteins nebulin and titin that are present in human disease are known to affect the contractility of striated muscle. Loss of nebulin is associated with reduced actin filament length and impairment of myosin binding to actin, whereas titin is thought to regulate muscle passive elasticity and is likely involved in length-dependent activation. Here, we sought to assess the modulation of muscle function by these sarcomeric proteins by using the computational platform muscle simulation code (MUSICO) to quantitatively separate the effects of structural changes, kinetics of cross-bridge cycling, and calcium sensitivity of the thin filaments. The simulations show that variation in thin filament length cannot by itself account for experimental observations of the contractility in nebulin-deficient muscle, but instead must be accompanied by a decreased myosin binding rate. Additionally, to match the observed calcium sensitivity, the rate of TnI detachment from actin needed to be increased. Simulations for cardiac muscle provided quantitative estimates of the effects of different titin-based passive elasticities on muscle force and activation in response to changes in sarcomere length and interfilament lattice spacing. Predicted force-pCa relations showed a decrease in both active tension and sensitivity to calcium with a decrease in passive tension and sarcomere length. We conclude that this behavior is caused by partial redistribution of the muscle load between active muscle force and titin-dependent passive force, and also by redistribution of stretch along the thin filament, which together modulate the release of TnI from actin. These data help advance understanding of how nebulin and titin mutations affect muscle function.