Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Autoinhibition of cMyBP-C by its middle domains

Cardiac myosin binding protein-C (cMyBP-C) is a sarcomere regulatory protein consisting of 11 well-folded immunoglobulin-like (Ig-like) and fibronectin type-III domains with the individual domains numbered C0-C10. Despite progress in understanding the functions of the N' and C'-terminal ends of the protein, our understanding of the functional effects of the middle domains (C3-C4-C5-C6-C7) is still limited. Here we aimed to determine the functional significance of the middle domains by replacing endogenous cMyBP-C with recombinant proteins with and without the middle domains using our "cut and paste" SpyC3 mouse model. Specifically, we deleted domains C3-C7 or substituted these domains with unrelated Ig-like domains from titin to behave as inert "spacer" domains. Replacement with the spacer constructs resulted in a significant increase in myofilament calcium sensitivity, an almost instantaneous redevelopment of tension after a slack re-stretch protocol, and altered stretch activation responses, suggesting that the middle domains are functionally relevant and normally exert inhibitory effects on force development. We also investigated the significance of a potentially flexible linker between domains C4 and C5 and a unique 28 amino acid loop insertion in C5. Whereas deletion of the C5 loop had no effect on force, deletion of the linker between C4 and C5 had comparable effects to deletion of domains C3-C7. Taken together, these data indicate that the middle domains play an important role in limiting the activating effects of the C0-C2 domains and that the C4C5 linker contributes to these effects.

Stochastic force generation in an isometric binary mechanical system

Accurate models of muscle contraction are necessary for understanding muscle performance and the molecular modifications that enhance it (e.g., therapeutics, posttranslational modifications, etc.). As a thermal system containing millions of randomly fluctuating atoms that on the thermal scale of a muscle fiber generate unidirectional force and power output, muscle mechanics are constrained by the laws of thermodynamics. According to a thermodynamic muscle model, muscle's power stroke occurs with the shortening of an entropic spring consisting of an ensemble of force-generating myosin motor switches, each induced by actin binding and gated by inorganic phosphate release. This model differs fundamentally from conventional molecular power stroke models that assign springs to myosin motors in that it is physically impossible to describe an entropic spring in terms of the springs of its molecular constituents. A simple two-state thermodynamic model (a binary mechanical system) accurately accounts for muscle force-velocity relationships, force transients following rapid mechanical and chemical perturbations, and a thermodynamic work loop. Because this model transforms our understanding of muscle contraction, it must continue to be tested. Here, we show that a simple stochastic kinetic simulation of isometric muscle force predicts four phases of a force-generating loop that bifurcates between periodic and stochastic beating through mechanisms framed by two thermodynamic equations. We compare these model predictions with experimental data including observations of spontaneous oscillatory contractions (SPOCs) in muscles and periodic force generation in small myosin ensembles.

On the rate-limiting dynamics of force development in muscle

Skeletal muscles produce forces relatively slowly compared with the action potentials that excite them. The dynamics of force production are governed by multiple processes, such as calcium activation, cycling of cross-bridges between myofilaments, and contraction against elastic tissues and the body. These processes have been included piecemeal in some muscle models, but not integrated to reveal which are the most rate limiting. We therefore examined their integrative contributions to force development in two conventional types of muscle models: Hill-type and cross-bridge. We found that no combination of these processes can self-consistently reproduce classic data such as twitch and tetanus. Rather, additional dynamics are needed following calcium activation and facilitating cross-bridge cycling, such as for cooperative myofilament interaction and reconfiguration. We provisionally lump such processes into a simple first-order model of 'force facilitation dynamics' that integrate into a cross-bridge-type muscle model. The proposed model self-consistently reproduces force development for a range of excitations including twitch and tetanus and electromyography-to-force curves. The model's step response reveals relatively small timing contributions of calcium activation (3%), cross-bridge cycling (3%) and contraction (27%) to overall force development of human quadriceps, with the remainder (67%) explained by force facilitation. The same set of model parameters predicts the change in force magnitude (gain) and timing (phase delay) as a function of excitatory firing rate, or as a function of cyclic contraction frequency. Although experiments are necessary to reveal the dynamics of muscle, integrative models are useful for identifying the main rate-limiting processes.

Muscle short-range stiffness behaves like a maxwell element, not a spring: Implications for joint stability

INTRODUCTION

Muscles play a critical role in supporting joints during activities of daily living, owing, in part, to the phenomenon of short-range stiffness. Briefly, when an active muscle is lengthened, bound cross-bridges are stretched, yielding forces greater than what is predicted from the force length relationship. For this reason, short-range stiffness has been proposed as an attractive mechanism for providing joint stability. However, there has yet to be a forward dynamic simulation employing a cross-bridge model, that demonstrates this stabilizing role. Therefore, the purpose of this investigation was to test whether Huxley-type muscle elements, which exhibit short-range stiffness, can stabilize a joint while at constant activation.

METHODS

We analyzed the stability of an inverted pendulum (moment of inertia: 2.7 kg m2) supported by Huxley-type muscle models that reproduce the short-range stiffness phenomenon. We calculated the muscle forces that would provide sufficient short-range stiffness to stabilize the system based in minimizing the potential energy. Simulations consisted of a 50 ms long, 5 Nm square-wave perturbation, with numerical simulations carried out in ArtiSynth.

RESULTS

Despite the initial analysis predicting shared activity of antagonist and agonist muscles to maintain stable equilibrium, the inverted pendulum model was not stable, and did not maintain an upright posture even with fully activated muscles.

DISCUSSION & CONCLUSION

Our simulations suggested that short-range stiffness cannot be solely responsible for joint stability, even for modest perturbations. We argue that short-range stiffness cannot achieve stability because its dynamics do not behave like a typical spring. Instead, an alternative conceptual model for short-range stiffness is that of a Maxwell element (spring and damper in series), which can be obtained as a first-order approximation to the Huxley model. We postulate that the damping that results from short-range stiffness slows down the mechanical response and allows the central nervous system time to react and stabilize the joint. We speculate that other mechanisms, like reflexes or residual force enhancement/depression, may also play a role in joint stability. Joint stability is due to a combination of factors, and further research is needed to fully understand this complex system.

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.

Modeling thick filament activation suggests a molecular basis for force depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single, skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single-molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force after stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Elucidating Events within the Black Box of Enzyme Catalysis in Energy Metabolism: Insights into the Molecular Mechanism of ATP Hydrolysis by F1-ATPase

Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. This work presents a new theory of oxygen exchange and tests it on oxygen exchange data recorded on ATP hydrolysis by mitochondrial F1-ATPase (MF1). The apparent rate constant of oxygen exchange governing the intermediate Pi-HOH exchange accompanying ATP hydrolysis is determined by kinetic analysis over a ~50,000-fold range of substrate ATP concentration (0.1-5000 μM) and a corresponding ~200-fold range of reaction velocity (3.5-650 [moles of Pi/{moles of F1-ATPase}-1 s-1]). Isotopomer distributions of [18O]Pi species containing 0, 1, 2, and 3 labeled oxygen atoms predicted by the theory have been quantified and shown to be in perfect agreement with the experimental distributions over the entire range of medium ATP concentrations without employing adjustable parameters. A novel molecular mechanism of steady-state multisite ATP hydrolysis by the F1-ATPase has been proposed. Our results show that steady-state ATP hydrolysis by F1-ATPase occurs with all three sites occupied by Mg-nucleotide. The various implications arising from models of energy coupling in ATP synthesis/hydrolysis by the ATP synthase/F1-ATPase have been discussed. Current models of ATP hydrolysis by F1-ATPase, including those postulated from single-molecule data, are shown to be effectively bisite models that contradict the data. The trisite catalysis formulated by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis since its first appearance 25 years ago is shown to be in better accord with the experimental record. The total biochemical information on ATP hydrolysis is integrated into a consistent model by the torsional mechanism of ATP synthesis/hydrolysis and shown to elucidate the elementary chemical and mechanical events within the black box of enzyme catalysis in energy metabolism by F1-ATPase.

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.

Modeling Thick Filament Activation Suggests a Molecular Basis for Force Depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part, due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force following stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Mechanism of elastic energy storage of honey bee abdominal muscles under stress relaxation

Energy storage of passive muscles plays an important part in frequent activities of honey bee abdomens due to the muscle distribution and open circulatory system. However, the elastic energy and mechanical properties of structure in passive muscles remain unclear. In this article, stress relaxation tests on passive muscles from the terga of the honey bee abdomens were performed under different concentrations of blebbistatin and motion parameters. In stress relaxation, the load drop with the rapid and slow stages depending on stretching velocity and stretching length reflects the features of myosin-titin series structure and cross-bridge-actin cyclic connections in muscles. Then a model with 2 parallel modules based on the 2 feature structures in muscles was thus developed. The model described the stress relaxation and stretching of passive muscles from honey bee abdomen well for a good fitting in stress relaxation and verification in loading process. In addition, the stiffness change of cross-bridge under different concentrations of blebbistatin is obtained from the model. We derived the elastic deformation of cross-bridge and the partial derivatives of energy expressions on motion parameters from this model, which accorded the experimental results. This model reveals the mechanism of passive muscles from honey bee abdomens suggesting that the temporary energy storage of cross-bridge in terga muscles under abdomen bending provides potential energy for springback during the periodic abdomen bending of honey bee or other arthropod insects. The finding also provides an experimental and theoretical basis for the novel microstructure and material design of bionic muscle.

Structural OFF/ON transitions of myosin in relaxed porcine myocardium predict calcium-activated force

Contraction in striated muscle is initiated by calcium binding to troponin complexes, but it is now understood that dynamic transition of myosin between resting, ordered OFF states on thick filaments and active, disordered ON states that can bind to thin filaments is critical in regulating muscle contractility. These structural OFF to ON transitions of myosin are widely assumed to correspond to transitions from the biochemically defined, energy-sparing, super-relaxed (SRX) state to the higher ATPase disordered-relaxed (DRX) state. Here we examined the effect of 2'-deoxy-ATP (dATP), a naturally occurring energy substrate for myosin, on the structural OFF to ON transitions of myosin motors in porcine cardiac muscle thick filaments. Small-angle X-ray diffraction revealed that titrating dATP in relaxation solutions progressively moves the myosin heads from ordered OFF states on the thick filament backbone to disordered ON states closer to thin filaments. Importantly, we found that the structural OFF to ON transitions are not equivalent to the biochemically defined SRX to DRX transitions and that the dATP-induced structural OFF to ON transitions of myosin motors in relaxed muscle are strongly correlated with submaximal force augmentation by dATP. These results indicate that structural OFF to ON transitions of myosin in relaxed muscle can predict the level of force attained in calcium-activated cardiac muscle. Computational modeling and stiffness measurements suggest a final step in the OFF to ON transition may involve a subset of DRX myosins that form weakly bound cross-bridges prior to becoming active force-producing cross-bridges.

Thermodynamics and Kinetics of a Binary Mechanical System: Mechanisms of Muscle Contraction

Biological motors function at the interface of biology, physics, and chemistry, and it remains unsettled what rules from which disciplines account for how these motors work. Myosin motors are enzymes that catalyze the hydrolysis of ATP through a mechanism involving a switch-like myosin structural change (a lever arm rotation) induced by actin binding that generates a small displacement of an actin filament. In muscle, individual myosin motors are widely assumed to function as molecular machines having mechanical properties that resemble those of muscle. In a fundamental departure from this perspective, here, I show that muscle more closely resembles a heat engine with mechanical properties that emerge from the thermodynamics of a myosin motor ensemble. The transformative impact of thermodynamics on our understanding of how a heat engine works guides a parallel transformation in our understanding of how muscle works. I consider the simplest possible model of force generation: a binary mechanical system. I develop the mechanics, energetics, and kinetics of this system and show that a single binding reaction generates force when muscle is held at a fixed length and performs work when muscle is allowed to shorten. This creates a network of thermodynamic binding pathways that resembles many of the characteristic mechanical and energetic behaviors of muscle including the muscle force-velocity relationship, heat output by shortening muscle, four phases of a muscle tension transient, spontaneous oscillatory contractions, and force redevelopment. Analogous to the thermodynamic (Carnot) cycle for a heat engine, isothermal and adiabatic binding and detachment reactions create a thermodynamic cycle for muscle that resembles cardiac pressure-volume loops (i.e., how the heart works). This paper provides an outline for how to re-interpret muscle mechanic data using thermodynamics - an ongoing effort that will continue providing novel insights into how muscle and molecular motors work.

From the Matrix to the Nucleus and Back: Mechanobiology in the Light of Health, Pathologies, and Regeneration of Oral Periodontal Tissues

Among oral tissues, the periodontium is permanently subjected to mechanical forces resulting from chewing, mastication, or orthodontic appliances. Molecularly, these movements induce a series of subsequent signaling processes, which are embedded in the biological concept of cellular mechanotransduction (MT). Cell and tissue structures, ranging from the extracellular matrix (ECM) to the plasma membrane, the cytosol and the nucleus, are involved in MT. Dysregulation of the diverse, fine-tuned interaction of molecular players responsible for transmitting biophysical environmental information into the cell's inner milieu can lead to and promote serious diseases, such as periodontitis or oral squamous cell carcinoma (OSCC). Therefore, periodontal integrity and regeneration is highly dependent on the proper integration and regulation of mechanobiological signals in the context of cell behavior. Recent experimental findings have increased the understanding of classical cellular mechanosensing mechanisms by both integrating exogenic factors such as bacterial gingipain proteases and newly discovered cell-inherent functions of mechanoresponsive co-transcriptional regulators such as the Yes-associated protein 1 (YAP1) or the nuclear cytoskeleton. Regarding periodontal MT research, this review offers insights into the current trends and open aspects. Concerning oral regenerative medicine or weakening of periodontal tissue diseases, perspectives on future applications of mechanobiological principles are discussed.