Poorly understood aspects of striated muscle contraction

Hole behavior captured by analysis of instantaneous amplitude and phase of sarcosynced oscillations reveals wave characteristics of sarcomeric oscillations

In this study, we performed signal analysis based on instantaneous amplitude and phase of sarcomeric oscillations, which are generated by skeletal muscle under constant calcium concentration conditions and in which sarcomeres repeatedly contract and relax autonomously. In addition to the changes in sarcomere length that have been attracting attention, we named the Z-line oscillations that partition sarcomeres sarcosynced oscillations, and analyzed their instantaneous amplitude and phase. As a result, the behavior of pairs of sarcosynced oscillations and sarcomeric oscillations, which are produced when propagating waves propagate in one direction or collide, was clearly visualized. By focusing on the behavior of the hole, which is a dip in the instantaneous amplitude accompanied by a sudden jump in the instantaneous phase in sarcosynced oscillations, we were able to discern the wave characteristics. Transient disruption occurred in the propagating waves even when they traveled in one direction. Its properties were captured by the sarcomeric defect hole (SD hole), a dip in the instantaneous amplitude accompanied by a jump in the instantaneous phase in sarcosynced oscillations. When propagating waves collide, the collision site, its persistence, movement, and disappearance process are captured as sarcomeric collision holes (SC holes) of sarcosynced oscillations. These holes are important indicators for understanding the oscillation properties of sarcomeres. In conclusion, although sarcosynced oscillations and sarcomeric oscillations are closely related, they exhibit different oscillations, and the study of the SD holes and SC holes caused by them will contribute to a detailed understanding of the muscle characteristics of sarcomeres. This finding has important implications for improving our understanding of the efficiency of muscle function and its regulatory mechanisms.

New paradigms in actomyosin energy transduction: Critical evaluation of non-traditional models for orthophosphate release

Release of the ATP hydrolysis product ortophosphate (Pi) from the active site of myosin is central in chemo-mechanical energy transduction and closely associated with the main force-generating structural change, the power-stroke. Despite intense investigations, the relative timing between Pi-release and the power-stroke remains poorly understood. This hampers in depth understanding of force production by myosin in health and disease and our understanding of myosin-active drugs. Since the 1990s and up to today, models that incorporate the Pi-release either distinctly before or after the power-stroke, in unbranched kinetic schemes, have dominated the literature. However, in recent years, alternative models have emerged to explain apparently contradictory findings. Here, we first compare and critically analyze three influential alternative models proposed previously. These are either characterized by a branched kinetic scheme or by partial uncoupling of Pi-release and the power-stroke. Finally, we suggest critical tests of the models aiming for a unified picture.

Varying thin filament activation in the framework of the Huxley'57 model

Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

Multistep orthophosphate release tunes actomyosin energy transduction

Muscle contraction and a range of critical cellular functions rely on force-producing interactions between myosin motors and actin filaments, powered by turnover of adenosine triphosphate (ATP). The relationship between release of the ATP hydrolysis product ortophosphate (Pi) from the myosin active site and the force-generating structural change, the power-stroke, remains enigmatic despite its central role in energy transduction. Here, we present a model with multistep Pi-release that unifies current conflicting views while also revealing additional complexities of potential functional importance. The model is based on our evidence from kinetics, molecular modelling and single molecule fluorescence studies of Pi binding outside the active site. It is also consistent with high-speed atomic force microscopy movies of single myosin II molecules without Pi at the active site, showing consecutive snapshots of pre- and post-power stroke conformations. In addition to revealing critical features of energy transduction by actomyosin, the results suggest enzymatic mechanisms of potentially general relevance.

Release of the ATP hydrolysis product orthophosphate (Pi) from the myosin active site is central in force generation but is poorly understood. Here, Moretto et al. present evidence for multistep Pi-release reconciling apparently contradictory results.

Critical Evaluation of Current Hypotheses for the Pathogenesis of Hypertrophic Cardiomyopathy

Hereditary hypertrophic cardiomyopathy (HCM), due to mutations in sarcomere proteins, occurs in more than 1/500 individuals and is the leading cause of sudden cardiac death in young people. The clinical course exhibits appreciable variability. However, typically, heart morphology and function are normal at birth, with pathological remodeling developing over years to decades, leading to a phenotype characterized by asymmetric ventricular hypertrophy, scattered fibrosis and myofibrillar/cellular disarray with ultimate mechanical heart failure and/or severe arrhythmias. The identity of the primary mutation-induced changes in sarcomere function and how they trigger debilitating remodeling are poorly understood. Support for the importance of mutation-induced hypercontractility, e.g., increased calcium sensitivity and/or increased power output, has been strengthened in recent years. However, other ideas that mutation-induced hypocontractility or non-uniformities with contractile instabilities, instead, constitute primary triggers cannot yet be discarded. Here, we review evidence for and criticism against the mentioned hypotheses. In this process, we find support for previous ideas that inefficient energy usage and a blunted Frank–Starling mechanism have central roles in pathogenesis, although presumably representing effects secondary to the primary mutation-induced changes. While first trying to reconcile apparently diverging evidence for the different hypotheses in one unified model, we also identify key remaining questions and suggest how experimental systems that are built around isolated primarily expressed proteins could be useful.

A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue

The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.

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.

Unraveling a Force-Generating Allosteric Pathway of Actomyosin Communication Associated with ADP and Pi Release

The actomyosin system generates mechanical work with the execution of the power stroke, an ATP-driven, two-step rotational swing of the myosin-neck that occurs post ATP hydrolysis during the transition from weakly to strongly actin-bound myosin states concomitant with P_i release and prior to ADP dissociation. The activating role of actin on product release and force generation is well documented; however, the communication paths associated with weak-to-strong transitions are poorly characterized. With the aid of mutant analyses based on kinetic investigations and simulations, we identified the W-helix as an important hub coupling the structural changes of switch elements during ATP hydrolysis to temporally controlled interactions with actin that are passed to the central transducer and converter. Disturbing the W-helix/transducer pathway increased actin-activated ATP turnover and reduced motor performance as a consequence of prolonged duration of the strongly actin-attached states. Actin-triggered P_i release was accelerated, while ADP release considerably decelerated, both limiting maximum ATPase, thus transforming myosin-2 into a high-duty-ratio motor. This kinetic signature of the mutant allowed us to define the fractional occupancies of intermediate states during the ATPase cycle providing evidence that myosin populates a cleft-closure state of strong actin interaction during the weak-to-strong transition with bound hydrolysis products before accomplishing the power stroke.

Sarcomere Length Nonuniformity and Force Regulation in Myofibrils and Sarcomeres

The smallest contractile unit in striated muscles is the sarcomere. Although some of the classic features of contraction assume a uniform behavior of sarcomeres within myofibrils, the occurrence of sarcomere length nonuniformities has been well recognized for years, but it is yet not well understood. In the past years, there has been a great advance in experiments using isolated myofibrils and sarcomeres that has allowed scientists to directly evaluate sarcomere length nonuniformity. This review will focus on studies conducted with these preparations to develop the hypotheses that 1) force production in myofibrils is largely altered and regulated by intersarcomere dynamics and that 2) the mechanical work of one sarcomere in a myofibril is transmitted to other sarcomeres in series. We evaluated studies looking into myofibril activation, relaxation, and force changes produced during activation. We conclude that force production in myofibrils is largely regulated by intersarcomere dynamics, which arises from the cooperative work of the contractile and elastic elements within a myofibril.

Myosin and gelsolin cooperate in actin filament severing and actomyosin motor activity

Actin is a major intracellular protein with key functions in cellular motility, signaling, and structural rearrangements. Its dynamic behavior, such as polymerization and depolymerization of actin filaments in response to intracellular and extracellular cues, is regulated by an abundance of actin binding proteins. Out of these, gelsolin is one of the most potent for filament severing. However, myosin motor activity also fragments actin filaments through motor-induced forces, suggesting that these two proteins could cooperate to regulate filament dynamics and motility. To test this idea, we used an in vitro motility assay, where actin filaments are propelled by surface-adsorbed heavy meromyosin (HMM) motor fragments. This allows studies of both motility and filament dynamics using isolated proteins. Gelsolin, at both nanomolar and micromolar Ca²⁺ concentration, appreciably enhanced actin filament severing caused by HMM-induced forces at 1 mM MgATP, an effect that was increased at higher HMM motor density. This finding is consistent with cooperativity between actin filament severing by myosin-induced forces and by gelsolin. We also observed reduced sliding velocity of the HMM-propelled filaments in the presence of gelsolin, providing further support of myosin-gelsolin cooperativity. Total internal reflection fluorescence microscopy–based single molecule studies corroborated that the velocity reduction was a direct effect of gelsolin binding to the filament and revealed different filament severing pattern of stationary and HMM propelled filaments. Overall, the results corroborate cooperative effects between gelsolin-induced alterations in the actin filaments and changes due to myosin motor activity leading to enhanced F-actin severing of possible physiological relevance.

Hypothesis: Single Actomyosin Properties Account for Ensemble Behavior in Active Muscle Shortening and Isometric Contraction

Muscle contraction results from cyclic interactions between myosin II motors and actin with two sets of proteins organized in overlapping thick and thin filaments, respectively, in a nearly crystalline lattice in a muscle sarcomere. However, a sarcomere contains a huge number of other proteins, some with important roles in muscle contraction. In particular, these include thin filament proteins, troponin and tropomyosin; thick filament proteins, myosin binding protein C; and the elastic protein, titin, that connects the thin and thick filaments. Furthermore, the order and 3D organization of the myofilament lattice may be important per se for contractile function. It is possible to model muscle contraction based on actin and myosin alone with properties derived in studies using single molecules and biochemical solution kinetics. It is also possible to reproduce several features of muscle contraction in experiments using only isolated actin and myosin, arguing against the importance of order and accessory proteins. Therefore, in this paper, it is hypothesized that “single molecule actomyosin properties account for the contractile properties of a half sarcomere during shortening and isometric contraction at almost saturating Ca concentrations”. In this paper, existing evidence for and against this hypothesis is reviewed and new modeling results to support the arguments are presented. Finally, further experimental tests are proposed, which if they corroborate, at least approximately, the hypothesis, should significantly benefit future effective analysis of a range of experimental studies, as well as drug discovery efforts.

The influence of biological maturation and neuromuscular performance on peak bone mineral density in children

BACKGROUND

The growth and development cycle of the adult is characterized by substantial changes in physical size and maturity, and is controlled by the simultaneous influence of genetic components and the environment. Changes in the development of bones, muscles and adipose tissue are among the most important aspects of adolescent physical development. The aim of this research was to examine the correlation between bone mineral density (BMD) and neuromuscular performance in children at different stages of maturation.

METHODS

The study included 31 participants of both sexes (11.7±1.89 years). Body composition was assessed through bone densitometry using an energy duo X-ray source. The neuromuscular performance of the upper limbs was analyzed by the medicine ball hand grip and throwing tests. The lower limbs by the vertical counter-motion jump test, and skeletal maturation was analyzed by bone age. Maturation was used as an effect control between the association of BMD and neuromuscular performance.

RESULTS

The results demonstrated significant associations between the performance of upper (P<0.0001) and lower (P=0.01) limbs and BMD. On inter-group comparison for only the accelerated maturational stage, male participants had greater BMD than female participants (P=0.001; effect size 3.13). Regarding the maturational stages, male participants in the accelerated maturational stage demonstrated higher BMD than those in the normal and delayed maturational stages (P=0.04; effect size 3.10), whereas female participants did not demonstrate significant differences in BMD accumulation.

CONCLUSIONS

BMD has a strong correlation with the neuromuscular performance of upper and lower limbs of children of both sexes.

Lysine acetylation of F-actin decreases tropomyosin-based inhibition of actomyosin activity

Recent proteomics studies of vertebrate striated muscle have identified lysine acetylation at several sites on actin. Acetylation is a reversible post-translational modification that neutralizes lysine's positive charge. Positively charged residues on actin, particularly Lys³²⁶ and Lys³²⁸, are predicted to form critical electrostatic interactions with tropomyosin (Tpm) that promote its binding to filamentous (F)-actin and bias Tpm to an azimuthal location where it impedes myosin attachment. The troponin (Tn) complex also influences Tpm's position along F-actin as a function of Ca²⁺ to regulate exposure of myosin-binding sites and, thus, myosin cross-bridge recruitment and force production. Interestingly, Lys³²⁶ and Lys³²⁸ are among the documented acetylated residues. Using an acetic anhydride-based labeling approach, we showed that excessive, nonspecific actin acetylation did not disrupt characteristic F-actin-Tpm binding. However, it significantly reduced Tpm-mediated inhibition of myosin attachment, as reflected by increased F-actin-Tpm motility that persisted in the presence of Tn and submaximal Ca²⁺ Furthermore, decreasing the extent of chemical acetylation, to presumptively target highly reactive Lys³²⁶ and Lys³²⁸, also resulted in less inhibited F-actin-Tpm, implying that modifying only these residues influences Tpm's location and, potentially, thin filament regulation. To unequivocally determine the residue-specific consequences of acetylation on Tn-Tpm-based regulation of actomyosin activity, we assessed the effects of K326Q and K328Q acetyl (Ac)-mimetic actin on Ca²⁺-dependent, in vitro motility parameters of reconstituted thin filaments (RTFs). Incorporation of K328Q actin significantly enhanced Ca²⁺ sensitivity of RTF activation relative to control. Together, our findings suggest that actin acetylation, especially Lys³²⁸, modulates muscle contraction via disrupting inhibitory Tpm positioning.

Hierarchical modeling of force generation in cardiac muscle

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

The load dependence and the force-velocity relation in intact myosin filaments from skeletal and smooth muscles

In the present study we evaluated the load dependence of force produced by isolated muscle myosin filaments interacting with fluorescently labeled actin filaments, using for the first time whole native myosin filaments. We used a newly developed approach that allowed the use of physiological levels of ATP. Single filaments composed of either skeletal or smooth muscle myosin and single filaments of actin were attached between pairs of nano-fabricated cantilevers of known stiffness. The filaments were brought into contact to produce force, which caused sliding of the actin filaments over the myosin filaments. We applied load to the system by either pushing or pulling the filaments during interactions and observed that increasing the load increased the force produced by myosin and decreasing the load decreased the force. We also performed additional experiments in which we clamped the filaments at predetermined levels of force, which caused the filaments to slide to adjust the different loads, allowing us to measure the velocity of length changes to construct a force-velocity relation. Force values were in the range observed previously with myosin filaments and molecules. The force-velocity curves for skeletal and smooth muscle myosins resembled the relations observed for muscle fibers. The technique can be used to investigate many issues of interest and debate in the field of muscle biophysics.

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

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

Blebbistatin Effects Expose Hidden Secrets in the Force-Generating Cycle of Actin and Myosin

Cyclic interactions between myosin II motors and actin filaments driven by ATP turnover underlie muscle contraction and have key roles in the motility of nonmuscle cells. A remaining enigma in the understanding of this interaction is the relationship between the force-generating structural change and the release of the ATP-hydrolysis product, inorganic phosphate (Pi), from the active site of myosin. Here, we use the small molecular compound blebbistatin to probe otherwise hidden states and transitions in this process. Different hypotheses for the Pi release mechanism are tested by interpreting experimental results from in vitro motility assays and isolated muscle fibers in terms of mechanokinetic actomyosin models. The data fit with ideas that actomyosin force generation is preceded by Pi release, which in turn is preceded by two serial transitions after/coincident with cross-bridge attachment. Blebbistatin changes the rate limitation of the cycle from the first to the second of these transitions, uncovering functional roles of an otherwise short-lived pre-power stroke state that has been implicated by structural data.

On the Shape of the Force-Velocity Relationship in Skeletal Muscles: The Linear, the Hyperbolic, and the Double-Hyperbolic

The shape of the force-velocity (F-V) relationship has important implications for different aspects of muscle physiology, such as muscle efficiency and fatigue, the understanding of the pathophysiology of several myopathies or the mechanisms of muscle contraction per se, and may be of relevance for other fields, such as the development of robotics and prosthetic applications featuring natural muscle-like properties. However, different opinions regarding the shape of the F-V relationship and the underlying mechanisms exist in the literature. In this review, we summarize relevant evidence on the shape of the F-V relationship obtained over the last century. Studies performed at multiple scales ranging from the sarcomere to the organism level have described the concentric F-V relationship as linear, hyperbolic or double-hyperbolic. While the F-V relationship has most frequently been described as a rectangular hyperbola, a large number of studies have found deviations from the hyperbolic function at both ends of the F-V relation. Indeed, current evidence suggests that the F-V relation in skeletal muscles follows a double-hyperbolic pattern, with a breakpoint located at very high forces/low velocities, which may be a direct consequence of the kinetic properties of myofilament cross-bridge formation. Deviations at low forces/high velocities, by contrast, may be related to a recently discovered, calcium-independent regulatory mechanism of muscle contraction, which may also explain the low metabolic cost of very fast muscle shortening contractions. Controversial results have also been reported regarding the eccentric F-V relationship, with studies in prepared muscle specimens suggesting that maximum eccentric force is substantially greater than isometric force, whereas in vivo studies in humans show only a modest increase, no change, or even a decrease in force in lengthening contractions. This review discusses possible reasons reported in the literature for these discrepant findings, including the testing procedures (familiarization, pre-load condition, and temperature) and a potential neural inhibition at higher lengthening velocities. Finally, some unresolved questions and recommendations for F-V testing in humans are reported at the end of this document.

Nonlinear Actomyosin Elasticity in Muscle?

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

A new myofilament contraction model with ATP consumption for ventricular cell model

A new contraction model of cardiac muscle was developed by combining previously described biochemical and biophysical models. The biochemical component of the new contraction model represents events in the presence of Ca2+-crossbridge attachment and power stroke following inorganic phosphate release, detachment evoked by the replacement of ADP by ATP, ATP hydrolysis, and recovery stroke. The biophysical component focuses on Ca2+ activation and force (F b) development assuming an equivalent crossbridge. The new model faithfully incorporates the major characteristics of the biochemical and biophysical models, such as F b activation by transient Ca2+ ([Ca2+]-F b), [Ca2+]-ATP hydrolysis relations, sarcomere length-F b, and F b recovery after jumps in length under the isometric mode and upon sarcomere shortening after a rapid release of mechanical load under the isotonic mode together with the load-velocity relationship. ATP consumption was obtained for all responses. When incorporated in a ventricular cell model, the contraction model was found to share approximately 60% of the total ATP usage in the cell model.

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

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

Sarcomere Stiffness during Stretching and Shortening of Rigor Skeletal Myofibrils

In this study, we measured the stiffness of skeletal muscle myofibrils in rigor. Using a custom-built atomic force microscope, myofibrils were first placed in a rigor state then stretched and shortened at different displacements (0.1–0.3 μm per sarcomere) and nominal speeds (0.4 and 0.8 μm/s). During stretching, the myofibril stiffness was independent of both displacement and speed (average of 987 nN/μm). During shortening, the myofibril stiffness was independent of displacement, but dependent on speed (1234 nN/μm at 0.4 μm/s; 1106 nN/μm at 0.8 μm/s). Furthermore, the myofibril stiffness during shortening was greater than that during stretching and the difference depended on speed (31% at 0.4 μm/s; 8% at 0.8 μm/s). The results suggest that the myofibrils exhibit nonlinear viscoelastic properties that may be derived from myofibril filaments, similar to what has been observed in muscle fibers.

The force-generation process in active muscle is strain sensitive and endothermic: a temperature-perturbation study

In experiments on active muscle, we examined the tension decline and its temperature sensitivity at the onset of ramp shortening and at a range of velocities. A segment (∼1.5 mm long) of a skinned muscle fibre isolated from rabbit psoas muscle was held isometrically (sarcomere length ∼2.5 µm) at 8-9°C, maximally Ca²⁺-activated and a ramp shortening applied. The tension decline with a ramp shortening showed an early decrease of slope (the P₁ transition) followed by a slower decrease in slope (the P₂ transition) to the steady (isotonic) force. The tension level at the initial P₁ transition and the time to that transition decreased as the velocity was increased; the length change to this transition increased with shortening velocity to a steady value of ∼8 nm half-sarcomere^-1 A small, rapid, temperature jump (T-jump) (3-4°C, <0.2 ms) applied coincident with the onset of ramp shortening showed force enhancement by T-jump and changed the tension decline markedly. Analyses showed that the rate of T-jump-induced force rise increased linearly with increase of shortening velocity. These results provide crucial evidence that the strain-sensitive cross-bridge force generation, or a step closely coupled to it, is endothermic.

Kinetic coupling of phosphate release, force generation and rate-limiting steps in the cross-bridge cycle

A basic goal in muscle research is to understand how the cyclic ATPase activity of cross-bridges is converted into mechanical force. A direct approach to study the chemo-mechanical coupling between P_i release and the force-generating step is provided by the kinetics of force response induced by a rapid change in [P_i]. Classical studies on fibres using caged-P_i discovered that rapid increases in [P_i] induce fast force decays dependent on final [P_i] whose kinetics were interpreted to probe a fast force-generating step prior to P_i release. However, this hypothesis was called into question by studies on skeletal and cardiac myofibrils subjected to P_i jumps in both directions (increases and decreases in [P_i]) which revealed that rapid decreases in [P_i] trigger force rises with slow kinetics, similar to those of calcium-induced force development and mechanically-induced force redevelopment at the same [P_i]. A possible explanation for this discrepancy came from imaging of individual sarcomeres in cardiac myofibrils, showing that the fast force decay upon increase in [P_i] results from so-called sarcomere 'give'. The slow force rise upon decrease in [P_i] was found to better reflect overall sarcomeres cross-bridge kinetics and its [P_i] dependence, suggesting that the force generation coupled to P_i release cannot be separated from the rate-limiting transition. The reasons for the different conclusions achieved in fibre and myofibril studies are re-examined as the recent findings on cardiac myofibrils have fundamental consequences for the coupling between P_i release, rate-limiting steps and force generation. The implications from P_i-induced force kinetics of myofibrils are discussed in combination with historical and recent models of the cross-bridge cycle.

Chemomechanical regulation of myosin Ic cross-bridges: Deducing the elastic properties of an ensemble from single-molecule mechanisms

Myosin Ic is thought to be the principal constituent of the motor that adjusts mechanical responsiveness during adaptation to prolonged stimuli by hair cells, the sensory receptors of the inner ear. In this context myosin molecules operate neither as filaments, as occurs in muscles, nor as single or few molecules, as characterizes intracellular transport. Instead, myosin Ic molecules occur in a complex cluster in which they may exhibit cooperative properties. To better understand the motor’s remarkable function, we introduce a theoretical description of myosin Ic’s chemomechanical cycle based on experimental data from recent single-molecule studies. The cycle consists of distinct chemical states that the myosin molecule stochastically occupies. We explicitly calculate the probabilities of the occupancy of these states and show their dependence on the external force, the availability of actin, and the nucleotide concentrations as required by thermodynamic constraints. This analysis highlights that the strong binding of myosin Ic to actin is dominated by the ADP state for small external forces and by the ATP state for large forces. Our approach shows how specific parameter values of the chemomechanical cycle for myosin Ic result in behaviors distinct from those of other members of the myosin family. Integrating this single-molecule cycle into a simplified ensemble description, we predict that the average number of bound myosin heads is regulated by the external force and nucleotide concentrations. The elastic properties of such an ensemble are determined by the average number of myosin cross-bridges. Changing the binding probabilities and myosin’s stiffness under a constant force results in a mechanical relaxation which is large enough to account for fast adaptation in hair cells.

Myosin molecules are biological nanomachines that transduce chemical energy into mechanical work and thus produce directed motion in living cells. These molecules proceed through cyclic reactions in which they change their conformational states upon the binding and release of nucleotides while attaching to and detaching from filaments. The myosin family consists of many distinct members with diverse functions such as muscle contraction, cargo transport, cell migration, and sensory adaptation. How these functions emerge from the biophysical properties of the individual molecules is an open question. We present an approach that integrates recent findings from single-molecule experiments into a thermodynamically consistent description of myosin Ic and demonstrate how the specific parameter values of the cycle result in a distinct function. The free variables of our description are the chemical input and external force, both of which are experimentally accessible and define the cellular environment in which these proteins function. We use this description to predict the elastic properties of an ensemble of molecules and discuss the implications for myosin Ic’s function in the inner ear as a tension regulator mediating adaptation, a hallmark of biological sensory systems. In this situation myosin molecules cooperate in an intermediate regime, neither as a large ensemble as in muscle nor as a single or a few molecules as in intracellular transport.

A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes

Experimental data from human cardiac myocytes at body temperature is crucial for a quantitative understanding of clinically relevant cardiac function and development of whole-organ computational models. However, such experimental data is currently very limited. Specifically, important measurements to characterize changes in tension development in human cardiomyocytes that occur with perturbations in cell length are not available. To address this deficiency, in this study we present an experimental data set collected from skinned human cardiac myocytes, including the passive and viscoelastic properties of isolated myocytes, the steady-state force calcium relationship at different sarcomere lengths, and changes in tension following a rapid increase or decrease in length, and after constant velocity shortening. This data set is, to our knowledge, the first characterization of length and velocity-dependence of tension generation in human skinned cardiac myocytes at body temperature. We use this data to develop a computational model of contraction and passive viscoelasticity in human myocytes. Our model includes troponin C kinetics, tropomyosin kinetics, a three-state crossbridge model that accounts for the distortion of crossbridges, and the cellular viscoelastic response. Each component is parametrized using our experimental data collected in human cardiomyocytes at body temperature. Furthermore we are able to confirm that properties of length-dependent activation at 37°C are similar to other species, with a shift in calcium sensitivity and increase in maximum tension. We revise our model of tension generation in the skinned isolated myocyte to replicate reported tension traces generated in intact muscle during isometric tension, to provide a model of human tension generation for multi-scale simulations. This process requires changes to calcium sensitivity, cooperativity, and crossbridge transition rates. We apply this model within multi-scale simulations of biventricular cardiac function and further refine the parametrization within the whole organ context, based on obtaining a healthy ejection fraction. This process reveals that crossbridge cycling rates differ between skinned myocytes and intact myocytes.

Residual force enhancement is regulated by titin in skeletal and cardiac myofibrils

KEY POINTS

When a skeletal muscle is stretched while it contracts, the muscle produces a relatively higher force than the force from an isometric contraction at the same length: a phenomenon referred to as residual force enhancement. Residual force enhancement is puzzling because it cannot be directly explained by the classical force-length relationship and the sliding filament theory of contraction, the main paradigms in the muscle field. We used custom-built instruments to measure residual force enhancement in skeletal myofibrils, and, for the first time, in cardiac myofibrils. Our data report that residual force enhancement is present in skeletal muscles, but not cardiac muscles, and is regulated by the different isoforms of the titin protein filaments.

ABSTRACT

When a skeletal muscle contracts isometrically, the muscle produces a force that is relative to the final isometric sarcomere length (SL). However, when the same final SL is reached by stretching the muscle while it contracts, the muscle produces a relatively higher force: a phenomenon commonly referred to as residual force enhancement. In this study, we investigated residual force enhancement in rabbit skeletal psoas myofibrils and, for the first time, cardiac papillary myofibrils. A custom-built atomic force microscope was used in experiments that stretched myofibrils before and after inhibiting myosin and actin interactions to determine whether the different cardiac and skeletal titin isoforms regulate residual force enhancement. At SLs ranging from 2.24 to 3.13 μm, the skeletal myofibrils enhanced the force by an average of 9.0%, and by 29.5% after hindering myosin and actin interactions. At SLs ranging from 1.80 to 2.29 μm, the cardiac myofibrils did not enhance the force before or after hindering myosin and actin interactions. We conclude that residual force enhancement is present only in skeletal muscles and is dependent on the titin isoforms.

Actomyosin based contraction: one mechanokinetic model from single molecules to muscle?

Bridging the gaps between experimental systems on different hierarchical scales is needed to overcome remaining challenges in the understanding of muscle contraction. Here, a mathematical model with well-characterized structural and biochemical actomyosin states is developed to that end. We hypothesize that this model accounts for generation of force and motion from single motor molecules to the large ensembles of muscle. In partial support of this idea, a wide range of contractile phenomena are reproduced without the need to invoke cooperative interactions or ad hoc states/transitions. However, remaining limitations exist, associated with ambiguities in available data for model definition e.g.: (1) the affinity of weakly bound cross-bridges, (2) the characteristics of the cross-bridge elasticity and (3) the exact mechanistic relationship between the force-generating transition and phosphate release in the actomyosin ATPase. Further, the simulated number of attached myosin heads in the in vitro motility assay differs several-fold from duty ratios, (fraction of strongly attached ATPase cycle times) derived in standard analysis. After addressing the mentioned issues the model should be useful in fundamental studies, for engineering of myosin motors as well as for studies of muscle disease and drug development.

Decavanadate Toxicology and Pharmacological Activities: V10 or V1, Both or None?

This review covers recent advances in the understanding of decavanadate toxicology and pharmacological applications. Toxicological in vivo studies point out that V10 induces several changes in several oxidative stress parameters, different from the ones observed for vanadate (V1). In in vitro studies with mitochondria, a particularly potent V10 effect, in comparison with V1, was observed in the mitochondrial depolarization (IC50 = 40 nM) and oxygen consumption (99 nM). It is suggested that mitochondrial membrane depolarization is a key event in decavanadate induction of necrotic cardiomyocytes death. Furthermore, only decavanadate species and not V1 potently inhibited myosin ATPase activity stimulated by actin (IC50 = 0.75 μM) whereas exhibiting lower inhibition activities for Ca(2+)-ATPase activity (15 μM) and actin polymerization (17 μM). Because both calcium pump and actin decavanadate interactions lead to its stabilization, it is likely that V10 interacts at specific locations with these proteins that protect against hydrolysis but, on the other hand, it may induce V10 reduction to oxidovanadium(IV). Putting it all together, it is suggested that the pharmacological applications of V10 species and compounds whose mechanism of action is still to be clarified might involve besides V10 and V1 also vanadium(IV) species.