The myofilament elasticity and its effect on kinetics of force generation by the myosin motor

Resolving the kinetics of an ensemble of muscle myosin motors via a temperature-dependent fitting procedure

A data fitting procedure is devised and thoroughly tested to provide self-consistent estimates of the relevant mechanokinetic parameters involved in a plausible scheme underpinning the output of an ensemble of myosin II molecular motors mimicking the contraction of skeletal muscle. The method builds on a stochastic model accounting for the force exerted by the motor ensemble operated both in the low and high force-generating regimes corresponding to different temperature ranges. The proposed interpretative framework is successfully challenged against simulated data, meant to mimic the experimental output of a one-dimensional synthetic nanomachine powered by pure muscle myosin isoforms.

The Mechanism of Modulation of Cardiac Force by Temperature

In maximally Ca2+-activated demembranated fibres from the mammalian skeletal muscle, the depression of the force by lowering the temperature below the physiological level (~35 °C) is explained by the reduction of force in the myosin motor. Instead, cooling is reported to not affect the force per motor in Ca2+-activated cardiac trabeculae from the rat ventricle. Here, the mechanism of the cardiac performance depression by cooling is reinvestigated with fast sarcomere-level mechanics. We determine the changes in the half-sarcomere compliance of maximally Ca2+-activated demembranated rat trabeculae in the range of temperatures of 10-30 °C and analyse the data in terms of a simplified mechanical model of the half-sarcomere to extract the contribution of myofilaments and myosin motors. We find that the changes in the ensemble force are due to changes in the force per motor, while the fraction of actin-attached motors remains constant independent of temperature. The results demonstrate that in the cardiac myosin, as in the skeletal muscle myosin, the force-generating transition is endothermic. The underlying large heat absorption indicates the interaction of extended hydrophobic surfaces within the myosin motor, like those suggested by the crystallographic model of the working stroke.

Quantifying Active and Passive Stiffness in Plantar Flexor Muscles Following Intermittent Maximal Isometric Contractions Using Shear Wave Elastography

OBJECTIVE

This study aimed: (i) to investigate the impact of fatigue, triggered by maximal isometric contraction exercises, on the active and passive stiffness of plantar flexors (PF), and (ii) to examine the relationship between changes in mechanical parameters and neuromuscular alterations after fatigue.

METHODS

A healthy cohort (n = 12; age = 27.3 ± 5.5 y; BMI = 24.4 ± 2.35 kg/m²) was instructed to perform 60 isometric contractions, each lasting 4 s with a 1-s rest interval, using an ergometer. Several measures were taken before and after the fatigue protocol. First, the stiffness of the PF-tendon complex (PFC) was quantified during passive ankle mobilization both during and after the fatigue protocol using the ergometer. Additionally, from shear wave elastography, the active and passive stiffness of the gastrocnemius medialis (GM) were measured during passive ankle mobilization and isometric maximal voluntary contraction (MVC), respectively. Finally, the peak torque and the rate of torque development (RFD) of PF were assessed during the MVC using the ergometer. Ankle muscle activities (surface electromyograph [SEMG]) were recorded during all evaluations using electromyography.

RESULTS

After the fatigue protocol, the results revealed a decline in active stiffness, peak torque of PF, RFD and SEMG activity of the GM (p < 0.001). Furthermore, significant correlation was identified between the decrease of the peak torque of PF and the active stiffness of the GM (r = 0.6; p < 0.05). A decrease in the PFC stiffness (p < 0.001) and a decrease in the shear modulus of the GM at 20° (p < 0.001) were also observed.

CONCLUSION

Isometric fatiguing exercises modify the mechanical properties of both the contractile and elastic components. Notably, decreases in both passive and active stiffness may be critical for athletes, as these changes could potentially increase the risk of injury.

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

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

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.

Elastic domains of giant proteins in striated muscle: Modeling compliance with rulers

Chase examines a study using the MUSICO model of striated muscle to evaluate the function of giant elastic proteins titin and nebulin.

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.

Standard Loading Profile in Matrix Rigidity Sensing

It is important to learn features of locally applied forces by cells during matrix rigidity sensing, since the function of mechanosensing proteins would be affected by force magnitude, loading velocity, or even loading history. Here, we investigate a rigidity-sensing apparatus consisting of a contractile unit on matrices. Strikingly, our analysis indicates that the matrix rigidity is not only sensed with a fixed step size in displacement but also with a fixed apparent loading velocity. The fixed step size is shown to be correlated with the monomer size of actin filament. This work suggests that the loading profile during rigidity sensing is regulated by various aspects of the contractile unit, which then serves as the standard in sensing varied rigidity of the matrix.

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

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

Minimum number of myosin motors accounting for shortening velocity under zero load in skeletal muscle

KEY POINTS

Myosin filament mechanosensing determines the efficiency of the contraction by adapting the number of switched ON motors to the load. Accordingly, the unloaded shortening velocity (V₀ ) is already set at the end of latency relaxation (LR), ∼10 ms after the start of stimulation, when the myosin filament is still in the OFF state. Here the number of actin-attached motors per half-myosin filament (n) during V₀ shortening imposed either at the end of LR or at the plateau of the isometric contraction is estimated from the relation between half-sarcomere compliance and force during the force redevelopment after shortening. The value of n decreases progressively with shortening and, during V₀ shortening starting at the end of LR, is 1-4. Reduction of n is accounted for by a constant duty ratio of 0.05 and a parallel switching OFF of motors, explaining the very low rate of ATP utilization found during unloaded shortening.

ABSTRACT

The maximum velocity at which a skeletal muscle can shorten (i.e. the velocity of sliding between the myosin filament and the actin filament under zero load, V₀ ) is already set at the end of the latency relaxation (LR) preceding isometric force generation, ∼10 ms after the start of electrical stimulation in frog muscle fibres at 4°C. At this time, Ca²⁺ -induced activation of the actin filament is maximal, while the myosin filament is in the OFF state characterized by most of the myosin motors lying on helical tracks on the filament surface, making them unavailable for actin binding and ATP hydrolysis. Here, the number of actin-attached motors per half-thick filament during V₀ shortening (n) is estimated by imposing, on tetanized single fibres from Rana esculenta (at 4°C and sarcomere length 2.15 μm), small 4 kHz oscillations and determining the relation between half-sarcomere (hs) compliance and force during the force development following V₀ shortening. When V₀ shortening is superimposed on the maximum isometric force T₀ , n decreases progressively with the increase of shortening (range 30-80 nm per hs) and, when V₀ shortening is imposed at the end of LR, n can be as low as 1-4. Reduction of n is accounted for by a constant duty ratio of the myosin motor of ∼0.05 and a parallel switching OFF of the thick filament, providing an explanation for the very low rate of ATP utilization during extended V₀ shortening.

Modulation of Skeletal Muscle Contraction by Myosin Phosphorylation

The striated muscle sarcomere is a highly organized and complex enzymatic and structural organelle. Evolutionary pressures have played a vital role in determining the structure-function relationship of each protein within the sarcomere. A key part of this multimeric assembly is the light chain-binding domain (LCBD) of the myosin II motor molecule. This elongated "beam" functions as a biological lever, amplifying small interdomain movements within the myosin head into piconewton forces and nanometer displacements against the thin filament during the cross-bridge cycle. The LCBD contains two subunits known as the essential and regulatory myosin light chains (ELC and RLC, respectively). Isoformic differences in these respective species provide molecular diversity and, in addition, sites for phosphorylation of serine residues, a highly conserved feature of striated muscle systems. Work on permeabilized skeletal fibers and thick filament systems shows that the skeletal myosin light chain kinase catalyzed phosphorylation of the RLC alters the "interacting head motif" of myosin motor heads on the thick filament surface, with myriad consequences for muscle biology. At rest, structure-function changes may upregulate actomyosin ATPase activity of phosphorylated cross-bridges. During activation, these same changes may increase the Ca2+ sensitivity of force development to enhance force, work, and power output, outcomes known as "potentiation." Thus, although other mechanisms may contribute, RLC phosphorylation may represent a form of thick filament activation that provides a "molecular memory" of contraction. The clinical significance of these RLC phosphorylation mediated alterations to contractile performance of various striated muscle systems are just beginning to be understood. © 2017 American Physiological Society. Compr Physiol 7:171-212, 2017.

Contribution of elastic tissues to the mechanics and energetics of muscle function during movement

Muscle force production occurs within an environment of tissues that exhibit spring-like behavior, and this elasticity is a critical determinant of muscle performance during locomotion. Muscle force and power output both depend on the speed of contraction, as described by the isotonic force-velocity curve. By influencing the speed of contractile elements, elastic structures can have a profound effect on muscle force, power and work. In very rapid movements, elastic mechanisms can amplify muscle power by storing the work of muscle contraction slowly and releasing it rapidly. When energy must be dissipated rapidly, such as in landing from a jump, energy stored rapidly in elastic elements can be released more slowly to stretch muscle contractile elements, reducing the power input to muscle and possibly protecting it from damage. Elastic mechanisms identified so far rely primarily on in-series tendons, but many structures within muscles exhibit spring-like properties. Actomyosin cross-bridges, actin and myosin filaments, titin, and the connective tissue scaffolding of the extracellular matrix all have the potential to store and recover elastic energy during muscle contraction. The potential contribution of these elements can be assessed from their stiffness and estimates of the strain they undergo during muscle function. Such calculations provide boundaries for the possible roles these springs might play in locomotion, and may help to direct future studies of the uses of elastic elements in muscle.

Size and speed of the working stroke of cardiac myosin in situ

The power in the myocardium sarcomere is generated by two bipolar arrays of the motor protein cardiac myosin II extending from the thick filament and pulling the thin, actin-containing filaments from the opposite sides of the sarcomere. Despite the interest in the definition of myosin-based cardiomyopathies, no study has yet been able to determine the mechanokinetic properties of this motor protein in situ. Sarcomere-level mechanics recorded by a striation follower is used in electrically stimulated intact ventricular trabeculae from the rat heart to determine the isotonic velocity transient following a stepwise reduction in force from the isometric peak force TP to a value T(0.8-0.2 TP). The size and the speed of the early rapid shortening (the isotonic working stroke) increase by reducing T from ∼3 nm per half-sarcomere (hs) and 1,000 s(-1) at high load to ∼8 nm⋅hs(-1) and 6,000 s(-1) at low load. Increases in sarcomere length (1.9-2.2 μm) and external [Ca(2+)]o (1-2.5 mM), which produce an increase of TP, do not affect the dependence on T, normalized for TP, of the size and speed of the working stroke. Thus, length- and Ca(2+)-dependent increase of TP and power in the heart can solely be explained by modulation of the number of myosin motors, an emergent property of their array arrangement. The motor working stroke is similar to that of skeletal muscle myosin, whereas its speed is about three times slower. A new powerful tool for investigations and therapies of myosin-based cardiomyopathies is now within our reach.

Work Done by Titin Protein Folding Assists Muscle Contraction

Current theories of muscle contraction propose that the power stroke of a myosin motor is the sole source of mechanical energy driving the sliding filaments of a contracting muscle. These models exclude titin, the largest protein in the human body, which determines the passive elasticity of muscles. Here, we show that stepwise unfolding/folding of titin immunoglobulin (Ig) domains occurs in the elastic I band region of intact myofibrils at physiological sarcomere lengths and forces of 6-8 pN. We use single-molecule techniques to demonstrate that unfolded titin Ig domains undergo a spontaneous stepwise folding contraction at forces below 10 pN, delivering up to 105 zJ of additional contractile energy, which is larger than the mechanical energy delivered by the power stroke of a myosin motor. Thus, it appears inescapable that folding of titin Ig domains is an important, but as yet unrecognized, contributor to the force generated by a contracting muscle.

Temperature effect on the chemomechanical regulation of substeps within the power stroke of a single Myosin II

Myosin IIs in the skeletal muscle are highly efficient nanoscale machines evolved in nature. Understanding how they function can not only bring insights into various biological processes but also provide guidelines to engineer synthetic nanoscale motors working in the vicinity of thermal noise. Though it was clearly demonstrated that the behavior of a skeletal muscle fiber, or that of a single myosin was strongly affected by the temperature, how exactly the temperature affects the kinetics of a single myosin is not fully understood. By adapting the newly developed transitional state model, which successfully explained the intriguing motor force regulation during skeletal muscle contraction, here we systematically explain how exactly the power stroke of a single myosin proceeds, with the consideration of the chemomechanical regulation of sub-steps within the stroke. The adapted theory is then utilized to investigate the temperature effect on various aspects of the power stroke. Our analysis suggests that, though swing rates, the isometric force, and the maximal stroke size all strongly vary with the temperature, the temperature can have a very small effect on the releasable elastic energy within the power stroke.

Force and number of myosin motors during muscle shortening and the coupling with the release of the ATP hydrolysis products

KEY POINTS

Muscle contraction is due to cyclical ATP-driven working strokes in the myosin motors while attached to the actin filament. Each working stroke is accompanied by the release of the hydrolysis products, orthophosphate and ADP. The rate of myosin-actin interactions increases with the increase in shortening velocity. We used fast half-sarcomere mechanics on skinned muscle fibres to determine the relation between shortening velocity and the number and strain of myosin motors and the effect of orthophosphate concentration. A model simulation of the myosin-actin reaction explains the results assuming that orthophosphate and then ADP are released with rates that increase as the motor progresses through the working stroke. The ADP release rate further increases by one order of magnitude with the rise of negative strain in the final motor conformation. These results provide the molecular explanation of the relation between the rate of energy liberation and shortening velocity during muscle contraction. The chemo-mechanical cycle of the myosin II--actin reaction in situ has been investigated in Ca(2+)-activated skinned fibres from rabbit psoas, by determining the number and strain (s) of myosin motors interacting during steady shortening at different velocities (V) and the effect of raising inorganic phosphate (Pi) concentration. It was found that in control conditions (no added Pi ), shortening at V ≤ 350 nm s(-1) per half-sarcomere, corresponding to force (T) greater than half the isometric force (T0 ), decreases the number of myosin motors in proportion to the reduction of T, so that s remains practically constant and similar to the T0 value independent of V. At higher V the number of motors decreases less than in proportion to T, so that s progressively decreases. Raising Pi concentration by 10 mM, which reduces T0 and the number of motors by 40-50%, does not influence the dependence on V of number and strain. A model simulation of the myosin-actin reaction in which the structural transitions responsible for the myosin working stroke and the release of the hydrolysis products are orthogonal explains the results assuming that Pi and then ADP are released with rates that increase as the motor progresses through the working stroke. The rate of ADP release from the conformation at the end of the working stroke is also strain-sensitive, further increasing by one order of magnitude within a few nanometres of negative strain. These results provide the molecular explanation of the relation between the rate of energy liberation and the load during muscle contraction.

Poorly understood aspects of striated muscle contraction

Muscle contraction results from cyclic interactions between the contractile proteins myosin and actin, driven by the turnover of adenosine triphosphate (ATP). Despite intense studies, several molecular events in the contraction process are poorly understood, including the relationship between force-generation and phosphate-release in the ATP-turnover. Different aspects of the force-generating transition are reflected in the changes in tension development by muscle cells, myofibrils and single molecules upon changes in temperature, altered phosphate concentration, or length perturbations. It has been notoriously difficult to explain all these events within a given theoretical framework and to unequivocally correlate observed events with the atomic structures of the myosin motor. Other incompletely understood issues include the role of the two heads of myosin II and structural changes in the actin filaments as well as the importance of the three-dimensional order. We here review these issues in relation to controversies regarding basic physiological properties of striated muscle. We also briefly consider actomyosin mutation effects in cardiac and skeletal muscle function and the possibility to treat these defects by drugs.

The contributions of filaments and cross-bridges to sarcomere compliance in skeletal muscle

Force generation in the muscle sarcomere is driven by the head domain of the myosin molecule extending from the thick filament to form cross-bridges with the actin-containing thin filament. Following attachment, a structural working stroke in the head pulls the thin filament towards the centre of the sarcomere, producing, under unloaded conditions, a filament sliding of ∼ 11 nm. The mechanism of force generation by the myosin head depends on the relationship between cross-bridge force and movement, which is determined by compliances of the cross-bridge (C(cb)) and filaments. By measuring the force dependence of the spacing of the high-order myosin- and actin-based X-ray reflections from sartorius muscles of Rana esculenta we find a combined filament compliance (Cf) of 13.1 ± 1.2 nm MPa(-1), close to recent estimates from single fibre mechanics (12.8 ± 0.5 nm MPa(-1)). C(cb) calculated using these estimates is 0.37 ± 0.12 nm pN(-1), a value fully accounted for by the compliance of the myosin head domain, 0.38 ± 0.06 nm pN(-1), obtained from the intensity changes of the 14.5 nm myosin-based X-ray reflection in response to 3 kHz oscillations imposed on single muscle fibres in rigor. Thus, a significant contribution to C(cb) from the myosin tail that joins the head to the thick filament is excluded. The low C(cb) value indicates that the myosin head generates isometric force by a small sub-step of the 11 nm stroke that drives filament sliding at low load. The implications of these results for the mechanism of force generation by myosins have general relevance for cardiac and non-muscle myosins as well as for skeletal muscle.