Is the cross-bridge stiffness proportional to tension during muscle fiber activation?

Three-dimensional mapping of ultrasound-derived skeletal muscle shear wave velocity

Introduction: The mechanical properties of skeletal muscle are indicative of its capacity to perform physical work, state of disease, or risk of injury. Ultrasound shear wave elastography conducts a quantitative analysis of a tissue's shear stiffness, but current implementations only provide two-dimensional measurements with limited spatial extent. We propose and assess a framework to overcome this inherent limitation by acquiring numerous and contiguous measurements while tracking the probe position to create a volumetric scan of the muscle. This volume reconstruction is then mapped into a parameterized representation in reference to geometric and anatomical properties of the muscle. Such an approach allows to quantify regional differences in muscle stiffness to be identified across the entire muscle volume assessed, which could be linked to functional implications. Methods: We performed shear wave elastography measurements on the vastus lateralis (VL) and the biceps femoris long head (BFlh) muscle of 16 healthy volunteers. We assessed test-retest reliability, explored the potential of the proposed framework in aggregating measurements of multiple subjects, and studied the acute effects of muscular contraction on the regional shear wave velocity post-measured at rest. Results: The proposed approach yielded moderate to good reliability (ICC between 0.578 and 0.801). Aggregation of multiple subject measurements revealed considerable but consistent regional variations in shear wave velocity. As a result of muscle contraction, the shear wave velocity was elevated in various regions of the muscle; showing pre-to-post regional differences for the radial assessement of VL and longitudinally for BFlh. Post-contraction shear wave velocity was associated with maximum eccentric hamstring strength produced during six Nordic hamstring exercise repetitions. Discussion and Conclusion: The presented approach provides reliable, spatially resolved representations of skeletal muscle shear wave velocity and is capable of detecting changes in three-dimensional shear wave velocity patterns, such as those induced by muscle contraction. The observed systematic inter-subject variations in shear wave velocity throughout skeletal muscle additionally underline the necessity of accurate spatial referencing of measurements. Short high-effort exercise bouts increase muscle shear wave velocity. Further studies should investigate the potential of shear wave elastography in predicting the muscle's capacity to perform work.

Effects of muscular endurance and tendon extensibility on endurance of joint stiffness

In some sporting events (e.g., long-distance running), the ability to maintain joint stiffness is considered an essential physical ability. However, the determinants of joint stiffness endurance remain unclear. This study aimed to examine the effects of muscular endurance and tendon extensibility on joint stiffness endurance. Thirteen males performed the fatigue task (5 sets of 50 hopping). Ankle joint stiffness during drop jump was measured before and after fatigue task. The maximum number of repetitions at 30% of one repetition maximum for plantar flexion was measured as muscular endurance. Maximal elongation of the Achilles tendon was measured during ramp (with a low strain rate of tendon) and ballistic (with a high strain rate of tendon) contractions as tendon extensibility. Joint stiffness significantly decreased by 7.5% after the fatigue task (p = 0.033). The maximum number of repetitions at 30% of 1RM (79.6 ± 48.7 repetitions) was not significantly correlated with the relative change in joint stiffness (r = 0.283, p = 0.348). The maximal elongation of the Achilles tendon measured during ramp and ballistic contractions were not significantly associated with the relative change in joint stiffness (r = 0.326, p = 0.277 for ramp contraction; r = 0.438, p = 0.135 for ballistic contraction). These results suggest that muscular endurance and tendon extensibility were unrelated to joint stiffness endurance.

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

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

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.

Directional Dependence of Experimental Trunk Stiffness: Role of Muscle-Stiffness Variation of Nonneural Origin

Trunk stiffness is an important parameter for trunk stability analysis and needs to be evaluated accurately. Discrepancies regarding the dependence of trunk stiffness on the direction of movement in the sagittal plane suggest inherent sources of error that require explanation. In contrast to the common assumption that the muscle stiffness remains constant prior to the induction of a reflex during position perturbations, it is postulated that muscle-stiffness changes of nonneural origin occur and alter the experimental trunk stiffness, causing it to depend on the sagittal direction. This is confirmed through reinterpretation of existing test data for a healthy subject, numerical simulation, and sensitivity analysis using a biomechanical model. The trunk stiffness is determined through a static approach (in forward and backward directions) and compared with the model stiffness for assumed scenarios involving deactivated muscles. The difference in stiffness between the opposite directions reaches 17.5% without a preload and decreases when a moderate vertical preload is applied. The increased muscle activation induced by preloads or electrical stimuli explains the apparent discrepancies observed in previous studies. The experimental stiffness invariably remains between low and high model-stiffness estimates based on extreme scenarios of the postulated losses of muscle activation, thereby confirming our hypothesis.

Reduced Active Muscle Stiffness after Intermittent Submaximal Isometric Contractions

PURPOSE

Whether muscle stiffness is influenced by fatigue remains unclear. Classical methods used to assess muscle stiffness provide a global measure at the joint level. As fatigue may selectively affect specific muscles, a joint-level approach may not be sensitive enough to detect potential changes in muscle stiffness. Taking advantage of ultrasound shear wave elastography, this study aimed to determine the influence of a fatiguing protocol involving intermittent submaximal isometric contractions on muscle shear modulus (an index of stiffness).

METHODS

Shear modulus was measured on either the vastus lateralis (n = 9) or the abductor digiti minimi (n = 10) before and after 15 min of intermittent submaximal isometric contractions at 60% of maximal voluntary contraction (MVC) (4 s ON, 4 s OFF). An index of active muscle stiffness was estimated PRE- and POST-fatigue as the slope of the linear regression established between shear modulus and absolute joint force up to 60% MVC.

RESULTS

After the fatiguing exercise, MVC was significantly decreased by 22% ± 7% and 32% ± 15% for knee extension and little finger abduction, respectively (P < 0.001). When compared to PRE-fatigue, the index of active muscle stiffness was 12% ± 15% lower for the vastus lateralis (P < 0.031) and 44% ± 19% lower for the abductor digiti minimi (P < 0.001) POST-fatigue.

CONCLUSIONS

Although the present results cannot clearly determine the involved mechanisms, they demonstrate a decreased active muscle stiffness after a fatiguing task involving intermittent submaximal isometric contractions. Further studies should now determine whether this change in stiffness affects performance and risk of injury.

Changes in the Viscoelastic Properties of the Vastus Lateralis Muscle With Fatigue

We investigated the in vivo effects of voluntary fatiguing isometric contractions of the knee extensor muscles on the viscoelastic properties of the vastus lateralis (VL). Twelve young males (29.0 ± 4.5 years) performed an intermittent voluntary fatigue protocol consisting of 6 sets × 10 repetitions of 5-s voluntary maximal isometric contractions with 5-s passive recovery periods between repetitions. Voluntary and evoked torque were assessed before, immediately after, and 20 min after exercise. The shear modulus (μ) of the VL muscle was estimated at rest and during a ramped isometric contraction using a conventional elastography technique. An index of active muscle stiffness was then calculated (slope from the relationship between shear modulus and absolute torque). Resting muscle viscosity (η) was quantified using a shear-wave spectroscopy sequence to measure the shear-wave dispersion. Voluntary and evoked torque decreased by ∼37% (P < 0.01) immediately after exercise. The resting VL μ was lower at the end of the fatigue protocol (-57.9 ± 5.4%, P < 0.001), whereas the resting VL η increased (179.0 ± 123%, P < 0.01). The active muscle stiffness index also decreased with fatigue (P < 0.05). By 20 min post-fatigue, there were no significant differences from the pre-exercise values for VL η and the active muscle stiffness index, contrary to the resting VL μ. We show that the VL μ is greatly reduced and η greatly enhanced by fatigue, reflecting a more compliant and viscous muscle. The quantification of both shear μ and η moduli in vivo may contribute to a better understanding of the mechanical behavior of muscles during fatigue in sports medicine, as well as in clinical situations.

Contracting striated muscle has a dynamic I-band spring with an undamped stiffness 100 times larger than the passive stiffness

KEY POINTS

Fast sarcomere-level mechanics in contracting intact fibres from frog skeletal muscle reveal an I-band spring with an undamped stiffness 100 times larger than the known static stiffness. This undamped stiffness remains constant in the range of sarcomere length 2.7-3.1 µm, showing the ability of the I-band spring to adapt its length to the width of the I-band. The stiffness and tunability of the I-band spring implicate titin as a force contributor that, during contraction, allows weaker half-sarcomeres to equilibrate with in-series stronger half-sarcomeres, preventing the development of sarcomere length inhomogeneity. This work opens new possibilities for the detailed in situ description of the structural-functional basis of muscle dysfunctions related to mutations or site-directed mutagenesis in titin that alter the I-band stiffness.

ABSTRACT

Force and shortening in the muscle sarcomere are due to myosin motors from thick filaments pulling nearby actin filaments toward the sarcomere centre. Thousands of serially linked sarcomeres in muscle make the shortening (and the shortening speed) macroscopic, while the intrinsic instability of in-series force generators is likely prevented by the cytoskeletal protein titin that connects the thick filament with the sarcomere end, working as an I-band spring that accounts for the rise of passive force with sarcomere length (SL). However, current estimates of titin stiffness, deduced from the passive force-SL relation and single molecule mechanics, are much smaller than what is required to avoid the development of large inhomogeneities among sarcomeres. In this work, using 4 kHz stiffness measurements on a population of sarcomeres selected along an intact fibre isolated from frog skeletal muscle contracting at different SLs (temperature 4°C), we measure the undamped stiffness of an I-band spring that at SL > 2.7 µm attains a maximum constant value of ∼6 pN nm-1 per half-thick filament, two orders of magnitude larger than expected from titin-related passive force. We conclude that a titin-like dynamic spring in the I-band, made by an undamped elastic element in-series with damped elastic elements, adapts its length to the SL with kinetics that provide force balancing among serially linked sarcomeres during contraction. In this way, the I-band spring plays a fundamental role in preventing the development of SL inhomogeneity.

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

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

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.

Thick-Filament Extensibility in Intact Skeletal Muscle

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

The force and stiffness of myosin motors in the isometric twitch of a cardiac trabecula and the effect of the extracellular calcium concentration

KEY POINTS

Fast sarcomere-level mechanics in intact trabeculae, which allows the definition of the mechano-kinetic properties of cardiac myosin in situ, is a fundamental tool not only for understanding the molecular mechanisms of heart performance and regulation, but also for investigating the mechanisms of the cardiomyopathy-causing mutations in the myosin and testing small molecules for therapeutic interventions. The approach has been applied to measure the stiffness and force of the myosin motor and the fraction of motors attached during isometric twitches of electrically paced trabeculae under different extracellular Ca2+ concentrations. Although the average force of the cardiac myosin motor (∼6 pN) is similar to that of the fast myosin isoform of skeletal muscle, the stiffness (1.07 pN nm-1 ) is 2- to 3-fold smaller. The increase in the twitch force developed in the presence of larger extracellular Ca2+ concentrations is fully accounted for by a proportional increase in the number of attached motors.

ABSTRACT

The mechano-kinetic properties of the cardiac myosin were studied in situ, in trabeculae dissected from the right ventricle of the rat heart, by measuring the stiffness of the half-sarcomere both at the twitch force peak (Tp ) of an electrically paced intact trabecula at different extracellular Ca2+ concentrations ([Ca2+ ]o ), and in the same trabecula after skinning and induction of rigor. Taking into account the contribution of filament compliance to half-sarcomere compliance and the lattice geometry, we found that the stiffness of the cardiac myosin motor is 1.07 ± 0.09 pN nm-1 , which is slightly larger than that of the slow myosin isoform of skeletal muscle (0.6-0.8 pN nm-1 ) and 2- to 3-fold smaller than that of the fast skeletal muscle isoform. The increase in Tp from 61 ± 4 kPa to 93 ± 9 kPa, induced by raising [Ca2+ ]o from 1 to 2.5 mm at sarcomere length ∼2.2 μm, is accompanied by an increase of the half-sarcomere stiffness that is explained by an increase of the fraction of actin-attached motors from 0.08 ± 0.01 to 0.12 ± 0.02, proportional to Tp . Consequently, each myosin motor bears an average force of 6.14 ± 0.52 pN independently of Tp and [Ca2+ ]o . The application of fast sarcomere-level mechanics to intact trabeculae to define the mechano-kinetic properties of the cardiac myosin in situ represents a powerful tool for investigating cardiomyopathy-causing mutations in the myosin motor and testing specific therapeutic interventions.

Effects of myosin inhibitors on the X-ray diffraction patterns of relaxed and calcium-activated rabbit skeletal muscle fibers

We studied the effect of myosin inhibitors, N-benzyl-p-toluenesulfonamide (BTS), blebbistatin, and butanedione monoxime (BDM) on X-ray diffraction patterns from rabbit psoas fibers under relaxing and contracting conditions. The first two inhibitors suppressed the contractile force almost completely at a 100 μM concentration, and a similar effect was obtained at 50 mM for BDM. However, still substantial changes were observed in the diffraction patterns upon calcium-activation of inhibited muscle fibers. (1) The 2nd actin layer-line reflection was enhanced normally, indicating that calcium binding to troponin and the subsequent movement of tropomyosin are not inhibited, (2) the myosin layer-line reflections became much weaker, and (3) the 1,1/1,0 intensity ratio of the equatorial reflections was increased. The observations (2) and (3) indicate that, even in the presence of the inhibitors at a saturating concentration, myosin heads leave the helix on the thick filaments and approach the thin filaments. Interestingly, the d1,0 spacing of the filament lattice remained unchanged upon activation of inhibited fibers, in contrast to the case of normal activation in which the spacing is decreased. This suggests that the normal activated myosin heads exert a pull in both axial and radial directions, but in the presence of the inhibitors, the pull is suppressed, and as a result, the heads simply bind to actin without exerting any force. The results support the idea that the inhibitors do not block the myosin binding to actin, but block the step of force-producing transition of the bound actomyosin complex.

Mechanical parameters of the molecular motor myosin II determined in permeabilised fibres from slow and fast skeletal muscles of the rabbit

KEY POINTS

The different performance of slow and fast muscles is mainly attributed to diversity of the myosin heavy chain (MHC) isoform expressed within them. In this study fast sarcomere-level mechanics has been applied to Ca²⁺ -activated single permeabilised fibres isolated from soleus (containing the slow myosin isoform) and psoas (containing the fast myosin isoform) muscles of rabbit for a comparative definition of the mechano-kinetics of force generation by slow and fast myosin isoforms in situ. The stiffness and the force of the slow myosin isoform are three times smaller than those of the fast isoform, suggesting that the stiffness of the myosin motor is a determinant of the isoform-dependent functional diversity between skeletal muscles. These results open the question of the mechanism that can reconcile the reduced performance of the slow MHC with the higher efficiency of the slow muscle.

ABSTRACT

The skeletal muscle exhibits large functional differences depending on the myosin heavy chain (MHC) isoform expressed in its molecular motor, myosin II. The differences in the mechanical features of force generation by myosin isoforms were investigated in situ by using fast sarcomere-level mechanical methods in permeabilised fibres (sarcomere length 2.4 μm, temperature 12°C, 4% dextran T-500) from slow (soleus, containing the MHC-1 isoform) and fast (psoas, containing the MHC-2X isoform) skeletal muscle of the rabbit. The stiffness of the half-sarcomere was determined at the plateau of Ca²⁺ -activated isometric contractions and in rigor and analysed with a model that accounted for the filament compliance to estimate the stiffness of the myosin motor (ε). ε was 0.56 ± 0.04 and 1.70 ± 0.37 pN nm^-1 for the slow and fast isoform, respectively, while the average strain per attached motor (s₀ ) was similar (∼3.3 nm) in both isoforms. Consequently the force per motor (F₀  = εs₀ ) was three times smaller in the slow isoform than in the fast isoform (1.89 ± 0.43 versus 5.35 ± 1.51 pN). The fraction of actin-attached motors responsible for maximum isometric force at saturating Ca²⁺ (T_0,4.5 ) was 0.47 ± 0.09 in soleus fibres, 70% larger than that in psoas fibres (0.29 ± 0.08), so that F₀ in slow fibres was decreased by only 53%. The lower stiffness and force of the slow myosin isoform open the question of the molecular basis of the higher efficiency of slow muscle with respect to fast muscle.

Phosphate increase during fatigue affects crossbridge kinetics in intact mouse muscle at physiological temperature

KEY POINTS

Actomyosin ATP hydrolysis occurring during muscle contraction releases inorganic phosphate [P_i ] in the myoplasm. High [P_i ] reduces force and affects force kinetics in skinned muscle fibres at low temperature. These effects decrease at high temperature, raising the question of their importance under physiological conditions. This study provides the first analysis of the effects of P_i on muscle performance in intact mammalian fibres at physiological temperature. Myoplasmic [P_i ] was raised by fatiguing the fibres with a series of tetanic contractions. [P_i ] increase reduces muscular force mainly by decreasing the force of the single molecular motor, the crossbridge, and alters the crossbridge response to fast length perturbation indicating faster kinetics. These results are in agreement with schemes of actomyosin ATPase and the crossbridge cycle including a low- or no-force state and show that fibre length changes perturb the P_i -sensitive force generation of the crossbridge cycle.

ABSTRACT

Actomyosin ATP hydrolysis during muscle contraction releases inorganic phosphate, increasing [P_i ] in the myoplasm. Experiments in skinned fibres at low temperature (10-12°C) have shown that [P_i ] increase depresses isometric force and alters the kinetics of actomyosin interaction. However, the effects of P_i decrease with temperature and this raises the question of the role of P_i under physiological conditions. The present experiments were performed to investigate this point. Intact fibre bundles isolated from the flexor digitorum brevis of C57BL/6 mice were stimulated with a series of tetanic contractions at 1.5 s intervals at 33°C. As show previously the most significant change induced by a bout of contractile activity similar to the initial 10 tetani of the series was an increase of [P_i ] without significant Ca²⁺ or pH changes. Measurements of force, stiffness and responses to fast stretches and releases were therefore made on the 10th tetanus of the series and compared with control. We found that (i) tetanic force at the 10th tetanus was ∼20% smaller than control without a significant decrease of crossbridge stiffness; and (ii) the force recovery following quick stretches and releases was faster than in control. These results indicate that at physiological temperature the increase of [P_i ] occurring during early fatigue reduces tetanic force mainly by depressing the individual crossbridge force and accelerating crossbridge kinetics.

Residual Force Enhancement Following Eccentric Contractions: A New Mechanism Involving Titin

Eccentric muscle properties are not well characterized by the current paradigm of the molecular mechanism of contraction: the cross-bridge theory. Findings of force contributions by passive structural elements a decade ago paved the way for a new theory. Here, we present experimental evidence and theoretical support for the idea that the structural protein titin contributes to active force production, thereby explaining many of the unresolved properties of eccentric muscle contraction.

Non-crossbridge stiffness in active muscle fibres

Stretching of an activated skeletal muscle induces a transient tension increase followed by a period during which the tension remains elevated well above the isometric level at an almost constant value. This excess of tension in response to stretching has been called 'static tension' and attributed to an increase in fibre stiffness above the resting value, named 'static stiffness'. This observation was originally made, by our group, in frog intact muscle fibres and has been confirmed more recently, by us, in mammalian intact fibres. Following stimulation, fibre stiffness starts to increase during the latent period well before crossbridge force generation and it is present throughout the whole contraction in both single twitches and tetani. Static stiffness is dependent on sarcomere length in a different way from crossbridge force and is independent of stretching amplitude and velocity. Static stiffness follows a time course which is distinct from that of active force and very similar to the myoplasmic calcium concentration time course. We therefore hypothesize that static stiffness is due to a calcium-dependent stiffening of a non-crossbridge sarcomere structure, such as the titin filament. According to this hypothesis, titin, in addition to its well-recognized role in determining the muscle passive tension, could have a role during muscle activity.

S1P3 receptor influences key physiological properties of fast-twitch extensor digitorum longus muscle

To examine the role of sphingosine 1-phosphate (S1P) receptor 3 (S1P3) in modulating muscle properties, we utilized transgenic mice depleted of the receptor. Morphological analyses of extensor digitorum longus (EDL) muscle did not show evident differences between wild-type and S1P3-null mice. The body weight of 3-mo-old S1P3-null mice and the mean cross-sectional area of transgenic EDL muscle fibers were similar to those of wild-type. S1P3 deficiency enhanced the expression level of S1P1 and S1P2 receptors mRNA in S1P3-null EDL muscle. The contractile properties of S1P3-null EDL diverge from those of wild-type, largely more fatigable and less able to recover. The absence of S1P3 appears responsible for a lower availability of calcium during fatigue. S1P supplementation, expected to stimulate residual S1P receptors and signaling, reduced fatigue development of S1P3-null muscle. Moreover, in the absence of S1P3, denervated EDL atrophies less than wild-type. The analysis of atrophy-related proteins in S1P3-null EDL evidences high levels of the endogenous regulator of mitochondria biogenesis peroxisome proliferative-activated receptor-γ coactivator 1α (PGC-1α); preserving mitochondria could protect the muscle from disuse atrophy. In conclusion, the absence of S1P3 makes the muscle more sensitive to fatigue and slows down atrophy development after denervation, indicating that S1P3 is involved in the modulation of key physiological properties of the fast-twitch EDL muscle.

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.

High ionic strength depresses muscle contractility by decreasing both force per cross-bridge and the number of strongly attached cross-bridges

An increase in ionic strength (IS) lowers Ca(2+) activated tension in muscle fibres, however, its molecular mechanism is not well understood. In this study, we used single rabbit psoas fibres to perform sinusoidal analyses. During Ca(2+) activation, the effects of ligands (ATP, Pi, and ADP) at IS ranging 150-300 mM were studied on three rate constants to characterize elementary steps of the cross-bridge cycle. The IS effects were studied because a change in IS modifies the inter- and intra-molecular interactions, hence they may shed light on the molecular mechanisms of force generation. Both the ATP binding affinity (K1) and the ADP binding affinity (K 0) increased to 2-3x, and the Pi binding affinity (K5) decreased to 1/2, when IS was raised from 150 to 300 mM. The effect on ATP/ADP can be explained by stereospecific and hydrophobic interaction, and the effect on Pi can be explained by the electrostatic interaction with myosin. The increase in IS increased cross-bridge detachment steps (k2 and k-4), indicating that electrostatic repulsion promotes these steps. However, IS did not affect attachment steps (k-2 and k4). Consequently, the equilibrium constant of the detachment step (K2) increased by ~100%, and the force generation step (K4) decreased by ~30%. These effects together diminished the number of force-generating cross-bridges by 11%. Force/cross-bridge (T56) decreased by 26%, which correlates well with a decrease in the Debye length that limits the ionic atmosphere where ionic interactions take place. We conclude that the major effect of IS is a decrease in force/cross-bridge, but a decrease in the number of force generating cross-bridge also takes place. The stiffness during rigor induction did not change with IS, demonstrating that in-series compliance is not much affected by IS.

Force enhancement after stretch in mammalian muscle fiber: no evidence of cross-bridge involvement

Stretching of activated skeletal muscles induces a force increase above the isometric level persisting after stretch, known as residual force enhancement (RFE). RFE has been extensively studied; nevertheless, its mechanism remains debated. Unlike previous RFE studies, here the excess of force after stretch, termed static tension (ST), was investigated with fast stretches (amplitude: 3-4% sarcomere length; duration: 0.6 ms) applied at low tension during the tetanus rise in fiber bundles from flexor digitorum brevis (FDB) mouse muscle at 30°C. ST was measured at sarcomere length between 2.6 and 4.4 μm in normal and N-benzyl-p-toluene sulphonamide (BTS)-added (10 μM) Tyrode solution. The results showed that ST has the same characteristics and it is equivalent to RFE. ST increased with sarcomere length, reached a peak at 3.5 μm, and decreased to zero at ∼4.5 μm. At 4 μm, where active force was zero, ST was still 50% of maximum. BTS reduced force by ∼75% but had almost no effect on ST. Following stimulation, ST developed earlier than force, with a time course similar to internal Ca(2+) concentration: it was present 1 ms after the stimulus, at zero active force, and peaked at ∼3-ms delay. At 2.7 μm, activation increased the passive sarcomere stiffness by a factor of ∼7 compared with the relaxed state All our data indicate that ST, or RFE, is independent of the cross-bridge presence and it is due to the Ca(2+)-induced stiffening of a sarcomeric structure identifiable with titin.

Phosphate and acidosis act synergistically to depress peak power in rat muscle fibers

Skeletal muscle fatigue is characterized by the buildup of H(+) and inorganic phosphate (Pi), metabolites that are thought to cause fatigue by inhibiting muscle force, velocity, and power. While the individual effects of elevated H(+) or Pi have been well characterized, the effects of simultaneously elevating the ions, as occurs during fatigue in vivo, are still poorly understood. To address this, we exposed slow and fast rat skinned muscle fibers to fatiguing levels of H(+) (pH 6.2) and Pi (30 mM) and determined the effects on contractile properties. At 30°C, elevated Pi and low pH depressed maximal shortening velocity (Vmax) by 15% (4.23 to 3.58 fl/s) in slow and 31% (6.24 vs. 4.55 fl/s) in fast fibers, values similar to depressions from low pH alone. Maximal isometric force dropped by 36% in slow (148 to 94 kN/m(2)) and 46% in fast fibers (148 to 80 kN/m(2)), declines substantially larger than what either ion exerted individually. The strong effect on force combined with the significant effect on velocity caused peak power to decline by over 60% in both fiber types. Force-stiffness ratios significantly decreased with pH 6.2 + 30 mM Pi in both fiber types, suggesting these ions reduced force by decreasing the force per bridge and/or increasing the number of low-force bridges. The data indicate the collective effects of elevating H(+) and Pi on maximal isometric force and peak power are stronger than what either ion exerts individually and suggest the ions act synergistically to reduce muscle function during fatigue.

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.

Force produced after stretch in sarcomeres and half-sarcomeres isolated from skeletal muscles

The goal of this study was to evaluate if isolated sarcomeres and half-sarcomeres produce a long-lasting increase in force after a stretch is imposed during activation. Single and half-sarcomeres were isolated from myofibrils using micro-needles, which were also used for force measurements. After full force development, both preparations were stretched by different magnitudes. The sarcomere length (SL) or half-sarcomere length variations (HSL) were extracted by measuring the initial and final distances from the Z-line to the adjacent Z-line or to a region externally adjacent to the M-line of the sarcomere, respectively. Half-sarcomeres generated approximately the same amount of isometric force (29.0 ± SD 15.5 nN·μm⁻²) as single sarcomeres (32.1 ± SD 15.3 nN·μm⁻²) when activated. In both cases, the steady-state forces after stretch were higher than the forces during isometric contractions at similar conditions. The results suggest that stretch-induced force enhancement is partly caused by proteins within the half-sarcomere.

The non-linear elasticity of the muscle sarcomere and the compliance of myosin motors

Force in striated muscle is due to attachment of the heads of the myosin, the molecular motors extending from the myosin filament, to the actin filament in each half-sarcomere, the functional unit where myosin motors act in parallel. Mechanical and X-ray structural evidence indicates that at the plateau of isometric contraction (force T0), less than half of the elastic strain of the half-sarcomere is due to the strain in the array of myosin motors (s), with the remainder being accounted for by the compliance of filaments acting as linear elastic elements in series with the motor array. Early during the development of isometric force, however, the half-sarcomere compliance has been found to be less than that expected from the linear elastic model assumed above, and this non-linearity may affect the estimate of s. This question is investigated here by applying nanometre-microsecond-resolution mechanics to single intact fibres from frog skeletal muscle at 4 °C, to record the mechanical properties of the half-sarcomere throughout the development of force in isometric contraction. The results are interpreted with mechanical models to estimate the compliance of the myosin motors. Our conclusions are as follows: (i) early during the development of an isometric tetanus, an elastic element is present in parallel with the myosin motors, with a compliance of ∼200 nm MPa(-1) (∼20 times larger than the compliance of the motor array at T0); and (ii) during isometric contraction, s is 1.66 ± 0.05 nm, which is not significantly different from the value estimated with the linear elastic model.

Stiffness, working stroke, and force of single-myosin molecules in skeletal muscle: elucidation of these mechanical properties via nonlinear elasticity evaluation

In muscles, the arrays of skeletal myosin molecules interact with actin filaments and continuously generate force at various contraction speeds. Therefore, it is crucial for myosin molecules to generate force collectively and minimize the interference between individual myosin molecules. Knowledge of the elasticity of myosin molecules is crucial for understanding the molecular mechanisms of muscle contractions because elasticity directly affects the working and drag (resistance) force generation when myosin molecules are positively or negatively strained. The working stroke distance is also an important mechanical property necessary for elucidation of the thermodynamic efficiency of muscle contractions at the molecular level. In this review, we focus on these mechanical properties obtained from single-fiber and single-molecule studies and discuss recent findings associated with these mechanical properties. We also discuss the potential molecular mechanisms associated with reduction of the drag effect caused by negatively strained myosin molecules.

Force decline during fatigue is due to both a decrease in the force per individual cross-bridge and the number of cross-bridges

Fatigue occurring during exercise can be defined as the inability to maintain the initial force or power output. As fatigue becomes pronounced, force and maximum velocity of shortening are greatly reduced and force relaxation is prolonged. In principle, force loss during fatigue can result from a decrease in the number of cross-bridges generating force or a decrease of the individual cross-bridge force or to both mechanisms. The present experiments were made to investigate this point in single fibres or small fibre bundles isolated from flexor digitorum brevis (FDB) of C57BL/6 mice at 22-24◦C. During a series of 105 tetanic contractions, we measured force and fibre stiffness by applying small sinusoidal length oscillations at 2.5 or 4 kHz frequency to the activated preparation and measuring the resulting force changes. Stiffness data were corrected for the influence of compliance in series with the cross-bridge ensemble. The results show that the force decline during the first 20 tetani is due to the reduction of force developed by the individual cross-bridges and thereafter as fatigue becomes more severe, the number of cross-bridges decreases. In spite of the force reduction in the early phase of fatigue, there was an increased rate of tetanic force development and relaxation. In the latter stages of fatigue, the rate of force development and relaxation became slower. Thus, the start of fatigue is characterised by decreased cross-bridge force development and as fatigue becomes more marked, the number of cross-bridges decreases. These findings are discussed in the context of the current hypotheses about fatigue mechanisms.

Crossbridge and filament compliance in muscle: implications for tension generation and lever arm swing

The stiffness of myosin heads attached to actin is a crucial parameter in determining the kinetics and mechanics of the crossbridge cycle. It has been claimed that the stiffness of myosin heads in the anterior tibialis muscle of the common frog (Rana temporaria) is as high as 3.3 pN/nm, substantially higher than its value in rabbit muscle (~1.7 pN/nm). However, the crossbridge stiffness measurement has a large error since the contribution of crossbridges to half-sarcomere compliance is obtained by subtracting from the half-sarcomere compliance the contributions of the thick and thin filaments, each with a substantial error. Calculation of its value for isometric contraction also depends on the fraction of heads that are attached, for which there is no consensus. Surprisingly, the stiffness of the myosin head from the edible frog, Rana esculenta, determined in the same manner, is only 60% of that in Rana temporaria. In our view it is unlikely that the value of such a crucial parameter could differ so substantially between two frog species. Since the means of the myosin head stiffness in these two species are not significantly different, we suggest that the best estimate of the stiffness of the myosin heads for frog muscle is the average of these data, a value similar to that for rabbit muscle. This would allow both frog and rabbit muscles to operate the same low-cooperativity mechanism for the crossbridge cycle with only one or two tension-generating steps. We review evidence that much of the compliance of the myosin head is located in the pliant region where the lever arm emerges from the converter and propose that tension generation ("tensing") caused by the rotation and movement of the converter is a separate event from the passive swinging of the lever arm in its working stroke in which the strain energy stored in the pliant region is used to do work.

Effects of blebbistatin and Ca2+ concentration on force produced during stretch of skeletal muscle fibers

When activated muscle fibers are stretched at low speeds [≤2 optimal length ( Lo)/s], force increases in two phases, marked by a change in slope [critical force (Pc)] that happens at a critical sarcomere length extension ( Lc). Some studies attribute Pc to the number of attached cross bridges before stretch, while others attribute it to cross bridges in a pre-power-stroke state. In this study, we reinvestigated the mechanisms of forces produced during stretch by altering either the number of cross bridges attached to actin or the cross-bridge state before stretch. Two sets of experiments were performed: 1) activated fibers were stretched by 3% Lo at speeds of 1.0, 2.0, and 3.0 Lo/s in different pCa2+ (4.5, 5.0, 5.5, 6.0), or 2) activated fibers were stretched by 3% Lo at 2 Lo/s in pCa2+ 4.5 containing either 5 μM blebbistatin(+/−) or its inactive isomer (+/+). All stretches started at a sarcomere length (SL) of 2.5 μm. When fibers were activated at a pCa2+ of 4.5, Pc was 2.47 ± 0.11 maximal force developed before stretch (Po) and decreased with lower concentrations of Ca2+. Lc was not Ca2+ dependent; the pooled experiments provided a Lc of 14.34 ± 0.34 nm/half-sarcomere (HS). Pc and Lc did not change with velocities of stretch. Fibers activated in blebbistatin(+/−) showed a higher Pc (2.94 ± 0.17 Po) and Lc (16.30 ± 0.38 nm/HS) than control fibers (Pc 2.31 ± 0.08 Po; Lc 14.05 ± 0.63 nm/HS). The results suggest that forces produced during stretch are caused by both the number of cross bridges attached to actin and the cross bridges in a pre-power-stroke state. Such cross bridges are stretched by large amplitudes before detaching from actin and contribute significantly to the force developed during stretch.

Force and power generating mechanism(s) in active muscle as revealed from temperature perturbation studies

The basic characteristics of the process of force and power generation in active muscle that have emerged from temperature studies are examined. This is done by reviewing complementary findings from temperature-dependence studies and rapid temperature-jump (T-jump) experiments and from intact and skinned fast mammalian muscle fibres. In isometric muscle, a small T-jump leads to a characteristic rise in force showing that crossbridge force generation is endothermic (heat absorbed) and associated with increased entropy (disorder). The sensitivity of the T-jump force generation to added inorganic phosphate (Pi) indicates that a T-jump enhances an early step in the actomyosin (crossbridge) ATPase cycle before Pi-release. During muscle lengthening when steady force is increased, the T-jump force generation is inhibited. Conversely, during shortening when steady force is decreased, the T-jump force generation is enhanced in a velocity-dependent manner, showing that T-jump force generation is strain sensitive. Within the temperature range of ∼5–35◦C, the temperature dependence of steady active force is sigmoidal both in isometric and in shortening muscle. However, in shortening muscle, the endothermic character of force generation becomes more pronounced with increased velocity and this can, at least partly, account for the marked increase with warming of the mechanical power output of active muscle.

Significant impact on muscle mechanics of small nonlinearities in myofilament elasticity

Important mechanisms in muscle contraction have recently been reevaluated based on analyses that rely on the assumption of linear myofilament elasticity. However, the present theoretical study shows that nonlinearity of this elasticity, even when so minor that it may be difficult to detect in experimental data, could have great impact on the interpretation of muscle mechanical experiments. This is illustrated by using simulated stiffness and strain-versus-force data for muscle fibers shortening at different constant velocities. There is substantial quantitative agreement, for this condition, between models with distributed myofilament compliance and models where the compliance of the myofilaments and the actomyosin cross-bridges are lumped together into two separate elastic elements acting in series. The data thus support the usefulness of the latter, simpler, type of model in the analysis. However, most importantly, the data emphasize the importance of caution before reevaluating fundamental mechanisms of muscle contraction based on analyses relying on the assumption of linear myofilament elasticity.