Mechanism of force enhancement during stretching of skeletal muscle fibres investigated by high time-resolved stiffness measurements

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

Simple Summary

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

Abstract

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

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.

Development of a transient thrust stand with sub-millisecond resolution

A transient thrust stand has been developed to offer 0.1 ms time-resolved force measurements up to 22 N. The system uses a predictor-based subspace system identification (PBSID) algorithm to obtain a high order state space model of the thrust stand. The state space model defines high-frequency vibration modes within the thrust stand. The high-frequency vibration modes are necessary to provide the time response of 0.1 ms. Thruster forces are then estimated using an augmented Kalman filter (AKF) to combine sensor traces from four accelerometers, a velocity sensor, and a displacement transducer. Fusing low-frequency displacement data with high-frequency acceleration measurements provides accurate force data from 0 kHz to 10 kHz. Combining the AKF with the PBSID state space model inherently attenuates external noise sources such as pumps. The transient thrust stand uses a torsional configuration to minimize influence from external vibrations and achieve high force resolution independent of thruster weight. Results demonstrated that the system was capable of obtaining dynamic thrust profiles with less than 5% error and a time resolution of 0.1 ms. To date, no thrust stand is capable of measuring up to 22 N forces with a time response of 10 kHz.

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.

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.

Cross-bridge mechanism of residual force enhancement after stretching in a skeletal muscle

A muscle model that uses a modified Langevin equation with actomyosin potentials was used to describe the residual force enhancement after active stretching. Considering that the new model uses cross-bridge theory to describe the residual force enhancement, it is different from other models that use passive stretching elements. Residual force enhancement was simulated using a half sarcomere comprising 100 myosin molecules. In this paper, impulse is defined as the integral of an excess force from the steady isometric force over the time interval for which a stretch is applied. The impulse was calculated from the force response due to fast and slow muscle stretches to demonstrate the viscoelastic property of the cross-bridges. A cross-bridge mechanism was proposed as a way to describe the residual force enhancement on the basis of the impulse results with reference to the compliance of the actin filament. It was assumed that the period of the actin potential increased by 0.5% and the amplitude of the potential decreased by 0.5% when the half sarcomere was stretched by 10%. The residual force enhancement after 21.0% sarcomere stretching was 6.9% of the maximum isometric force of the muscle; this value was due to the increase in the number of cross-bridges.

Reinterpretation of the Tension Response of Muscle to Stretches and Releases

We have reexamined the experimental time courses of tension in frog muscle after rapid length steps. The early tension recoveries are biexponential. After 3 nm/hs stretches and releases, the rates of the immediate rapid tension changes are similar but the subsequent tension fall after a stretch is much slower than the rise after a release. After 1.5 nm/hs length steps, the entire tension responses are more nearly mirror images. To identify the underlying processes, we used a model of the muscle cross-bridge cycle with two tension-generating (tensing) steps. Analysis of the time course of the tension, the rates of the steps in the cycle, and their contributions to tension provided insights into previously puzzling features of the experimental response. After a stretch, the initial rapid tension fall in the model is caused principally by the reversal of the first tensing step, but after a few milliseconds the tensing step resumes its forward direction. We conclude that the remaining response should not be included in phase 2, the period of early tension recovery. With this exclusion, T₂, the tension at the end of this period, rises with an increase of stretch. The rate of early tension recovery also increases with stretch size, showing that the reversal of the first tensing step is strain sensitive. After small length steps, the fast and slow components of the early tension recovery are both caused mainly by the first tensing step. The fast component is triggered by the initial sliding of the filaments, and the slow component is due to further sliding that occurs as the tension recovers. With small length steps (<0.5 nm/hs), the time course of the response to a stretch is the reverse of that to a release.

Active shortening protects against stretch-induced force deficits in human skeletal muscle

Skeletal muscle contraction results from molecular interactions of myosin "crossbridges" with adjacent actin filament binding sites. The binding of myosin to actin can be "weak" or "strong," and only strong binding states contribute to force production. During active shortening, the number of strongly bound crossbridges declines with increasing shortening velocity. Forcibly stretching a muscle that is actively shortening at high velocity results in no apparent negative consequences, whereas stretch of an isometrically (fixed-length) contracting muscle causes ultrastructural damage and a decline in force-generating capability. Our working hypothesis is that stretch-induced damage is uniquely attributable to the population of crossbridges that are strongly bound. We tested the hypothesis that stretch-induced force deficits decline as the prevailing shortening velocity is increased. Experiments were performed on permeabilized segments of individual skeletal muscle fibers obtained from human subjects. Fibers were maximally activated and allowed either to generate maximum isometric force (Fo), or to shorten at velocities that resulted in force maintenance of ≈50% Fo or ≈2% Fo For each test condition, a rapid stretch equivalent to 0.1 × optimal fiber length was applied. Relative to prestretch Fo, force deficits resulting from stretches applied during force maintenance of 100, ≈50, and ≈2% Fo were 23.2 ± 8.6, 7.8 ± 4.2, and 0.3 ± 3.3%, respectively (means ± SD, n = 20). We conclude that stretch-induced damage declines with increasing shortening velocity, consistent with the working hypothesis that the fraction of strongly bound crossbridges is a causative factor in the susceptibility of skeletal muscle to stretch-induced damage.NEW & NOTEWORTHY Force deficits caused by stretch of contracting muscle are most severe when the stretch is applied during an isometric contraction, but prevented if the muscle is shortening at high velocity when the stretch occurs. This study indicates that velocity-controlled modulation of the number of strongly bound crossbridges is the basis for the observed relationship between stretch-induced muscle damage and prevailing shortening velocity.

Muscle and Limb Mechanics

Understanding of the musculoskeletal system has evolved from the collection of individual phenomena in highly selected experimental preparations under highly controlled and often unphysiological conditions. At the systems level, it is now possible to construct complete and reasonably accurate models of the kinetics and energetics of realistic muscles and to combine them to understand the dynamics of complete musculoskeletal systems performing natural behaviors. At the reductionist level, it is possible to relate most of the individual phenomena to the anatomical structures and biochemical processes that account for them. Two large challenges remain. At a systems level, neuroscience must now account for how the nervous system learns to exploit the many complex features that evolution has incorporated into muscle and limb mechanics. At a reductionist level, medicine must now account for the many forms of pathology and disability that arise from the many diseases and injuries to which this highly evolved system is inevitably prone. © 2017 American Physiological Society. Compr Physiol 7:429-462, 2017.

Possible Cause of Nonlinear Tension Rise in Activated Muscle Fiber during Stretching

Tension in contracting muscle fiber under conditions of ramp stretching rapidly increases, but after reaching a critical stretch P_c sharply decreases. To find out the cause of these changes in muscle fiber tension, we stopped stretching before and after reaching P_c and left the fiber stretched for 50 msec. After rapid tension drop, the transient tension rise not accompanied by fiber stiffness increase was observed only in fibers heated to 25°C and stretched to P_c. Under other experimental conditions, this growth was absent. We suppose that stretch of the fiber to P_c induces transition of stereo-specifically attached myosin heads to pre-power stroke state and when the stretching is stopped, they make their step on actin and generate force. When the tension reaches P_c, all stereospecifically attached myosin heads turn out to be non-stereospecifically, or weakly attached to actin, and are unable to make the force-generating step.

MgADP activation contributes to force enhancement during fast stretch of isolated skeletal myofibrils

BACKGROUND

When an activated muscle is rapidly stretched, force rises and peaks while muscle lengthens. The peak force is normally called critical-force (Pc). The mechanism behind this increase in force is not well understood, but it has been associated with crossbridges operating in different states.

METHODS

Myofibrils were attached between a cantilever and a micro-needle, and activated with Ca(2+) or MgADP. During activation, the myofibrils were stretched by 3% SLo at 10 SLo·s(-1). A crossbridge model was developed to better understand the effects of MgADP in myofibrils activation.

RESULTS

Despite a similar stretch magnitude, MgADP activation produced a higher Pc (1.37 ± 0.07 P/Po) than Ca(2+) activation (Pc = 1.23 ± 0.03 P/Po). These results suggest that myofibrils activated with MgADP become stiffer than myofibrils activated with Ca(2+).

CONCLUSIONS

MgADP induces a fraction of crossbridges to form a "rigor-like" state that precedes ADP release, and that may not contribute to isometric forces. Such interpretation was strengthened by the results obtained with the developed crossbridge model, which showed that MgADP bias crossbridges into the rigor-like state. This state would be crucial to initiate a cooperative activation of crossbridges and actin, and to resist to unbinding from actin when the myofibrils are stretched.

SIGNIFICANCE

Our results suggest a new mechanism contributing for force output during stretch, which underlies basic mechanisms of 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.

Index of mechanical efficiency in competitive and recreational long distance runners

The purpose of this investigation was to compare external work and net energy expenditure during a bout of repetitive stretch-shortening cycles between competitive and recreational long-distance runners. Participants were divided into either competitive or recreational runners based on their maximal oxygen consumption and self-reported 1600 m times. The stretch-shortening cycle involved a repetitive hopping protocol on a force plate while measuring oxygen consumption and lactate accumulation for a total of 10 min. External work and net energy expenditure were calculated for 3 min after steady state was achieved and the ratio between these variables was utilised as an index of mechanical efficiency. Lower extremity stiffness was calculated during this interval as well. Net energy expenditure was significantly lower in competitive runners (152.6 ± 33.3 kJ) in comparison to recreational runners (200.6 ± 41.4 kJ) (P = 0.02) given similar amounts of external work performed in both groups (competitive runners = 65.6 ± 20.1 kJ, recreational runners = 68.8 ± 12.1 kJ) (P = 0.67). Index of mechanical efficiency was significantly different between competitive runners (43.2 ± 9.0%) and recreational runners (34.8 ± 5.3%) (P = 0.03). No significant differences were found in lower extremity stiffness (P = 0.64). Competitive distance runners can perform similar levels of external work with lower net energy expenditure and thus a higher index of mechanical efficiency during repetitive stretch-shortening cycles in comparison to recreational runners with similar values of lower extremity stiffness. This ability could possibly be due differences in muscle-tendon length changes, muscle pre-activation, cross-bridge potentiation and short-latency reflex responses as a result of training which should be considered for future investigation.

A re-interpretation of the rate of tension redevelopment (k(TR)) in active muscle

A slackening to zero tension by large length release (~20%) and a restretch of active muscle fibres cause a fall and a redevelopment in tension. According to the model of Brenner (Proc Natl Acad Sci USA 85(9):3265-3269, 1988), the rate constant of tension redevelopment (k TR) is the sum of attachment and detachment rate constants, hence is limited by the fast reaction. Here we propose a model in which, after restretch, cross-bridges cycle many times by stretching series elastic elements, hence k(TR) is limited by a slow reaction. To set up this model, we made an assumption that the stepping rate (v) decreases linearly with tension (F), which is consistent with the Fenn effect. The distance traveled by a cross-bridge stretches series elastic elements with stiffness σ. With these assumptions, we set up a first order differential equation, which results in an exponential time course with the rate constant k(TR) = ση(0)ν(0)(1 - λ)/F(1), where λ = ν(1)/ν(0), η = step size, the subscript 0 indicates unloaded condition, and the subscript 1 indicate isometric condition. We demonstrate that the ATP hydrolysis rate (=[myosin head]/ν(0)) is proportionate to k(TR) as the ambient temperature is changed, and that the published data fit to this relationship well if λ = 0.28. We conclude that k(TR) is limited by the cross-bridge turnover rate; hence it represents the rate constant of the slowest reaction of the cross-bridge cycle, i.e. the ADP isomerization step before ADP is released.

Effect of temperature on crossbridge force changes during fatigue and recovery in intact mouse muscle fibers

Repetitive or prolonged muscle contractions induce muscular fatigue, defined as the inability of the muscle to maintain the initial tension or power output. In the present experiments, made on intact fiber bundles from FDB mouse, fatigue and recovery from fatigue were investigated at 24°C and 35°C. Force and stiffness were measured during tetani elicited every 90 s during the pre-fatigue control phase and recovery and every 1.5 s during the fatiguing phase made of 105 consecutive tetani. The results showed that force decline could be split in an initial phase followed by a later one. Loss of force during the first phase was smaller and slower at 35°C than at 24°C, whereas force decline during the later phase was greater at 35°C so that total force depression at the end of fatigue was the same at both temperatures. The initial force decline occurred without great reduction of fiber stiffness and was attributed to a decrease of the average force per attached crossbridge. Force decline during the later phase was accompanied by a proportional stiffness decrease and was attributed to a decrease of the number of attached crossbridge. Similarly to fatigue, at both 24 and 35°C, force recovery occurred in two phases: the first associated with the recovery of the average force per attached crossbridge and the second due to the recovery of the pre-fatigue attached crossbridge number. These changes, symmetrical to those occurring during fatigue, are consistent with the idea that, i) initial phase is due to the direct fast inhibitory effect of [Pi]i increase during fatigue on crossbridge force; ii) the second phase is due to the delayed reduction of Ca(2+) release and /or reduction of the Ca(2+) sensitivity of the myofibrils due to high [Pi]i.

A cross-bridge cycle with two tension-generating steps simulates skeletal muscle mechanics

We examined whether cross-bridge cycle models with one or two tension-generating steps can account for the force-velocity relation of and tension response to length steps of frog skeletal muscle. Transition-state theory defined the strain dependence of the rate constants. The filament stiffness was non-Hookean. Models were refined against experimental data by simulated annealing and downhill simplex runs. Models with one tension-generating step were rejected, as they had a low efficiency and fitted the experimental data relatively poorly. The best model with two tension-generating steps (stroke distances 5.6 and 4.6 nm) and a cross-bridge stiffness of 1.7 pN/nm gave a good account of the experimental data. The two tensing steps allow an efficiency of up to 38% during shortening. In an isometric contraction, 54.7% of the attached heads were in a pre-tension-generating state, 44.5% of the attached heads had undergone the first tension-generating step, and only 0.8% had undergone both tension-generating steps; they bore 34%, 64%, and 2%, respectively, of the isometric tension. During slow shortening, the second tensing step made a greater contribution. During lengthening, up to 93% of the attached heads were in a pre-tension-generating state yet bore elevated tension by being dragged to high strains before detaching.