Non-linear myofilament elasticity in frog intact muscle fibres

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.

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.

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.

Temperature Effects on Force and Actin⁻Myosin Interaction in Muscle: A Look Back on Some Experimental Findings

Observations made in temperature studies on mammalian muscle during force development, shortening, and lengthening, are re-examined. The isometric force in active muscle goes up substantially on warming from less than 10 °C to temperatures closer to physiological (>30 °C), and the sigmoidal temperature dependence of this force has a half-maximum at ~10 °C. During steady shortening, when force is decreased to a steady level, the sigmoidal curve is more pronounced and shifted to higher temperatures, whereas, in lengthening muscle, the curve is shifted to lower temperatures, and there is a less marked increase with temperature. Even with a small rapid temperature-jump (T-jump), force in active muscle rises in a definitive way. The rate of tension rise is slower with adenosine diphosphate (ADP) and faster with increased phosphate. Analysis showed that a T-jump enhances an early, pre-phosphate release step in the acto-myosin (crossbridge) ATPase cycle, thus inducing a force-rise. The sigmoidal dependence of steady force on temperature is due to this endothermic nature of crossbridge force generation. During shortening, the force-generating step and the ATPase cycle are accelerated, whereas during lengthening, they are inhibited. The endothermic force generation is seen in different muscle types (fast, slow, and cardiac). The underlying mechanism may involve a structural change in attached myosin heads and/or their attachments on heat absorption.

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

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

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.

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.

Adaptation of active tone in the mouse descending thoracic aorta under acute changes in loading

Arteries can adapt to sustained changes in blood pressure and flow, and it is thought that these adaptive processes often begin with an altered smooth muscle cell activity that precedes any detectable changes in the passive wall components. Yet, due to the intrinsic coupling between the active and passive properties of the arterial wall, it has been difficult to delineate the adaptive contributions of active smooth muscle. To address this need, we used a novel experimental-computational approach to quantify adaptive functions of active smooth muscle in arterial rings excised from the proximal descending thoracic aorta of mice and subjected to short-term sustained circumferential stretches while stimulated with various agonists. A new mathematical model of the adaptive processes was derived and fit to data to describe and predict the effects of active tone adaptation. It was found that active tone was maintained when the artery was adapted close to the optimal stretch for maximal active force production, but it was reduced when adapted below the optimal stretch; there was no significant change in passive behavior in either case. Such active adaptations occurred only upon smooth muscle stimulation with phenylephrine, however, not stimulation with KCl or angiotensin II. Numerical simulations using the proposed model suggested further that active tone adaptation in vascular smooth muscle could play a stabilizing role for wall stress in large elastic arteries.

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.

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.

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.

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.

The Huxley-Simmons manoeuvre: is still lacking the experimental evidence that the quick release is a pure elastic phenomenon

The analysis of the quick release is usually made by fitting a straight line to the first few experimental points of the tension-length curve. The line is then extrapolated to zero force. The fact that the tension-length curve can be represented by a straight line does not grant, however, that the quick release is a pure elastic process. As a matter of fact the experimental precision is not such to exclude a small nonlinearity from the curve and thus to mistake a visco-elastic process for an elastic one. At least two are the consequences of such a mistake: (1) stiffness is overestimated; (2) energy balance is incorrect.

Flexible mechanisms: the diverse roles of biological springs in vertebrate movement

The muscles that power vertebrate locomotion are associated with springy tissues, both within muscle and in connective tissue elements such as tendons. These springs share in common the same simple action: they stretch and store elastic strain energy when force is applied to them and recoil to release energy when force decays. Although this elastic action is simple, it serves a diverse set of functions, including metabolic energy conservation, amplification of muscle power output, attenuation of muscle power input, and rapid mechanical feedback that may aid in stability. In recent years, our understanding of the mechanisms and importance of biological springs in locomotion has advanced significantly, and it has been demonstrated that elastic mechanisms are essential for the effective function of the muscle motors that power movement. Here, we review some recent advances in our understanding of elastic mechanisms, with an emphasis on two proposed organizing principles. First, we review the evidence that the various functions of biological springs allow the locomotor system to operate beyond the bounds of intrinsic muscle properties, including metabolic and mechanical characteristics, as well as motor control processes. Second, we propose that an energy-based framework is useful for interpreting the diverse functions of series-elastic springs. In this framework, the direction and timing of the flow of energy between the body, the elastic element and the contracting muscle determine the function served by the elastic mechanism (e.g. energy conservation vs power amplification). We also review recent work demonstrating that structures such as tendons remodel more actively and behave more dynamically than previously assumed.

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.

Actomyosin-ADP states, interhead cooperativity, and the force-velocity relation of skeletal muscle

Despite intense efforts to elucidate the molecular mechanisms that determine the maximum shortening velocity and the shape of the force-velocity relationship in striated muscle, our understanding of these mechanisms remains incomplete. Here, this issue is addressed by means of a four-state cross-bridge model with significant explanatory power for both shortening and lengthening contractions. Exploration of the parameter space of the model suggests that an actomyosin-ADP state (AM( *)ADP) that is separated from the actual ADP release step by a strain-dependent isomerization is important for determining both the maximum shortening velocity and the shape of the force-velocity relationship. The model requires a velocity-dependent, cross-bridge attachment rate to account for certain experimental findings. Of interest, the velocity dependence for shortening contraction is similar to that for population of the AM( *)ADP state (with a velocity-independent attachment rate). This accords with the idea that attached myosin heads in the AM( *)ADP state position the partner heads for rapid attachment to the next site along actin, corresponding to the apparent increase in attachment rate in the model.

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.

The mechanism of the resistance to stretch of isometrically contracting single muscle fibres

Rapid attachment to actin of the detached motor domain of myosin dimers with one motor domain already attached has been hypothesized to explain the stretch-induced changes in X-ray interference and stiffness of active muscle. Here, using half-sarcomere mechanics in single frog muscle fibres (2.15 microm sarcomere length and 4 degrees C), we show that: (1) an increase in stiffness of the half-sarcomere under stretch is specific to isometric contraction and does not occur in rigor, indicating that the mechanism of stiffness increase is an increase in the number of attached motors; (2) 2 ms after 100 micros stretches (amplitude 2-8 nm per half-sarcomere) imposed during an isometric tetanus, the stiffness of the array of myosin motors in each half-sarcomere (e(m)) increases above the isometric value (e(m0)); (3) e(m) has a sigmoidal dependence on the distortion of the motor domains (Delta z) attached in isometric contraction, with a maximum approximately 2 e(m0) for a distortion of approximately 6 nm; e(m) is influenced by detachment of motors at z > 6 nm; (4) at the end of the 100 micros stretch the relation between e(m)/e(m0) and Delta z lies slightly but not significantly above that at 2 ms. These results support the idea that stretch-induced sliding of the actin filament distorts the actin-attached motor domain of the myosin dimers away from the centre of the sarcomere, providing the steric conditions for rapid attachment of the second motor domain. The rate of new motor attachment must be as high as 7.5 x 10(4) s(1) and explains the rapid and efficient increase of the resistance of active muscle to stretch.