Absence of mechanical evidence for attached weakly binding cross-bridges in frog relaxed muscle fibres

Passive viscoelastic response of striated muscles

Muscle cells with sarcomeric structure exhibit highly non trivial passive mechanical response. The difficulty of its continuum modeling is due to the presence of long-range interactions transmitted by extended protein skeleton. To build a rheological model for muscle 'material', we use a stochastic micromodel, and derive a linear response theory for a half-sarcomere, which can be extended to the whole fibre. Instead of the first order rheological equation, anticipated by Hill on the phenomenological grounds, we obtain a novel second order equation which shows that tension depends not only on its current length and the velocity of stretching, but also on its acceleration. Expressing the model in terms of elementary rheological elements, we show that one contribution to the visco-elastic properties of the fibre originates in cross-bridges, while the other can be linked to inert elements which move in the sarcoplasm. We apply this model to explain the striking qualitative difference between the relaxation in experiments involving perturbation of length vs. those involving perturbation of force, and we use the values of the microscopic parameters for frog muscles to show that the model is in excellent quantitative agreement with physiological experiments.

Neural and non-neural related properties in the spastic wrist flexors: An optimization study

Quantifying neural and non-neural contributions to increased joint resistance in spasticity is essential for a better understanding of its pathophysiological mechanisms and evaluating different intervention strategies. However, direct measurement of spasticity-related manifestations, e.g., motoneuron and biophysical properties in humans, is extremely challenging. In this vein, we developed a forward neuromusculoskeletal model that accounts for dynamics of muscle spindles, motoneuron pools, muscle activation and musculotendon of wrist flexors and relies on the joint angle and resistant torque as the only input measurement variables. By modeling the stretch reflex pathway, neural and non-neural related properties of the spastic wrist flexors were estimated during the wrist extension test. Joint angle and resistant torque were collected from 17 persons with chronic stroke and healthy controls using NeuroFlexor, a motorized force measurement device during the passive wrist extension test. The model was optimized by tuning the passive and stretch reflex-related parameters to fit the measured torque in each participant. We found that persons with moderate and severe spasticity had significantly higher stiffness than controls. Among subgroups of stroke survivors, the increased neural component was mainly due to a lower muscle spindle rate at 50% of the motoneuron recruitment. The motoneuron pool threshold was highly correlated to the motoneuron pool gain in all subgroups. The model can describe the overall resistant behavior of the wrist joint during the test. Compared to controls, increased resistance was predominantly due to higher elasticity and neural components. We concluded that in combination with the NeuroFlexor measurement, the proposed neuromusculoskeletal model and optimization scheme served as suitable tools for investigating potential parameter changes along the stretch-reflex pathway in persons with spasticity.

Neural and nonneural contributions to wrist rigidity in Parkinson's disease: an explorative study using the NeuroFlexor

Objective. The NeuroFlexor is a novel method incorporating a biomechanical model for the measurement of neural and nonneural contributions to resistance induced by passive stretch. In this study, we used the NeuroFlexor method to explore components of passive movement resistance in the wrist and finger muscles in subjects with Parkinson's disease (PD). Methods. A cross-sectional comparison was performed in twenty-five subjects with PD with clinically identified rigidity and 14 controls. Neural (NC), elastic (EC), and viscous (VC) components of the resistance to passive extension of the wrist were calculated using the NeuroFlexor. Measurements were repeated during a contralateral activation maneuver. Results. PD subjects showed greater total resistance (P < 0.001) and NC (P = 0.002) compared to controls. EC and VC did not differ significantly between groups. Contralateral activation maneuver resulted in increased NC in the PD group but this increase was due to increased resting tension. Total resistance and NC correlated with clinical ratings of rigidity and with bradykinesia. Conclusions. The findings suggest that stretch induced reflex activity, but not nonneural resistance, is the major contributor to rigidity in wrist muscles in PD. The NeuroFlexor is a potentially valuable clinical and research tool for quantification of rigidity.

Mechanical properties of respiratory muscles

Striated respiratory muscles are necessary for lung ventilation and to maintain the patency of the upper airway. The basic structural and functional properties of respiratory muscles are similar to those of other striated muscles (both skeletal and cardiac). The sarcomere is the fundamental organizational unit of striated muscles and sarcomeric proteins underlie the passive and active mechanical properties of muscle fibers. In this respect, the functional categorization of different fiber types provides a conceptual framework to understand the physiological properties of respiratory muscles. Within the sarcomere, the interaction between the thick and thin filaments at the level of cross-bridges provides the elementary unit of force generation and contraction. Key to an understanding of the unique functional differences across muscle fiber types are differences in cross-bridge recruitment and cycling that relate to the expression of different myosin heavy chain isoforms in the thick filament. The active mechanical properties of muscle fibers are characterized by the relationship between myoplasmic Ca2+ and cross-bridge recruitment, force generation and sarcomere length (also cross-bridge recruitment), external load and shortening velocity (cross-bridge cycling rate), and cross-bridge cycling rate and ATP consumption. Passive mechanical properties are also important reflecting viscoelastic elements within sarcomeres as well as the extracellular matrix. Conditions that affect respiratory muscle performance may have a range of underlying pathophysiological causes, but their manifestations will depend on their impact on these basic elemental structures.

Validation of a New Biomechanical Model to Measure Muscle Tone in Spastic Muscles

Background. There is no easy and reliable method to measure spasticity, although it is a common and important symptom after a brain injury. Objective. The aim of this study was to develop and validate a new method to measure spasticity that can be easily used in clinical practice. Methods. A biomechanical model was created to estimate the components of the force resisting passive hand extension, namely ( a) inertia (IC), ( b) elasticity (EC), ( c) viscosity (VC), and ( d) neural components (NC). The model was validated in chronic stroke patients with varying degree of hand spasticity. Electromyography (EMG) was recorded to measure the muscle activity induced by the passive stretch. Results. The model was validated in 3 ways: ( a) NC was reduced after an ischemic nerve block, ( b) NC correlated with the integrated EMG across subjects and in the same subject during the ischemic nerve block, and ( c) NC was velocity dependent. In addition, the total resisting force and NC correlated with the modified Ashworth score. According to the model, the neural and nonneural components varied between patients. In most of the patients, but not in all, the NC dominated. Conclusions. The results suggest that the model allows valid measurement of spasticity in the upper extremity of chronic stroke patients and that it can be used to separate the neural component induced by the stretch reflex from resistance caused by altered muscle properties.

The viscoelastic properties of passive eye muscle in primates. II: testing the quasi-linear theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory.We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fung's model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition.While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.

The viscoelastic properties of passive eye muscle in primates. I: static forces and step responses

The viscoelastic properties of passive eye muscles are prime determinants of the deficits observed following eye muscle paralysis, the root cause of several types of strabismus. Our limited knowledge about such properties is hindering the ability of eye plant models to assist in formulating a patient's diagnosis and prognosis. To investigate these properties we conducted an extensive in vivo study of the mechanics of passive eye muscles in deeply anesthetized and paralyzed monkeys. We describe here the static length-tension relationship and the transient forces elicited by small step-like elongations. We found that the static force increases nonlinearly with length, as previously shown. As expected, an elongation step induces a fast rise in force, followed by a prolonged decay. The time course of the decay is however considerably more complex than previously thought, indicating the presence of several relaxation processes, with time constants ranging from 1 ms to at least 40 s. The mechanical properties of passive eye muscles are thus similar to those of many other biological passive tissues. Eye plant models, which for lack of data had to rely on (erroneous) assumptions, will have to be updated to incorporate these properties.

Structural changes in the myosin filament and cross-bridges during active force development in single intact frog muscle fibres: stiffness and X-ray diffraction measurements

Structural and mechanical changes occurring in the myosin filament and myosin head domains during the development of the isometric tetanus have been investigated in intact frog muscle fibres at 4 degrees C and 2.15 microm sarcomere length, using sarcomere level mechanics and X-ray diffraction at beamline ID2 of the European Synchrotron Radiation Facility (Grenoble, France). The time courses of changes in both the M3 and M6 myosin-based reflections were recorded with 5 ms frames using the gas-filled RAPID detector (MicroGap Technology). Following the end of the latent period (11 ms after the start of stimulation), force increases to the tetanus plateau value (T(0)) with a half-time of 40 ms, and the spacings of the M3 and M6 reflections (S(M3) and S(M6)) increase by 1.5% from their resting values, with time courses that lead that of force by approximately 10 and approximately 20 ms, respectively. These temporal relations are maintained when the increase of force is delayed by approximately 10 ms by imposing, from 5 ms after the first stimulus, 50 nm (half-sarcomere)(-1) shortening at the velocity (V(0)) that maintains zero force. Shortening at V(0) transiently reduces S(M3) following the latent period and delays the subsequent increase in S(M3), but only delays the S(M6) increase without a transient decrease. Shortening at V(0) imposed at the tetanus plateau causes an abrupt reduction of the intensity of the M3 reflection (I(M3)), whereas the intensity of the M6 reflection (I(M6)) is only slightly reduced. The changes in half-sarcomere stiffness indicate that the isometric force at each time point is proportional to the number of myosin heads bound to actin. The different sensitivities of the intensity and spacing of the M3 and M6 reflections to the mechanical responses support the view that the M3 reflection in active muscle originates mainly from the myosin heads attached to the actin filament and the M6 reflection originates mainly from a fixed structure in the myosin filament signalling myosin filament length changes during the tetanus rise.

Crossbridge properties investigated by fast ramp stretching of activated frog muscle fibres

Very fast ramp stretches at 9.5-33 sarcomere lengths s(-1) (l0 s(-1)) stretching speed, 16-25 nm per half-sarcomere (nm hs(-1)) amplitude were applied to activated intact frog muscle fibres at tetanus plateau, during the tetanus rise, during the isometric phase of relaxation and during isotonic shortening. Stretches produced an almost linear tension increase above the isometric level up to a peak, and fell to a lower value in spite of continued stretching, indicating that the fibre became suddenly very compliant. This suggests that peak tension (critical tension, P(c)) represents the tension at which crossbridges are forcibly detached by the stretch. The ratio of P(c) to the isometric tension at tetanus plateau (P0) was 2.37 +/- 0.12 (S.E.M.). This ratio did not change significantly at lower tension (P) during the tetanus rise but decreased with time during the relaxation and increased with speed during isotonic shortening. At tetanus plateau P(c) occurred when sarcomere elongation attained a critical length (L(c)) of 10.98 +/- 0.13 nm hs(-1), independently of the stretching speed. L(c) remained constant during the tetanus rise but decreased on the relaxation and increased during isotonic shortening. Length-clamp experiments on the relaxation showed that the lower values of P(c)/P ratio and L(c), were both due to the slow sarcomere stretching occurring during this phase. Our data show that P(c) can be used as a measure of crossbridge number, while L(c) is a measure of crossbridge mean extension. Accordingly, for a given tension, crossbridges on the isometric relaxation are fewer than during the rise, develop a greater individual force and have a greater mean extension, while during isotonic shortening crossbridges are in a greater number but develop a smaller individual force and have a smaller extension.

Resting tension characteristics in differentiating intact rat fast- and slow-twitch muscle fibers

The postnatal changes in resting muscle tension were investigated at 20 degrees C by using small muscle fiber bundles isolated from either the extensor digitorum longus or the soleus of both neonatal (7-21 days old) and adult rats. The results show that the tension-extension characteristics of the bundles depended on the age of the rats. For example, both the extensor digitorum longus and soleus bundles of rats older than 14 days showed characteristic differences that were absent in bundles from younger rats. Furthermore, the tension-extension relation of the adult slow muscle fiber bundles were similar to those of the two neonatal muscles and were shifted to longer sarcomere lengths relative to those of the adult fast-fiber bundles. Thus, at the extended sarcomere length of 2.9 microm, the adult fast muscle fiber bundles developed higher resting tensions (5.6 +/- 0.5 kN/m2) than either the two neonatal ( approximately 3 kN/m2) or the adult slow (3.1 +/- 0.4 kN/m2) muscle fiber bundles. At all ages examined, the resting tension responses to a ramp stretch were qualitatively similar and consisted of three components: a viscous, a viscoelastic, and an elastic tension. However, in rats older than 14 days, all three tension components showed clear fast- and slow-fiber type differences that were absent in younger rats. Bundles from 7-day-old rats also developed significantly lower resting tensions than the corresponding adult ones. Additionally, the resting tension characteristics of the adult muscles were not affected by chemical skinning. From these results, we conclude that in rats resting muscle tension, like active tension, differentiates within the first 3 wk after birth.

Cycling cross-bridges increase myocardial stiffness at submaximal levels of Ca2+ activation

Permeabilized multicellular preparations of canine myocardium were subjected to controlled length changes to investigate the extent to which cross-bridges augment passive stiffness components in myocardium at low levels of Ca(2+) activation. When the preparations were immersed in pCa 9.0 solution (negligible free [Ca(2+)]) they behaved as simple elastic systems (i.e., tension increased proportionately with length). In contrast, when the muscles were stretched in Ca(2+) activating solutions, tension rose much more rapidly during the initial phase of the movement than thereafter. Several lines of evidence suggest that the nonlinear response represents the displacement of populations of cycling cross-bridges that are perturbed by interfilamentary movement and take some time to recover. 1), The stiffness of the initial phase increased proportionately with the level of Ca(2+) activation. 2), The magnitude of the short-range response increased with stretch velocity. 3), The initial response was reversibly reduced by 5-mM 2,3-butanedione monoxime, a known cross-bridge inhibitor. The initial stiffness of the passive elastic (pCa 9.0) response was equivalent to the Ca(2+) dependent component at 2% (pCa approximately 6.2) of the maximal (pCa 4.5) level. These results suggest that cross-bridges may significantly affect diastolic chamber stiffness.

Sarcomeric visco-elasticity of chemically skinned skeletal muscle fibres of the rabbit at rest

The giant muscle protein titin (connectin), contained in the gap filament that connect a thick filament to the Z-line in a sarcomere, is generally considered to be responsible for the passive force (tension) and visco-elasticity in resting striated muscle. However, whether it can account for all the features of the resting tension response remains unclear. In this paper, we examine the basic features of the 'sarcomeric visco-elasticity' in a single resting mammalian muscle fibre and attempt to account for various tension components on the basis of known structural features of a sarcomere. At sarcomere length of approximately 2.6 microm, the force response to a ramp stretch of 2-5% is complex but can be resolved into four functionally different components. The behaviour displayed by the components ranges from pure viscous type (directly proportional to stretch velocity, ranging from 0.1 to 30 lengths s(-1)) to predominantly elastic type (insensitive to stretch velocity at 1-2 s time scale); simulations show two components of visco-elasticity with characteristically different relaxation times. The velocity-sensitive components (only) are enhanced by filament lattice compression (dextran - 500 kD) and by increased medium viscosity (dextran - 12 kD); also, the relaxation time of visco-elasticity is longer with increased medium viscosity. Amplitude of all the components and the relaxation time of visco-elasticity are increased at longer sarcomere length (range approximately 2.5 - 3.0 microm). The study, and quantitative analyses, extend our previous work on intact muscle fibres and suggest that the velocity-sensitive tension components in intact sarcomere arise from interactions between sarcomeric filaments, filament segments and inter-filamentary medium; the two components of visco-elasticity arise from distinct regions of titin (connectin) molecules.

History-dependent mechanical properties of permeabilized rat soleus muscle fibers

Permeabilized rat soleus muscle fibers were subjected to repeated triangular length changes (paired ramp stretches/releases, 0.03 l(0), +/- 0.1 l(0) s(-1) imposed under sarcomere length control) to investigate whether the rate of stiffness recovery after movement increased with the level of Ca(2+) activation. Actively contracting fibers exhibited a characteristic tension response to stretch: tension rose sharply during the initial phase of the movement before dropping slightly to a plateau, which was maintained during the remainder of the stretch. When the fibers were stretched twice, the initial phase of the response was reduced by an amount that depended on both the level of Ca(2+) activation and the elapsed time since the first movement. Detailed analysis revealed three new and important findings. 1) The rates of stiffness and tension recovery and 2) the relative height of the tension plateau each increased with the level of Ca(2+) activation. 3) The tension plateau developed more quickly during the second stretch at high free Ca(2+) concentrations than at low. These findings are consistent with a cross-bridge mechanism but suggest that the rate of the force-generating power-stroke increases with the intracellular Ca(2+) concentration and cross-bridge strain.

Passive mechanical properties of the medial gastrocnemius muscle of the cat

1. This is a report on the history dependence of the passive mechanical properties of the medial gastrocnemius muscle of the anaesthetised cat. 2. The muscle was conditioned with an isometric contraction at the test length, or at 3 mm longer than the test length and then returned to the test length, where the level of resting tension was measured, as well as tension changes during a slow stretch. 3. The level of resting tension depended on the form of conditioning and, at the optimum length for active tension, the history-dependent component was 9 % of the total passive tension. 4. During a slow stretch, tension initially rose steeply up to a yield point, beyond which it rose more gradually. The shape of the tension rise depended on the form of conditioning. The level of tension at the yield point consisted of a stretch-dependent component, the 'short-range tension' plus the resting tension for that length. 5. The short-range tension increased with muscle length to peak close to the optimum for active tension. The slope of the tension rise during a stretch, the short-range stiffness, peaked at 2 mm beyond the optimum. 6. The short-range tension was small immediately after a conditioning contraction but grew in size as the interval was increased up to 60 s, with a time constant of 9.9 +/- 0.6 s. After a series of conditioning movements, it recovered more rapidly, with a time constant of 6.6 +/- 0.5 s. 7. The history-dependent changes in passive tension and the response to stretch are interpreted in terms of the presence, in sarcomeres of resting muscle fibres, of crossbridges between actin and myosin which have very slow formation rates, both at rest and during movements.

Muscle contraction: viscous-like frictional forces and the impulsive model

Apart from a few experimental studies muscle viscosity has not received much recent analytical attention as a determinant of the contractile process. This is surprising, since any muscle cell is 80% water, and may undergo large shape changes during its working cycle. Intuitively, one might expect the viscosity of the solvent to be an important determinant of the physiological activity of muscle tissue. This was apparent to pioneers of the study of muscle contraction such as Hill and his contemporaries, whose putative theoretical formulations contained terms related to muscle viscosity. More recently, though, a hydrodynamic calculation by Huxley, using a solvent viscosity close to that of water, has been held to demonstrate that viscous forces are negligible in muscle contraction. We have re-examined the role of viscosity in contraction, postulating impulsive acto-myosin forces that are opposed by a viscous resistance between the filaments. The viscous force required, 10(4) times the hydrodynamic estimate, is close to recent experimental measurements, themselves 10(2)-10(3) times the hydrodynamic estimate. This also agrees with contemporary measurements of cytoplasmic viscosity in other biological cells using magnetic bead micro-rheometry. These are several orders of magnitude greater than the viscosity of water. In the course of the analysis, we have derived the force-velocity equation for an isolated half-sarcomere containing a single actin filament for the first time, and from first principles. We conclude that muscle viscosity is indeed important for the contractile process, and that it has been too readily discounted.

Muscle contraction: viscous-like frictional forces and the impulsive model

Apart from a few experimental studies muscle viscosity has not received much recent analytical attention as a determinant of the contractile process. This is surprising, since any muscle cell is 80% water, and may undergo large shape changes during its working cycle. Intuitively one might expect the viscosity of the solvent to be an important determinant of the physiological activity of muscle tissue. This was apparent to pioneers of the study of muscle contraction such as Hill and his contemporaries, whose putative theoretical formulations contained terms related to muscle viscosity. More recently, though, a hydrodynamic calculation by Huxley, using a solvent viscosity close to that of water, has been held to demonstrate that viscous forces are negligible in muscle contraction. We have re-examined the role of viscosity in contraction, postulating impulsive acto-myosin forces that are opposed by a viscous resistance between the filaments. The viscous force required, 10(4) times the hydrodynamic estimate, is close to recent experimental measurements, themselves 10(2)-10(3) times the hydrodynamic estimate. This also agrees with contemporary measurements of cytoplasmic viscosity in other biological cells using magnetic bead micro-rheometry. These are several orders of magnitude greater than the viscosity of water. In the course of the analysis we have derived the force-velocity equation for an isolated half-sarcomere containing a single actin filament for the first time, and from first principles. We conclude that muscle viscosity is indeed important for the contractile process, and that it has been too readily discounted.

A thixotropic effect in contracting rabbit psoas muscle: prior movement reduces the initial tension response to stretch

Paired ramp stretches and releases ('triangular length changes', typically 0.04 +/- 0.09L0 s-1; mean +/- s.e.m.) were imposed on permeabilised rabbit psoas fibre segments under sarcomere length control. In actively contracting fibres, the tension response to stretch was biphasic; tension rose more rapidly during the first 0. 005L0 of the imposed stretch than thereafter. Tension also dropped in a biphasic manner during shortening, and at the end of the length change was reduced below the steady state. If a second triangular length change was imposed shortly after the first, tension rose less sharply during the initial phase of lengthening, i.e. the stiffness of the muscle during the initial phase of the response was reduced in the second stretch. This is a thixotropic effect. If a third triangular length change was imposed on the muscle, the response was the same as that to the second. The time required to recover the original tension response was measured by varying the interval between triangular length changes. Recovery to steady state occurred at a rate of approximately 1 s-1. The stiffness of the muscle during the initial phase of the response scaled with the developed tension in pCa (= -log10[Ca2+]) solutions ranging from 6.3 (minimal activation) to 4.5 (saturating effect). The relative thixotropic reduction in stiffness measured using paired length changes was independent of the pCa of the activating solution. The thixotropic behaviour of contracting skeletal muscle can be explained by a cross-bridge model of muscle contraction in which the number of attached cross-bridges is temporarily reduced following an imposed movement.

The effect of polyethylene glycol on the mechanics and ATPase activity of active muscle fibers

We have used polyethylene glycol (PEG) to perturb the actomyosin interaction in active skinned muscle fibers. PEG is known to potentiate protein-protein interactions, including the binding of myosin to actin. The addition of 5% w/v PEG (MW 300 or 4000) to active fibers increased fiber tension and decreased shortening velocity and ATPase activity, all by 25-40%. Variation in [ADP] or [ATP] showed that the addition of PEG had little effect on the dissociation of the cross-bridge at the end of the power stroke. Myosin complexed with ADP and the phosphate analog V(i) or AlF(4) binds weakly to actin and is an analog of a pre-power-stroke state. PEG substantially enhances binding of these states both in active fibers and in solution. Titration of force with increasing [P(i)] showed that PEG increased the free energy available to drive the power stroke by about the same amount as it increased the free energy available from the formation of the actomyosin bond. Thus PEG potentiates the binding of myosin to actin in active fibers, and it provides a method for enhancing populations of some states for structural or mechanical studies, particularly those of the normally weakly bound transient states that precede the power stroke.

Do cross-bridges contribute to the tension during stretch of passive muscle?

The tension rise during stretch of passive skeletal muscle is biphasic, with an initial steep rise, followed by a subsequent more gradual change. The initial rise has been interpreted as being due to the presence of numbers of long-term, stable cross-bridges in resting muscle fibres. A point of weakness with the cross-bridge interpretation is that the initial stiffness reaches its peak value at muscle lengths beyond the optimum for myofilament overlap. To explain this result it has been suggested that despite the reduced overlap at longer lengths, the closer interfilament spacing and a higher sensitivity of the myofilaments to Ca2+ allows more stable cross-bridges to form. Recently the stretch responses of passive muscle have been re-examined and it has been suggested that it is not necessary to invoke cross-bridge mechanisms at all. Explanations based on a viscous resistance to interfilament sliding and mechanical properties of the elastic filaments, the gap filaments, were thought to adequately account for the observed tension changes. However, an important property of passive muscle, the dependence of stretch responses on the immediate history of contraction and length changes, thixotropy, cannot be explained simply in terms of viscous and viscoelastic properties. The review discusses the cross-bridge interpretation of muscle thixotropy and the relationship of passive stiffness to filament resting tension and latency relaxation. It is proposed that cross-bridges can exist in three states; one, responsible for the resting stiffness, requires resting levels of calcium. When, during activation, calcium levels rise, cross-bridges enter a low-force, high-stiffness state, signalled by latency relaxation, before they move to the third, force-generating state. It is concluded that, compared with viscoelastic models, a cross-bridge-based explanation of passive muscle properties is better able to accommodate the currently known facts although, as new information becomes available, this view may need to be revised.

Crossbridge head detachment rate constants determined from a model that explains the behavior of both weakly- and strongly-binding crossbridges

Experimentally it is observed that the head regions of weakly-binding myosin crossbridges (crossbridges with ATP or ADP.Pi at the nucleotide binding site) are mobile while attached to actin, while strongly-binding crossbridge heads, such as those with PPi or AMP-PNP at the nucleotide binding site, are immobile (Pate and Cooke, Biophys. J., 1988; Fajer et al., Biophys. J., 1988). I postulate that the fundamental difference between weakly- and strongly-binding crossbridges is not their difference in affinity for actin, but the difference in mobility of the myosin heads attached to actin. Because the heads of weakly-binding crossbridges are mobile while attached to actin, the heads function independently and their behavior can be described by a simple independent-head model. With strongly-binding crossbridges, when one head detaches, it cannot re-attach in a position of lesser strain while the other is attached immobile; both heads must be detached concurrently before the crossbridge can relocate to a position of less strain and relax any tension it supports. This makes the heads appear to act cooperatively. A double-headed crossbridge model is presented which takes into account the difference between weakly- and strongly-binding crossbridges. The model is quite successful at describing the experimental data. In particular, for weakly-binding crossbridges the time constant of the response to stretch is shown to be relatively insensitive to ionic strength and for strongly-binding crossbridges, the model predicts with great accuracy the large ionic strength dependence of the rate constant for force decay. When the experimental results are interpreted according to the model, an important conclusion that emerges is that in all cases (for both weakly- and strongly-binding crossbridges) unstrained crossbridge heads in the muscle fiber detach from actin with approximately the same rate constant as myosin subfragment-1 detaches from actin in solution.

A cross-bridge mechanism can explain the thixotropic short-range elastic component of relaxed frog skeletal muscle

1. The passive tension and sarcomere length of relaxed frog skeletal muscle fibres were measured in response to imposed length stretches. The tension response to a constant-velocity stretch exhibited a clear discontinuity. Tension rose more rapidly during the initial approximately 0.4 % L0 of the stretch than during the latter stages (where L0 is the resting length of the fibre). This initial tension response is attributed to the short-range elastic component (SREC). 2. The use of paired triangular stretches revealed that the maximum tension produced during the SREC response of the second stretch was significantly reduced by the first stretch. This history-dependent behaviour of the SREC reflects thixotropic stiffness changes that have been previously described in relaxed muscle. 3. The biphasic nature of the SREC tension response to movement was most apparent during the first imposed length change after a period at a fixed length, irrespective of the direction of movement. 4. If a relaxed muscle was subjected to an imposed triangular length change so that the muscle was initially stretched and subsequently shortened back to its original fibre length, the resting tension at the end of the stretch was reduced relative to its initial pre-stretch value. Following the end of the stretch, tension slowly increased towards its initial value but the tension recovery was not accompanied by a contemporaneous increase in sarcomere length. This finding suggests that the resting tension of a relaxed muscle fibre is not entirely due to passive elasticity. The results are compatible with the suggestion that a portion of the resting tension - the filamentary resting tension (FRT) - is produced by a low level of active force generation. 5. If a second identical stretch was imposed on the muscle at a time when the resting tension was reduced by the previous stretch, the maximal tension produced during the second stretch was the same as that produced during the first, despite the second stretch commencing from a lower initial resting tension. 6. In experiments using paired triangular length changes, an inter-stretch interval of zero did not produce a substantially greater thixotropic reduction in the second stretch elastic limit force than an inter-stretch interval in the range 0.5-1 s. 7. A theoretical model was developed in which the SREC and FRT arise as manifestations of a small number of slowly cycling cross-bridges linking the actin and myosin filaments of a relaxed skeletal muscle. The predictions of the model are compatible with many of the experimental observations. If the SREC and FRT are indeed due to cross-bridge activity, the model suggests that the cross-bridge attachment rate must increase during interfilamentary movement. A mechanism (based on misregistration between the actin binding sites and the myosin cross-bridges) by which this might arise is presented.

The filament lattice of striated muscle

The filament lattice of striated muscle is an overlapping hexagonal array of thick and thin filaments within which muscle contraction takes place. Its structure can be studied by electron microscopy or X-ray diffraction. With the latter technique, structural changes can be monitored during contraction and other physiological conditions. The lattice of intact muscle fibers can change size through osmotic swelling or shrinking or by changing the sarcomere length of the muscle. Similarly, muscle fibers that have been chemically or mechanically skinned can be compressed with bathing solutions containing very large inert polymeric molecules. The effects of lattice change on muscle contraction in vertebrate skeletal and cardiac muscle and in invertebrate striated muscle are reviewed. The force developed, the speed of shortening, and stiffness are compared with structural changes occurring within the lattice. Radial forces between the filaments in the lattice, which can include electrostatic, Van der Waals, entropic, structural, and cross bridge, are assessed for their contributions to lattice stability and to the contraction process.

Temperature-dependent changes in the viscoelasticity of intact resting mammalian (rat) fast- and slow-twitch muscle fibres

1. The tension and sarcomere length responses induced by ramp stretches (at amplitudes of 1-3 % fibre length (Lo) and speeds of 0.01-12 Lo s-1) were examined at different temperatures (range, 10-35 degrees C) in resting intact muscle fibre bundles isolated from the soleus (a slow-twitch muscle) and extensor digitorum longus (a fast-twitch muscle) of the rat. Some observations are also presented on the effects of chemical skinning on passive viscoelasticity at 10 degrees C. 2. As previously reported, the tension response to a ramp stretch, in different preparations and under various conditions, could be resolved into a viscous (P1), a viscoelastic (P2) and an elastic (P3) component and showed characteristic differences between slow and fast muscle fibres. 3. Chemical skinning of the muscle fibres led to a decrease in the amplitude of all three tension components. However, the fast-slow fibre differences remained after skinning. For example, the viscosity coefficient derived from P1 tension data decreased from 0.84 +/- 0.06 before skinning to 0.44 +/- 0.06 kN s m-2 after skinning in fast fibres; the corresponding values in slow fibres were 2.1 +/- 0.08 and 0.87 +/- 0.09 kN s m-2, respectively. 4. Increasing the experimental temperature from 10 to 35 degrees C led to a decrease in all the tension components in both fast and slow muscle fibre bundles. The decrease of P1 (viscous) tension was such that the viscosity coefficient calculated using P1 data was reduced from 0.84 +/- 0.1 to 0.43 +/- 0.05 kN s m-2 in fast fibres and from 2.0 +/- 0.1 to 1.0 +/- 0.1 kN s m-2 in slow fibres (Q10 of approximately 1.3 in both). 5. In both fast and slow muscle fibre preparations, the plateau tension of the viscoelastic component (P2) decreased by 60-80 % as the temperature was increased from 10 to 35 degrees C giving P2 tension a Q10 of approximately 1.4 in slow fibres and approximately 1.7 in the fast fibres. Additionally, the relaxation time of the viscoelasticity decreased from 11.9 +/- 1 ms (fast) and 43.1 +/- 1 ms (slow) at 10 degrees C to 3 +/- 0.5 ms (fast) at 25 C degrees and 8. 7 +/- 0.6 ms (slow) at 35 degrees C (Q10 of approximately 2.0 in slow and approximately 2.5 in fast fibres). 6. The fast-slow fibre differences in passive viscoelasticity remained at the high physiological temperatures. The physiological significance of such fibre-type differences and their possible underlying mechanisms are discussed.

Effect of viscosity on mechanics of single, skinned fibers from rabbit psoas muscle

Muscle contraction is highly dynamic and thus may be influenced by viscosity of the medium surrounding the myofilaments. Single, skinned fibers from rabbit psoas muscle were used to test this hypothesis. Viscosity within the myofilament lattice was increased by adding to solutions low molecular weight sugars (disaccharides sucrose or maltose or monosaccharides glucose or fructose). At maximal Ca2+ activation, isometric force (Fi) was inhibited at the highest solute concentrations studied, but this inhibition was not directly related to viscosity. Solutes readily permeated the filament lattice, as fiber diameter was unaffected by added solutes (except for an increased diameter with Fi < 30% of control). In contrast, there was a linear dependence upon 1/viscosity for both unloaded shortening velocity and also the kinetics of isometric tension redevelopment; these effects were unrelated to either variation in solution osmolarity or inhibition of force. All effects of added solute were reversible. Inhibition of both isometric as well as isotonic kinetics demonstrates that viscous resistance to filament sliding was not the predominant factor affected by viscosity. This was corroborated by measurements in relaxed fibers, which showed no significant change in the strain-rate dependence of elastic modulus when viscosity was increased more than twofold. Our results implicate cross-bridge diffusion as a significant limiting factor in cross-bridge kinetics and, more generally, demonstrate that viscosity is a useful probe of actomyosin dynamics.

Force responses to fast ramp stretches in stimulated frog skeletal muscle fibres

Force responses to fast ramp stretches at various velocities were recorded from single muscle fibres isolated from either lumbricalis digiti IV or tibialis anterior muscle of the frog (Rana esculenta) at sarcomere length between 2.15 and 3.25 microns at 15 degrees C. Stretches were applied at rest, at tetanus plateau and during the tetanus rise. Stretches with the same velocity but different accelerations were imposed to the fibre to evaluate the effect of fibre inertia on the force responses. Length changes were measured at sarcomere level with either a laser diffractometer or a striation follower apparatus. The force response to a fast ramp stretch could be divided into two phases. The initial fast one (phase 1) lasts for the acceleration period during which the stretching velocity rises up to the steady state. The second slower phase (phase 2) lasts for the remainder of the stretch and corresponds to the well-known elastic response of the fibre. Most of this paper is concerned with phase 1. The amplitude of the initial fast phase was proportional to the stretching velocity as expected from a viscous response. This viscosity was associated with a very short (about 10 microseconds) relaxation time. The amplitude of the fast phase increased progressively with tension during the tetanus rise and scaled down with sarcomere length approximately in the same way as tetanic tension and fibre stiffness. These data suggest that activated fibres have a significant internal viscosity which may arise from crossbridge interaction.

Crossbridge viscosity in activated frog muscle fibres

Force responses to fast ramp stretches at various velocities were recorded in single muscle fibres isolated from tibialis anterior muscle of the frog (Rana esculenta) at a sarcomere length between 2.15 and 3.25 microns at 15 degrees C. Stretches were applied at the tetanus plateau and during tetanus rise. Length changes were recorded at the sarcomere level using either a laser diffractometer or a striation follower apparatus. The immediate force response to the stretch is not simply elastic, as is usually assumed, but is composed of the sum of at least two components: (i) elastic (force proportional to the amount of stretch); and (ii) viscous (force proportional to the rate of stretch). The viscous response is associated with a short (about 10 microseconds) relaxation time. The amplitude of the viscous component increases progressively with tension during the tetanus rise and scales down with sarcomere length approximately in the same way as the tetanic tension. These results suggest that the viscosity of activated fibres may arise from crossbridge kinetics.

Basis of passive tension and stiffness in isolated rabbit myofibrils

By examining the mechanical properties of isolated skeletal and cardiac myofibrils in calcium-free, ATP-containing solution, we attempted to separate the stiffness contribution of titin filaments from that of weakly bound cross bridges. Efforts to enhance weak cross-bridge binding by lowering ionic strength were met by clear contractile responses. Even at low temperature, myofibrils bathed in low-ionic-strength relaxing solution generated increased force and exhibited sarcomere shortening, apparently caused by active contraction. At normal ionic strength, myofibril stiffness, estimated from the force response to rapid sinusoidal oscillations, increased steadily with sarcomere extension up to a strain limit. No obvious stiffness contribution from weak cross bridges was detectable. Instead, the stiffness response, which was frequency dependent at all sarcomere lengths, was apparently generated by the viscoelastic titin filaments. During imposed stretch-hold ramps, both peak force/stiffness and the amount of subsequent stress relaxation increased with higher stretch rates, larger stretch amplitudes, and longer sarcomere lengths. We conclude that, for a truly relaxed myofibril, both passive force and dynamic stiffness principally reflect the intrinsic viscoelastic properties of the titin filaments.

The viscous, viscoelastic and elastic characteristics of resting fast and slow mammalian (rat) muscle fibres

1. The tension and sarcomere length responses induced by ramp stretches (amplitude 1-3% of initial fibre length (Lzero) and speeds of 0.01-12 Lzero s-1) were examined, at 10 degrees C and sarcomere lengths of approximately 2.7 microns, in resting intact muscle fibre bundles isolated from the soleus (a slow muscle) and extensor digitorum longus (a fast muscle) of the rat. 2. In both fibre types, the tension response to moderately fast ramp stretches consists of a viscous, a viscoelastic and an elastic component. At low stretch velocities, where the viscous component is very small, the tension response consists of only the viscoelastic and elastic components. 3. The viscosity coefficient (mean +/- S.E.M., 2 +/- 0.01 kN s m-2, n = 12) and the relaxation time of the viscoelasticity (44 +/- 2 ms, n = 12) of the slow muscle fibres were significantly larger than those of the fast muscle fibres (0.8 +/- 0.1 kN s m-2 and 11 +/- 1 ms, respectively, n = 20). 4. The relaxation time, in either fibre type, is too long for the viscoelasticity to be due to rapidly cycling, weakly attached cross-bridges. Moreover, the tension components increased with sarcomere length and were insensitive to 5-10 mM 2,3-butanedione 2-monoxime (BDM), which inhibited active contractions. 5. The possibility that the fast-slow fibre differences may reflect differences in myoplasmic viscosity and connectin (titin) isoforms (in their gap filaments) is discussed.

Cross-bridge movement in rat slow skeletal muscle as a function of calcium concentration

A single fibre bundle from rat soleus muscle was chemically skinned with saponin and the transfer of myosin heads from the thick filaments to the thin filaments at a sarcomere length of 2.4 microm was measured as a function of Ca2+ concentration using an x-ray diffraction method at 4-7 degrees C. In the relaxed state, the 1,0 spacing was 42.08 nm. The spacing showed no significant decrease when the Ca2+ concentration was below the threshold (-log10 [Ca2+] or pCa 5.8). No significant transfer of the myosin heads occurred when the Ca2+concentration was below the threshold (pCa 5.8). When the muscle was maximally activated at pCa 4.4, the spacing decreased to 40.35 nm. During the maximum isometric contraction at pCa 4.4, 54. 9 +/- 6.5% (+/-SE of the mean) of the myosin heads were transferred to the thin filaments. The transfer of the myosin heads was approximately proportional to relative tension. These results suggest that myosin heads of both fast-twitch and slow-twitch skeletal muscles transferred on the common movement as a function of Ca2+ concentration.

Limits of titin extension in single cardiac myofibrils

Passive force and dynamic stiffness were measured in relaxed, single myofibrils from rabbit ventricle over a wide range of sarcomere lengths, from approximately 2-5 microns. Myofibril stretch up to sarcomere lengths of approximately 3 microns resulted in a steady increase in both force and stiffness. The shape of the length-force and the length-stiffness curves remained fully reproducible for repeated extensions to a sarcomere length of approximately 2.7 microns. Above this length, myofibrillar viscoelastic properties were apparently changed irreversibly, likely due to structural alterations within the titin (connectin) filaments. Stretch beyond approximately 3 microns sarcomere length resulted in a markedly reduced slope of the passive force curve, while the stiffness curve became flat. Thus, cardiac sarcomeres apparently reach a strain limit near a length of 3 microns. Above the strain limit, both curve types frequently showed a series of inflections, which we assumed to result from the disruption of titin-thick filament bonds and consequent addition of previously bound A-band titin segments to the elastic I-band titin portion. Indeed, we confirmed in immunofluorescence microscopic studies, using a monoclonal antibody against titin near the A/I junction, that upon sarcomere stretch beyond the strain limit length, the previously stationary antibody epitopes suddenly moved into the I-band, indicating A-band titin release. Altogether, the passive force/stiffness-length relation of cardiac myofibrils was qualitatively similar to, but quantitatively different from, that reported for skeletal myofibrils. From these results, we inferred that cardiac myofibrils have an approximately two times greater relative I-band titin extensibility than skeletal myofibrils. This could hint at differences in the maximum passive force-bearing capacity of titin filaments in the two muscle types.

The visco-elasticity of resting intact mammalian (rat) fast muscle fibres

Tension responses induced by ramp stretches (amplitude of 1-2% fibre length and speeds of 0.01-15 Los-1) were examined in resting intact muscle fibre bundles isolated from the extensor digitorum longus (a fast muscle) of the rat; sarcomere length of a 2 mm region was monitored near the tension transducer end by means of a He-Ne laser diffractometer. The experiments were done at 10 degrees C. During a ramp stretch, the tension rose rapidly (P1) and then slowly (P2) to reach a peak; after completion of the ramp, the tension decayed in complex manner to a steady level (P3) at approximately constant sarcomere length. At stretch velocities higher than approximately 1-2 Los-1, P1 tension increased in direct proportion to stretch velocity, indicating that it is due to viscous resistance; in a half sarcomere, the viscous resistance to filament sliding may be about 5 x 10(8) N s m-3. The steady tension level after the ramp (P3 tension) was independent of stretch velocity indicating that it represents an elastic tension. The amplitude of the slow tension rise (P2 tension corrected for P3) increased with stretch velocity up to a plateau (as in a visco-elastic component); the calculated relaxation time was 5-13 ms. Amplitudes of all three components were larger at longer sarcomere length (range 2.4-3 microns). The presence of 5-10 mM BDM which abolished the twitch and markedly depressed the tetanic responses, produced little or no change in the tension components. Our results show that none of the tension components to stretch in relaxed mammalian muscle fibres is due to active, cycling cross-bridges; the possibility that the resting sarcomeric visco-elasticity (net P2) resides in the connectin (= titin) containing gap filament is discussed.

Tension relaxation after stretch in resting mammalian muscle fibers: stretch activation at physiological temperatures

Tension responses to ramp stretches of 1-3% Lo (fiber length) in amplitude were examined in resting muscle fibers of the rat at temperatures ranging from 10 degrees C to 36 degrees C. Experiments were done using bundles of approximately 10 intact fibers isolated from the extensor digitorum longus (a fast muscle) and the soleus (a slow muscle). At low temperatures (below approximately 20 degrees C), the tension response consisted of an initial rise to a peak during the ramp followed by a complex tension decay to a plateau level; the tension decay occurred at approximately constant sarcomere length. The tension decay after a standard stretch at approximately 3-4.Lo/s contained a fast, an intermediate, and a (small amplitude) slow component, which at 10 degrees C (sarcomere length approximately 2.5 microns) were approximately 2000.s-1, approximately 150.s-1, and approximately 25.s-1 for fast fibers and approximately 2000.s-1, approximately 70.s-1 and approximately 8.s-1 for slow fibers, respectively. The fast component may represent the decay of interfilamentary viscous resistance, and the intermediate component may be due to viscoelasticity in the gap (titin, connectin) filament. The two- to threefold fast-slow muscle difference in the rate of passive tension relaxation (in the intermediate and the slow components) compares with previously reported differences in the speed of their active contractions; this suggests that "passive viscoelasticity" is appropriately matched to contraction speed in different muscle fiber types. At approximately 35 degrees C, the fast and intermediate components of tension relaxation were followed by a delayed tension rise at approximately 10.s-1 (fast fibers) and 2.5.s-1 (slow fibers); the delayed tension rise was accompanied by sarcomere shortening. BDM (5-10 mM) reduced the active twitch and tetanic tension responses and the delayed tension rise at 35 degrees C; the results indicate stretch sensitive activation in mammalian sarcomeres at physiological temperatures.

The Physiological Society, proceedings of the scientific meetings of February 1996, March 1996, October 1995

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