Variation of muscle stiffness with tension during tension transients and constant velocity shortening in the frog

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

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

The Closed State of the Thin Filament Is Not Occupied in Fully Activated Skeletal Muscle

Muscle contraction is powered by actin-myosin interaction controlled by Ca²⁺ via the regulatory proteins troponin (Tn) and tropomyosin (Tpm), which are associated with actin filaments. Tpm forms coiled-coil dimers, which assemble into a helical strand that runs along the whole ∼1 μm length of a thin filament. In the absence of Ca²⁺, Tn that is tightly bound to Tpm binds actin and holds the Tpm strand in the blocked, or B, state, where Tpm shields actin from the binding of myosin heads. Ca²⁺ binding to Tn releases the Tpm from actin so that it moves azimuthally around the filament axis to a closed, or C, state, where actin is partially available for weak binding of myosin heads. Upon transition of the weak actin-myosin bond into a strong, stereo-specific complex, the myosin heads push Tpm strand to the open, or O, state allowing myosin binding sites on several neighboring actin monomers to become open for myosin binding. We used low-angle x-ray diffraction at the European Synchrotron Radiation Facility to check whether the O- to C-state transition in fully activated fibers of fast skeletal muscle of the rabbit occurs during transition from isometric contraction to shortening under low load. No decrease in the intensity of the second actin layer line at reciprocal radii in the range of 0.15-0.275 nm^-1 was observed during shortening suggesting that an azimuthal Tpm movement from the O- to C-state does not occur, although during shortening muscle stiffness is reduced compared to the isometric state, and the intensities of other actin layer lines demonstrate a ∼2-fold decrease in the fraction of myosin heads strongly bound to actin. The data show that a small fraction of actin-bound myosin heads is sufficient for supporting the O-state and, therefore the C-state is not occupied in fully activated skeletal muscle that produces mechanical work at low load.

A simple model of cardiac muscle for multiscale simulation: Passive mechanics, crossbridge kinetics and calcium regulation

A simple model of cardiac muscle was designed for multiscale simulation of heart mechanics. Relaxed cardiac muscle was described as a transversally isotropic hyperelastic material. Active tension caused by actin-myosin crossbridges depends on the ensemble averaged strain of myosin heads bound to actin. Calcium activation was modeled by Ca²⁺ binding to troponin-C. To account for the dependence of troponin affinity for Ca²⁺ on myosin heads strongly bound to actin, the kinetics of troponin binding to Ca²⁺ in the overlap zone of the thin and thick filaments and outside it were separated. The changes in the length of these zones during muscle shortening or lengthening were accounted for explicitly. Simplified version of the model contains only 5 ordinary differential equations (ODE). Model parameters were estimated from a limited set of experiments with skeletal and cardiac muscle. Simulations have shown that model reproduces qualitatively a number of experimental observations: steady-state force-velocity and stiffness-velocity relations; mechanical responses to step changes in muscle length or load; steep Ca²⁺-tension relationship and its dependence on sarcomere length tension (the Frank-Starling mechanism); tension, shortening and Ca²⁺-transients in twitch isometric and isotonic contractions, tension development and redevelopment upon fast change in Ca²⁺ concentration or muscle release followed by re-stretch. We believe that the model can be effectively used for modeling contraction and relaxation of the heart.

Prophylactic knee bracing alters lower-limb muscle forces during a double-leg drop landing

Anterior cruciate ligament (ACL) injury can be a painful, debilitating and costly consequence of participating in sporting activities. Prophylactic knee bracing aims to reduce the number and severity of ACL injury, which commonly occurs during landing maneuvers and is more prevalent in female athletes, but a consensus on the effectiveness of prophylactic knee braces has not been established. The lower-limb muscles are believed to play an important role in stabilizing the knee joint. The purpose of this study was to investigate the changes in lower-limb muscle function with prophylactic knee bracing in male and female athletes during landing. Fifteen recreational athletes performed double-leg drop landing tasks from 0.30m and 0.60m with and without a prophylactic knee brace. Motion analysis data were used to create subject-specific musculoskeletal models in OpenSim. Static optimization was performed to calculate the lower-limb muscle forces. A linear mixed model determined that the hamstrings and vasti muscles produced significantly greater flexion and extension torques, respectively, and greater peak muscle forces with bracing. No differences in the timings of peak muscle forces were observed. These findings suggest that prophylactic knee bracing may help to provide stability to the knee joint by increasing the active stiffness of the hamstrings and vasti muscles later in the landing phase rather than by altering the timing of muscle forces. Further studies are necessary to quantify whether prophylactic knee bracing can reduce the load placed on the ACL during intense dynamic movements.

Mechanism of force enhancement during and after lengthening of active muscle: a temperature dependence study

The aim of the present study was to examine the temperature dependence of active force in lengthening and shortening muscle. Experiments were done, in vitro, on bundles of intact fibres (fibre length L(0) ~2 mm; sarcomere length ~2.5 μm) isolated from a rat fast muscle (flexor hallucis brevis) and a ramp length change of 5-7% L(0) was applied on the plateau of an isometric tetanic contraction. Ramp lengthening increased and ramp shortening decreased the muscle tension to new approximately steady levels in a velocity-dependent way. The isometric tension and the lower steady tension reached at a given shortening velocity, increased with warming from 10 to 35 °C and the relation between tension and reciprocal absolute temperature was sigmoidal. However, the tension-temperature curve of shortening muscle was sharper and shifted to higher temperature with increased velocity. In contrast, the enhanced steady tension during lengthening at a given velocity was largely temperature-insensitive within the same temperature range; we hypothesize that the tension-temperature curve may be shifted to lower temperatures in lengthening muscle. Consequently, when normalised to the isometric tension at each temperature, the tension during lengthening at a given velocity decreased exponentially with increase of temperature. The residual force enhancement that remains after ramp lengthening showed a similar behaviour and was markedly reduced in warming from 10 to 35 °C. The findings are consistent with the thesis that active force generation in muscle is endothermic and strain-sensitive; during shortening with a faster crossbridge cycle it becomes more pronounced, but during lengthening it becomes depressed as the cycle slows in a velocity-dependent way. The residual force enhancement may be caused by the same process in addition to non-crossbridge mechanism(s).

Estrogen and muscle stiffness have a negative relationship in females

PURPOSE

Hormonal fluctuations are one potential reason why females might have a greater rate of noncontact ACL injury. The hamstrings are capable of limiting anterior cruciate ligament (ACL) loading. This study examined whether relationships existed between reproductive hormones (estradiol-β-17, free testosterone, and progesterone) and hamstring neuromechanical variables (hamstring musculotendinous stiffness (MTS), rate of force production (RFP), time to 50% peak torque (T50%), and electromechanical delay (EMD)) in genders combined and independently.

METHODS

Muscle properties of the hamstrings and reproductive hormones were evaluated in 30 subjects (15 males and 15 females) that were free from lower extremity injury and had no history of ACL injury. Females were tested 3-5 days after the onset of menses and were not using oral contraceptive. Pearson correlation coefficients were calculated for each hormone and muscle property.

RESULTS

For genders combined, estrogen (mean = 46.0 ± 28.2 pg/mL) was negatively correlated with RFP (mean = 758.8 ± 507.6 N/kg s(-1), r = -0.43, P = 0.02) and MTS (mean = 12.8 ± 2.6 N/cm, r = -0.43, P = 0.02). Free testosterone (mean = 13.2 ± 13.0 pg/mL) was positively correlated with RFP (r = 0.56, P < 0.01) and MTS (r = 0.46, P = 0.01) but negatively correlated with T50% (mean = 114.7 ± 38.9 ms, r = -0.43, P = 0.02). When gender was considered separately, females demonstrated negative correlation between estrogen (mean = 68.0 ± 23.2 pg/mL) and MTS (mean = 11.7 ± 1.5 N/cm, r = -0.53, P = 0.05) and free testosterone (mean = 1.5 ± 0.6 pg/mL) and MTS (r = -0.52, P = 0.05). Males alone displayed no significant correlations between the selected hormones and muscle properties.

CONCLUSIONS

Correlations exist between muscle properties and reproductive hormones. Females, however, may be more sensitive to reproductive hormones and their fluctuations.

Cross-bridge properties in single intact frog fibers studied by fast stretches

Cross-bridges properties were measured under different experimental conditions by applying fast stretches to activated skeletal frog muscle fiber to -forcibly detach the cross-bridge ensemble. This allowed to measure the tension needed to detach the cross-bridges, P(c), and the sarcomere elongation at the rupture force, L(c). These two parameters are expected to be correlated with cross-bridges number (P(c)) and their mean extension (L(c)). Conditions investigated were: tetanus rise and plateau under normal Ringer and Ringer containing different BDM -concentrations, hyper (1.4T) and hypotonic (0.8T) solutions, 5 and 14 degrees C temperature. P(c) was linearly correlated with the tension (P) developed by the fibers under all the conditions examined, however the ratio P(c)/P changed depending on conditions being greater at low temperature and higher tonicity. These results indicate that, (a) P(c) can be used as a measure of attached cross-bridge number and (b) the force developed by the individual cross-bridge increases at high temperature and low tonicity. L(c) was not affected by tension developed, however it changed under different conditions, being greater at low temperature and high tonicity. These findings, suggests, in agreement with P(c) data, that cross-bridge extension is smaller at low temperature and high tonicity. By comparing these data with tetanic tension we concluded that potentiation or depression induced on tetanic force by tonicity or temperature changes are entirely accounted for by changes of the force developed by the individual cross-bridge.

Inferring crossbridge properties from skeletal muscle energetics

Work is generated in muscle by myosin crossbridges during their interaction with the actin filament. The energy from which the work is produced is the free energy change of ATP hydrolysis and efficiency quantifies the fraction of the energy supplied that is converted into work. The purpose of this review is to compare the efficiency of frog skeletal muscle determined from measurements of work output and either heat production or chemical breakdown with the work produced per crossbridge cycle predicted on the basis of the mechanical responses of contracting muscle to rapid length perturbations. We review the literature to establish the likely maximum crossbridge efficiency for frog skeletal muscle (0.4) and, using this value, calculate the maximum work a crossbridge can perform in a single attachment to actin (33 x 10(-21) J). To see whether this amount of work is consistent with our understanding of crossbridge mechanics, we examine measurements of the force responses of frog muscle to fast length perturbations and, taking account of filament compliance, determine the crossbridge force-extension relationship and the velocity dependences of the fraction of crossbridges attached and average crossbridge strain. These data are used in combination with a Huxley-Simmons-type model of the thermodynamics of the attached crossbridge to determine whether this type of model can adequately account for the observed muscle efficiency. Although it is apparent that there are still deficiencies in our understanding of how to accurately model some aspects of ensemble crossbridge behaviour, this comparison shows that crossbridge energetics are consistent with known crossbridge properties.

An analysis of the temperature dependence of force, during steady shortening at different velocities, in (mammalian) fast muscle fibres

We examined, over a wide range of temperatures (10–35°C), the isometric tension and tension during ramp shortening at different velocities (0.2–4 L₀/s) in tetanized intact fibre bundles from a rat fast (flexor hallucis brevis) muscle; fibre length (L₀) was 2.2 mm and sarcomere length ~2.5 μm. During a ramp shortening, the tension change showed an initial inflection of small amplitude (P₁), followed by a larger exponential decline towards an approximate steady level; the tension continued to decline slowly afterwards and the approximate steady tension at a given velocity was estimated as the tension (P₂) at the point of intersection between two linear slopes, as previously described (Roots et al. 2007). At a given temperature, the tension P₂ declined to a lower level and at a faster rate (from an exponential curve fit) as the shortening velocity was increased; the temperature sensitivity of the rate of tension decline during ramp shortening at different velocities was low (Q₁₀ 0.9–1.5). The isometric tension and the P₂ tension at a given shortening velocity increased with warming so that the relation between tension and (reciprocal) temperature was sigmoidal in both. In isometric muscle, the temperature T_0.5 for half-maximal tension was ~10°C, activation enthalpy change (∆H) was ~100 kJ mol⁻¹ and entropy change (∆S) ~350 J mol⁻¹ K⁻¹. In shortening, these were increased with increase of velocity so that at a shortening velocity (~4 L₀/s) producing maximal power at 35°C, T_0.5 was ~28°C, ∆H was ~200 kJ mol⁻¹ and ∆S ~ 700 J mol⁻¹ K⁻¹; the same trends were seen in the tension data from isotonic release experiments on intact muscle and in ramp shortening experiments on maximally Ca-activated skinned fibres. In general, our findings show that the sigmoidal relation between force and temperature can be extended from isometric to shortening muscle; the implications of the findings are discussed in relation to the crossbridge cycle. The data indicate that the endothermic, entropy driven process that underlies crossbridge force generation in isometric muscle (Zhao and Kawai 1994; Davis, 1998) is even more pronounced in shortening muscle, i.e. when doing external work.

Crossbridge properties during force enhancement by slow stretching in single intact frog muscle fibres

The mechanism of force enhancement during lengthening was investigated on single frog muscle fibres by using fast stretches to measure the rupture tension of the crossbridge ensemble. Fast stretches were applied to one end of the activated fibre and force responses were measured at the other. Sarcomere length was measured by a striation follower device. Fast stretching induced a linear increase of tension that reached a peak and fell before the end of the stretch indicating that a sudden increase of fibre compliance occurred due to forced crossbridge detachment induced by the fast loading. The peak tension (critical tension, Pc) and the sarcomere length needed to reach Pc (critical length, Lc) were measured at various tensions during the isometric tetanus rise and during force enhancement by slow lengthening. The data showed that Pc was proportional to the tension generated by the fibre under both isometric and slow lengthening conditions. However, for a given tension increase, Pc was 6.5 times greater during isometric than during lengthening conditions. Isometric critical length was 13.04 +/- 0.17 nm per half-sarcomere (nm hs(-1)) independently of tension. During slow lengthening critical length fell as the force enhancement increased. For 90% enhancement, Lc reduced to 8.19 +/- 0.039 nm hs(-1). Assuming that the rupture force of the individual crossbridge is constant, these data indicate that the increase of crossbridge number during lengthening accounts for only 15.4% of the total force enhancement. The remaining 84.6% is accounted for by the increased mean strain of the crossbridges.

Force generation examined by laser temperature-jumps in shortening and lengthening mammalian (rabbit psoas) muscle fibres

We examined the tension change induced by a rapid temperature jump (T-jump) in shortening and lengthening active muscle fibres. Experiments were done on segments of permeabilized single fibres (length (L0) approximately 2 mm, sarcomere length 2.5 microm) from rabbit psoas muscle; [MgATP] was 4.6 mm, pH 7.1, ionic strength 200 mm and temperature approximately 9 degrees C. A fibre was maximally Ca2+-activated in the isometric state and a approximately 3 degrees C, rapid (< 0.2 ms), laser T-jump applied when the tension was approximately steady in the isometric state, or during ramp shortening or ramp lengthening at a limited range of velocities (0-0.2 L0 s(-1)). The tension increased to 2- to 3 x P0 (isometric force) during ramp lengthening at velocities > 0.05 L0 s(-1), whereas the tension decreased to about < 0.5 x P0 during shortening at 0.1-0.2 L0 s(-1); the unloaded shortening velocity was approximately 1 L0 s(-1) and the curvature of the force-shortening velocity relation was high (a/P0 ratio from Hill's equation of approximately 0.05). In isometric state, a T-jump induced a tension rise of 15-20% to a new steady state; by curve fitting, the tension rise could be resolved into a fast (phase 2b, 40-50 s(-1)) and a slow (phase 3, 5-10 s(-1)) exponential component (as previously reported). During steady lengthening, a T-jump induced a small instantaneous drop in tension, followed by recovery, so that the final tension recorded with and without a T-jump was not significantly different; thus, a T-jump did not lead to a net increase of tension. During steady shortening, the T-jump induced a pronounced tension rise and both its amplitude and the rate (from a single exponential fit) increased with shortening velocity; at 0.1-0.2 L0 s(-1), the extent of fibre shortening during the T-jump tension rise was estimated to be approximately 1.2% L(0) and it was shorter at lower velocities. At a given shortening velocity and over the temperature range of 8-30 degrees C, the rate of T-jump tension rise increased with warming (Q10 approximately 2.7), similar to phase 2b (endothermic force generation) in isometric muscle. Results are discussed in relation to the previous findings in isometric muscle fibres which showed that a T-jump promotes an early step in the crossbridge-ATPase cycle that generates force. In general, the finding that the T-jump effect on active muscle tension is pronounced during shortening, but is depressed/inhibited during lengthening, is consistent with the expectations from the Fenn effect that energy liberation (and acto-myosin ATPase rate) in muscle are increased during shortening and depressed/inhibited during lengthening.

Active trunk stiffness during voluntary isometric flexion and extension exertions

OBJECTIVE

Compare muscle activity and trunk stiffness during isometric trunk flexion and extension exertions.

BACKGROUND

Elastic stiffness of the torso musculature is considered the primary stabilizing mechanism of the spine. Therefore, stiffness of the trunk during voluntary exertions provides insight into the stabilizing control of pushing and pulling tasks.

METHODS

Twelve participants maintained an upright posture against external flexion and extension loads applied to the trunk. Trunk stiffness, damping, and mass were determined from the dynamic relation between pseudorandom force disturbances and subsequent small-amplitude trunk movements recorded during the voluntary exertions. Muscle activity was recorded from rectus abdominus, external oblique, lumbar paraspinal, and internal oblique muscle groups.

RESULTS

Normalized electromyographic activity indicated greater antagonistic muscle recruitment during flexion exertions than during extension. Trunk stiffness was significantly greater during flexion exertions than during extension exertions despite similar levels of applied force. Trunk stiffness increased with exertion effort.

CONCLUSION

Theoretical and empirical analyses reveal that greater antagonistic cocontraction is required to maintain spinal stability during trunk flexion exertions than during extension exertions. Measured differences in active trunk stiffness were attributed to antagonistic activity during flexion exertions with possible contributions from spinal kinematics and muscle lines of action.

APPLICATION

When compared with trunk extension exertions, trunk flexion exertions such as pushing tasks require unique neuromuscular control that is not simply explained by differences in exertion direction. Biomechanical analyses of flexion tasks must consider the stabilizing muscle recruitment patterns when evaluating spinal compression and shear loads.

Effects of solution tonicity on crossbridge properties and myosin lever arm disposition in intact frog muscle fibres

The aims of this study were to investigate the effects of solution tonicity on muscle properties, and to verify their consistence with the lever arm theory of force generation. Experiments were made in single muscle fibres and in fibre bundles from the frog, using both fast stretches and time-resolved X-ray diffraction, in isotonic Ringer solution (1T), hypertonic (1.4T) and hypotonic (0.8T) solutions. Fast stretches (0.4-0.6 ms duration and 16-25 nm per half-sarcomere (nm hs(-1)) amplitude) were applied at various tensions during the force development in isometric tetani. Force increased during the stretch up to a peak (critical tension, Pc) at which it started to fall, in spite of continued stretching. In all solutions, Pc was proportional to the initial isometric tension developed. For a given isometric tension, Pc increased with solution tonicity and occurred at a precise sarcomere elongation (critical length, Lc) which also increased with tonicity. M3 meridional layer line intensity (I M3) was measured during the application of sinusoidal length oscillations (1 kHz frequency, and about 2% fibre length amplitude) at tetanus plateau. I M3 changed during the length oscillations in a sinusoidal manner in phase opposition to length changes, but a double peak distortion occurred at the peak of the release phase. The presence of the distortion, which decreased with tonicity, allowed calculation of the mean position of the myosin head (S1) during the oscillation cycle. In agreement with the lever arm theory, both X-ray diffraction and mechanical data show that solution tonicity affects S1 mean position and consequently crossbridge individual extension and force, with no effect on crossbridge number. The force needed to break the single crossbridge was insensitive to solution tonicity suggesting a non-ionic nature of the actomyosin bond.

Regulation of energy liberation during steady sarcomere shortening

Energy liberation rate ( Ė) during steady muscle shortening is a monotonic increasing or biphasic function of the shortening velocity ( V). The study examines three plausible hypotheses for explaining the biphasic Ė-V relationship (EVR): 1) the cross-bridge (XB) turnover rate from non-force-generating (weak) to force-generating (strong) conformation decreases as V increases; 2) XB kinetics is determined by the number of strong XBs (XB -XB cooperativity); and 3) the affinity of troponin for calcium is modulated by the number of strong XBs (XB -Ca cooperativity). The relative role of the various energy-regulating mechanisms is not well defined. The hypotheses were tested by coupling calcium kinetics with XB cycling. All three hypotheses yield identical steady-state characteristics: 1) hyperbolic force-velocity relationship; 2) quasi-linear stiffness-force relationship; and 3) biphasic EVR, where Ė declines at high V due to decrease in the number of cycling XBs or in the weak-to-strong transition rate. The hypotheses differ in the ability to describe the existence of both monotonic and biphasic EVRs and in the effect of intracellular free calcium concentration ([Ca2+]i) on the EVR peak. Monotonic and biphasic EVRs with a shift in EVR peak to higher velocity at higher [Ca2+]iare obtained only by XB -Ca cooperativity. XB -XB cooperativity provides only biphasic EVRs. A direct effect of V on XB kinetics predicts that EVR peak is obtained at the same velocity independently of [Ca2+]i. The study predicts that measuring the dependence of the EVR on [Ca2+]iallows us to test the hypotheses and to identify the dominant energy-regulating mechanism. The established XB -XB and XB -Ca mechanisms provide alternative explanations to the various reported EVRs.

Force enhancement and relaxation rates after stretch of activated muscle fibres

The residual force enhancement following muscle stretch might be associated with an increase in the proportion of attached cross-bridges, as supported by stiffness measurements. In this case, it could be caused by an increase in the attachment or a decrease in the detachment rate of cross-bridges, or a combination of the two. The purpose of this study was to investigate if the stretch-induced force enhancement is related to cross-bridge attachment/detachment kinetics. Single muscle fibres dissected from the lumbrical muscle of frog were place at a length approximately 20% longer than the plateau of the force-length relationship; they were maximally activated, and after full isometric force was reached, ramp stretches were imposed with amplitudes of 5 and 10% fibre length, at a speed of 40% fibre length s(-1). Experiments were performed in Ringer's solution, and with the addition of 2, 5 and 10 nM of 2,3-butanedione monoxime (BDM), a drug that places cross-bridges in a pre-power-stroke, state, inhibiting force production. The total force following stretch was higher than the corresponding force measured after isometric contraction at the corresponding length. This residual force enhancement was accompanied by an increase relaxation time. BDM, which decreases force production during isometric contractions, considerably increased the relative levels of force enhancement. BDM also increased relaxation times after stretch, beyond the levels observed during reference contractions in Ringer's solution, and beyond isometric control tests at the corresponding BDM concentrations. Together, these results support the idea that force enhancement is caused, at least in part, by a decrease in cross-bridge detachment rates, as manifested by the increased relaxation times following fibre stretch.

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.

Strong binding of myosin heads stretches and twists the actin helix

Calculation of the size of the power stroke of the myosin motor in contracting muscle requires knowledge of the compliance of the myofilaments. Current estimates of actin compliance vary significantly introducing uncertainty in the mechanical parameters of the motor. Using x-ray diffraction on small bundles of permeabilized fibers from rabbit muscle we show that strong binding of myosin heads changes directly the actin helix. The spacing of the 2.73-nm meridional x-ray reflection increased by 0.22% when relaxed fibers were put into low-tension rigor (<10 kN/m(2)) demonstrating that strongly bound myosin heads elongate the actin filaments even in the absence of external tension. The pitch of the 5.9-nm actin layer line increased by approximately 0.62% and that of the 5.1-nm layer line decreased by approximately 0.26%, suggesting that the elongation is accompanied by a decrease in its helical angle (approximately 166 degrees) by approximately 0.8 degrees. This effect explains the difference between actin compliance revealed from mechanical experiments with single fibers and from x-ray diffraction on whole muscles. Our measurement of actin compliance obtained by applying tension to fibers in rigor is consistent with the results of mechanical measurements.

Active stiffness of the ankle in response to inertial and elastic loads

Effective stiffness of the musculoskeletal system was examined as a function of the characteristics of an external load. Thirteen healthy subjects provided active contraction of the ankle plantarflexion musculature in a neutral ankle posture to support an external load. Musculoskeletal stiffness was computed from kinetic data recorded in response to dorsiflexion/plantarflexion perturbations. Ankle dynamics were recorded while supporting external loads of 19 and 38 kg with and without antagonistic co-contraction. External loads were applied using pure gravitational mass. In separate trials external loads were applied from stretch of steel springs in parallel with the plantarflexion musculature that also provided added parallel stiffness to the system. Adding external stiffness of 4.9 and 8.1 kN/m surprisingly failed to significantly change the stiffness of the ankle-plus-spring system. This suggests contributions from intrinsic muscle stiffness and reflex stiffness declined in response to added external stiffness. This could not be explained by load magnitudes, ankle postures, or co-activation as these were similar between the inertial and elastic loading conditions. However, non-linear parametric analyses suggest mean intrinsic stiffness of 35.5 kN/m and reflex gain of 11.6 kN/m with a constant reflex delay of 70 ms accurately described the empirical results. The phase response between the mechanical dynamics of the musculoskeletal system and delayed neuromotor feedback combine to provide robust control of system behavior.

Gender differences in active musculoskeletal stiffness. Part I. Quantification in controlled measurements of knee joint dynamics

Active females demonstrate increased risk for musculoskeletal injuries relative to equivalently-trained males. Although gender differences in factors such as passive laxity, skeletal geometry and kinematics have been examined, the effect of gender on active muscle stiffness has not been reported. Stiffness of the active quadriceps and hamstrings musculature were recorded during isometric knee flexion and extension exertions from twelve male and eleven female subjects. A second-order biomechanical model of joint dynamics was used to quantify stiffness from the transient motion response to an angular perturbation of the lower-leg. Female subjects demonstrated reduced active stiffness relative to male subjects at all torque levels, with levels 56-73% of the males. Effective stiffness increased linearly with the torque load, with stiffness increasing at a rate of 3.3 Nm/rad per unit of knee moment in knee flexion exertions (hamstrings) and 6.6 Nm/rad per unit of knee moment extension exertions (quadriceps). To account for gender differences in applied moment associated with leg mass, regressions analyses were completed that demonstrated a gender difference in the slope of stiffness-versus-knee moment relation. Further research is necessary to identify the cause of the observed biomechanical difference and implications for controlling injury.

Nitric oxide impairs Ca2+ activation and slows cross-bridge cycling kinetics in skeletal muscle

The effects of the nitric oxide (NO) donor spermine NONOate (Sp-NO, 1.0 mM) on cross-bridge recruitment and cross-bridge cycling kinetics were studied in permeabilized rabbit psoas muscle fibers. Fibers were activated at various Ca2+ concentrations (pCa, negative logarithm of Ca2+ concentration), and the pCa at which force was maximal (pCa 4.0) and approximately 50% of maximal (pCa50 5.6) were determined. Fiber stiffness was determined using 1-kHz sinusoidal length perturbations, and the fraction of cross bridges in the force-generating state was estimated by the ratio of stiffness during maximal (pCa 4.0) and submaximal (pCa 5.6) Ca2+ activation to stiffness during rigor (at pCa 4.0). Cross-bridge cycling kinetics were evaluated by measuring the rate constant for force redevelopment after quick release (by 15% of optimal fiber length, L(o)) and restretch of the fiber to L(o). Exposing fibers to Sp-NO for 10 min reduced force and the fraction of cross bridges in the force-generating state at maximal and submaximal (pCa50) Ca2+ activation. However, the effects of Sp-NO were more pronounced during submaximal Ca2+ activation. Sp-NO also reduced the rate constant for force redevelopment but only during submaximal Ca2+ activation. We conclude that Sp-NO reduces Ca2+ sensitivity by decreasing the number of cross bridges in the strongly bound state and also impairs cross-bridge cycling kinetics during submaximal activation.

Maximal and submaximal forces of slow fibers in human soleus after bed rest

The effects of 2 and 4 mo of bed rest, with or without exercise countermeasures, on the contractile properties of slow fibers in the human soleus muscle were examined. Mean fiber diameters were 8 and 36% smaller after 2 and 4 mo of bed rest, respectively, than the pre-bed rest level. Maximum tetanic force (P(o)), maximum activated force (F(max)) per cross-sectional area (CSA), and the common-logarithm value of free Ca(2+) concentration required for half-maximal activation (pCa(50)) also decreased after 2 and 4 mo of bed rest. In contrast, maximum unloaded shortening velocity (V(o)) was increased after 2 and 4 mo of bed rest. After 1 mo of recovery, fiber diameters, P(o), F(max) per CSA (P > 0.05), and pCa(50) were increased and V(o) decreased toward pre-bed rest levels. Effects of knee extension/flexion exercise by wearing an anti-G Penguin suit for 10 h daily, and the effects of loading or unloading of the plantar flexors with (Penguin-1) or without (Penguin-2) placing the elastic loading elements of the suit, respectively, were investigated during ~2 mo of bed rest. In the Penguin-1 group, mean fiber diameter, P(o), F(max) per CSA, V(o), and pCa(50) were similar before and after bed rest. However, the responses of fiber size and contractile properties to bed rest were not prevented in the Penguin-2 group, although the degree of the changes was less than those induced by bed rest without any countermeasure. These results indicate that long-term bed rest results in reductions of fiber size, force-generation capacity, and Ca(2+) sensitivity, and enhancement of shortening velocity in slow fibers of the soleus. The data indicate that continuous mechanical loading on muscle, such as stretching of muscle, is an effective countermeasure for the prevention of muscular adaptations to gravitational unloading.

Regulation of contraction in striated muscle

Ca(2+) regulation of contraction in vertebrate striated muscle is exerted primarily through effects on the thin filament, which regulate strong cross-bridge binding to actin. Structural and biochemical studies suggest that the position of tropomyosin (Tm) and troponin (Tn) on the thin filament determines the interaction of myosin with the binding sites on actin. These binding sites can be characterized as blocked (unable to bind to cross bridges), closed (able to weakly bind cross bridges), or open (able to bind cross bridges so that they subsequently isomerize to become strongly bound and release ATP hydrolysis products). Flexibility of the Tm may allow variability in actin (A) affinity for myosin along the thin filament other than through a single 7 actin:1 tropomyosin:1 troponin (A(7)TmTn) regulatory unit. Tm position on the actin filament is regulated by the occupancy of NH-terminal Ca(2+) binding sites on TnC, conformational changes resulting from Ca(2+) binding, and changes in the interactions among Tn, Tm, and actin and as well as by strong S1 binding to actin. Ca(2+) binding to TnC enhances TnC-TnI interaction, weakens TnI attachment to its binding sites on 1-2 actins of the regulatory unit, increases Tm movement over the actin surface, and exposes myosin-binding sites on actin previously blocked by Tm. Adjacent Tm are coupled in their overlap regions where Tm movement is also controlled by interactions with TnT. TnT also interacts with TnC-TnI in a Ca(2+)-dependent manner. All these interactions may vary with the different protein isoforms. The movement of Tm over the actin surface increases the "open" probability of myosin binding sites on actins so that some are in the open configuration available for myosin binding and cross-bridge isomerization to strong binding, force-producing states. In skeletal muscle, strong binding of cycling cross bridges promotes additional Tm movement. This movement effectively stabilizes Tm in the open position and allows cooperative activation of additional actins in that and possibly neighboring A(7)TmTn regulatory units. The structural and biochemical findings support the physiological observations of steady-state and transient mechanical behavior. Physiological studies suggest the following. 1) Ca(2+) binding to Tn/Tm exposes sites on actin to which myosin can bind. 2) Ca(2+) regulates the strong binding of M.ADP.P(i) to actin, which precedes the production of force (and/or shortening) and release of hydrolysis products. 3) The initial rate of force development depends mostly on the extent of Ca(2+) activation of the thin filament and myosin kinetic properties but depends little on the initial force level. 4) A small number of strongly attached cross bridges within an A(7)TmTn regulatory unit can activate the actins in one unit and perhaps those in neighboring units. This results in additional myosin binding and isomerization to strongly bound states and force production. 5) The rates of the product release steps per se (as indicated by the unloaded shortening velocity) early in shortening are largely independent of the extent of thin filament activation ([Ca(2+)]) beyond a given baseline level. However, with a greater extent of shortening, the rates depend on the activation level. 6) The cooperativity between neighboring regulatory units contributes to the activation by strong cross bridges of steady-state force but does not affect the rate of force development. 7) Strongly attached, cycling cross bridges can delay relaxation in skeletal muscle in a cooperative manner. 8) Strongly attached and cycling cross bridges can enhance Ca(2+) binding to cardiac TnC, but influence skeletal TnC to a lesser extent. 9) Different Tn subunit isoforms can modulate the cross-bridge detachment rate as shown by studies with mutant regulatory proteins in myotubes and in in vitro motility assays. (ABSTRACT TRUNCATED)

Cross-bridge attachment during high-speed active shortening of skinned fibers of the rabbit psoas muscle: implications for cross-bridge action during maximum velocity of filament sliding

To characterize the kinetics of cross-bridge attachment to actin during unloaded contraction (maximum velocity of filament sliding), ramp-shaped stretches with different stretch-velocities (2-40,000 nm per half-sarcomere per s) were applied to actively contracting skinned fibers of the rabbit psoas muscle. Apparent fiber stiffness observed during such stretches was plotted versus the speed of the imposed stretch (stiffness-speed relation) to derive the rate constants for cross-bridge dissociation from actin. The stiffness-speed relation obtained for unloaded shortening conditions was shifted by about two orders of magnitude to faster stretch velocities compared to isometric conditions and was almost identical to the stiffness-speed relation observed in the presence of MgATPgammaS at high Ca(2+) concentrations, i.e., under conditions where cross-bridges are weakly attached to the fully Ca(2+) activated thin filaments. These data together with several control experiments suggest that, in contrast to previous assumptions, most of the fiber stiffness observed during high-speed shortening results from weak cross-bridge attachment to actin. The fraction of strongly attached cross-bridges during unloaded shortening appears to be as low as some 1-5% of the fraction present during isometric contraction. This is about an order of magnitude less than previous estimates in which contribution of weak cross-bridge attachment to observed fiber stiffness was not considered. Our findings imply that 1) the interaction distance of strongly attached cross-bridges during high-speed shortening is well within the range consistent with conventional cross-bridge models, i.e., that no repetitive power strokes need to be assumed, and 2) that a significant part of the negative forces that limit the maximum speed of filament sliding might originate from weak cross-bridge interactions with actin.

Relationships between isometric and isotonic mechanical parameters and cross-bridge kinetics

1. Isometric and isotonic measures have been widely used both to characterize muscular contraction in striated muscle and to compare the mechanical properties of striated muscle types for a wide variety of species. The interrelationship of these measures and their interpretation, in terms of underlying cross-bridge mechanisms, requires clarification. 2. We demonstrate that a strain-dependent three-state model can simulate these isometric and isotonic mechanics and offer a unified explanation for these mechanics in terms of cross-bridge kinetics. 3. Our exploration reveals the partial view each individual measure of mechanics provides and emphasizes the complementary insights the various isometric and isotonic measures give of the underlying cross-bridge kinetics.

A strain-dependent ratchet model for [phosphate]- and [ATP]-dependent muscle contraction

A minimal strain-dependent ratchet model of muscle cross-bridge action is proposed which is broadly compatible with structural and kinetic constraints. Its essential features are: (1) dynamic binding of the S1-products complex to actin through a disorder-order transition coupled to the release of inorganic phosphate; (2) the absence of a force-generating rotation of the myosin head between the two force-holding states A.M.ADP and A.M; (3) strain-control of ADP release and ATP binding, giving net isometric tension and directed motility by the selective dissociation of negatively strained bound states. With a disordered pre-force state, the binding rate to state A.M.ADP need not be symmetric in x, the actin site displacement. With faster binding at positive x, the model predicts many steady-state and transient properties of striated muscle observed experimentally, including phases 2-4 of tension recovery from length changes and their dependence on excess phosphate (which enhances and accelerates phase 3) and reduced ATP (which gives a bimodal phase 2 and slows one mode). The response to large perturbations is often sensitive to the number of actin sites used, and to the inclusion of a 1 nm displacement of the neck region on release of ADP. The latter stabilizes the periodic tension behaviour produced by repeated releases.

Mechanism of action of endothelin in rat cardiac muscle: cross-bridge kinetics and myosin light chain phosphorylation

1. The molecular mechanism of inotropic action of endothelin was investigated in rat ventricular muscle by studying its effects on characteristics of isometric twitch, barium-induced steady contracture and the level of incorporation of 32Pi into myosin light chain 2. 2. Exposure of rat papillary muscle to endothelin caused an increase in isometric twitch force but did not alter the twitch-time parameters. 3. Endothelin did not significantly change the maximum contracture tension but did cause an increase in contracture tension at submaximal levels of activation, without changes in the tension-to-stiffness ratio and kinetics of attached cross-bridges. Kinetics of attached cross-bridges were deduced during steady contracture from complex-stiffness values, and in particular from the frequency at which muscle stiffness assumes a minimum value, fmin. Endothelin did not alter fmin. 4. Endothelin caused an increase in the level of incorporation of 32Pi into myosin light chain 2 without a concurrent change in the level of incorporation of 32Pi into troponin I. 5. We conclude that the inotropic action of endothelin is not due to an increase in the kinetics of attached cross-bridges, nor due to a change in the force per unit cross-bridge, but may result from an increased divalent cation sensitivity caused by elevated myosin light chain 2 phosphorylation, resembling post-tetanic potentiation in fast skeletal muscle fibres.

Increase in ATP consumption during shortening in skinned fibres from rabbit psoas muscle: effects of inorganic phosphate

1. The influence of inorganic phosphate (P(i)) on the relationship between ATP consumption and mechanical performance under isometric and dynamic conditions was investigated in chemically skinned single fibres or thin bundles from rabbit psoas muscle. Myofibrillar ATPase activity was measured photometrically by enzymatic coupling of the regeneration of ATP to the oxidation of NADH. NADH absorbance at 340 nm was determined inside a miniature (4 microliters) measuring chamber. 2. ATP consumption due to isovelocity shortenings was measured in the range between 0.0625 and 1 L0 s-1(L0: fibre length previous to shortening, corresponding to a sarcomere length of 2.64 microns), in solutions without added P(i) and with 30 mM P(i). To get an estimate of the amount of ATP utilized during the shortening phase, quick releases of various amplitudes were also performed. 3. After quick releases, sufficiently large that force dropped to zero, extra ATP was hydrolysed which was largely independent of the amplitude of the release and of the period of unloaded shortening. This extra amount, above the isometric ATP turnover, corresponded to about 0.7 and 0.5 ATP molecules per myosin head at 0 and 30 mM P(i), respectively. 4. ATP turnover during the isovelocity shortenings was higher than isometric turnover and increased with increasing shortening velocity up to about 2.7 times the isometric value. At low and moderate velocities of shortening (< 0.5 L0 s-1), P(i) reduced ATP turnover during isovelocity shortening and isometric ATP turnover to a similar extent, i.e. a decrease to about 77% between 0 and 30 mM added P(i). 5. The extra ATP turnover above the isometric value, resulting from isovelocity shortenings studied at different speeds, was proportional to the power output of the preparation, both in the absence and presence of added [P(i)]. 6. The effect of shortening velocity and [P(i)] on energy turnover can be understood in a cross-bridge model that consists of a detached, a non- or low-force-producing, and a force-producing state. In this model, mass action of P(i) influences the equilibrium between the force-producing and the non-or-low-force-producing cross-bridges, and shortening enhances cross-bridge detachment from both attached states.

Evidence for increased low force cross-bridge population in shortening skinned skeletal muscle fibers: implications for actomyosin kinetics

The dynamic characteristics of the low force myosin cross-bridges were determined in fully calcium-activated skinned rabbit psoas muscle fibers shortening under constant loads (0.04-0.7 x full isometric tension Po). The shortening was interrupted at various times by a ramp stretch (duration, 10 ms; amplitude, up to 1.8% fiber length) and the resulting tension response was recorded. Except for the earlier period of velocity transients, the tension response showed nonlinear dependence on stretch amplitude; i.e., the magnitude of the tension response started to rise disproportionately as the stretch exceeded a critical amplitude, as in the presence of inorganic phosphate (Pi). This result, as well as the result of stiffness measurement, suggests that the low force cross-bridges similar to those observed in the presence of Pi (presumably A.M.ADP.Pi) are significantly populated during shortening. The critical amplitude of the shortening fibers was greater than that of isometrically contracting fibers, suggesting that the low force cross-bridges are more negatively strained during shortening. As the load was reduced from 0.3 to 0.04 P0, the shortening velocity increased more than twofold, but the amount of the negative strain stayed remarkably constant (approximately 3 nm). This This insensitiveness of the negative strain to velocity is best explained if the dissociation of the low force cross-bridges is accelerated approximately in proportion to velocity. Along with previous reports, the results suggest that the actomyosin ATPase cycle in muscle fibers has at least two key reaction steps in which rate constants are sensitively regulated by shortening velocity and that one of them is the dissociation of the low force A.M.ADP.Pi cross-bridges. This step may virtually limit the rate of actomyosin ATPase turnover and help increase efficiency in fibers shortening at high velocities.

Relationship between muscle force and stiffness in the whole mammalian muscle: a simulation study

Several types of analyses in biomechanics require estimates of both muscle force and stiffness. Simulations were performed using the two-state cross-bridge Bond Distribution-Moment muscle model of Zahalak (1981), together with other parameters for passive elasticity and tendon compliance, to estimate instantaneous stiffness and to compare these estimates with the wide range of values reported in the literature. While the relatively simple cross-bridge theory appears to approximate the stiffness of skinned muscle fibers, the stiffness of a complete muscle-tendon unit become complex and non-linear due to relative changes in muscle-tendon length and interaction with activation and length dependent passive elastic components. It would appear that the variability in muscle stiffness values reported in the literature can be explained with the D-M approach.

Myofibrillar fatigue versus failure of activation

Two principal mechanisms underlying fatigue of isolated muscle fibers are described: failure of activation of the contractile system and reduced performance of the myofibrils due to altered kinetics of crossbridge function. The relative importance of these two mechanisms during development of fatigue is discussed.

Sarcomere function and crossbridge cycling

The power of the heart is dictated by the force development and velocity of shortening (V) of the cardiac sarcomere. Both depend on the amount of Ca++ released by the sarcoplasmic reticulum during the action potential. We have investigated the inter-relationship between force (F) sarcomere length (SL) and V and the intracellular Ca++ concentration ([Ca++]i) in trabeculae isolated from the right ventricle of rat heart. Activation of the contractile filaments during a normal heartbeat requires approximately 30 microM Ca++ ions, which rapidly bind to cytosolic ligands. Consequently the [Ca++]i transient detected by intracellular probes is less than 2 microM. Length dependent binding of Ca++ to Troponin-C is responsible for the shape of the F-SL relationship. Ca++ ions are bound to Troponin-C long enough to allow the F-SL relationship, and consequently the end-systolic pressure volume relationship in the intact ventricle, to be largely--but not completely--independent of the loading conditions. V increases hyperbolically with decreasing load during contraction against a load. Stiffness studies reveal that the number of attached crossbridges increases in linear proportion to an increase of the external load. At low external loads the V was large enough to induce a substantial viscoelastic load within the sarcomere itself. The F-V relationship of a single crossbridge appeared to be linear after correction for the observed viscoelastic properties of the muscle and for load dependence of the number of crossbridges. Maximal V of sarcomere shortening without an external load (Vo), depends on the level of activation by Ca++ ions because of the internal viscous load. Our studies of the rate of ATP hydrolysis by the actin-activated S1 fragment of myosin suggest that Vo is limited by the detachment rate of the crossbridge from actin. These studies also suggest that the difference between the fast (V1) and slow (V2) myosin iso-enzyme can be explained by a difference in the amino acid domain on S1 involved in binding of the crossbridge to the actin filament.

Faster force transient kinetics at submaximal Ca2+ activation of skinned psoas fibers from rabbit

The early, rapid phase of tension recovery (phase 2) after a step change in sarcomere length is thought to reflect the force-generating transition of myosin bound to actin. We have measured the relation between the rate of tension redevelopment during phase 2 (r), estimated from the half-time of tension recovery during phase 2 (r = t0.5(-1)), and steady-state force at varying [Ca2+] in single fibers from rabbit psoas. Sarcomere length was monitored continuously by laser diffraction of fiber segments (length approximately 1.6 mm), and sarcomere homogeneity was maintained using periodic length release/restretch cycles at 13-15 degrees C. At lower [Ca2+] and forces, r was elevated relative to that at pCa 4.0 for both releases and stretches (between +/- 8 nm). For releases of -3.4 +/- 0.7 nm.hs-1 at pCa 6.6 (where force was 10-20% of maximum force at pCa 4.0), r was 3.3 +/- 1.0 ms-1 (mean +/- SD; N = 5), whereas the corresponding value of r at pCa 4.0 was 1.0 +/- 0.2 ms-1 for releases of -3.5 +/- 0.5 nm.hs-1 (mean +/- SD; N = 5). For stretches of 1.9 +/- 0.7 nm.hs-1, r was 1.0 +/- 0.3 ms-1 (mean +/- SD; N = 9) at pCa 6.6, whereas r was 0.4 +/- 0.1 ms-1 at pCa 4.0 for stretches of 1.9 +/- 0.5 (mean +/- SD; N = 14). Faster phase 2 transients at submaximal Ca(2+)-activation were not caused by changes in myofilament lattice spacing because 4% Dextran T-500, which minimizes lattice spacing changes, was present in all solutions. The inverse relationship between phase 2 kinetics and force obtained during steady-state activation of skinned fibers appears to be qualitatively similar to observations on intact frog skeletal fibers during the development of tetanic force. The data are consistent with models that incorporate a direct effect of [Ca2+] on phase 2 kinetics of individual cross-bridges or, alternatively, in which phase 2 kinetics depend on cooperative interactions between cross-bridges.

Skeletal muscle stiffness in static and dynamic contractions

Series elastic stiffness of rat gastrocnemius medialis muscle was determined by means of sinusoidal movements (180 Hz, 0.25% of muscle length) for various contraction conditions. The effects of muscle length, activation level, velocity, prestretch, and temperature on the force-stiffness relationship were investigated. All force-stiffness curves were transformed to a linear force-alpha curve (Ettema and Huijing, 1993; Morgan, 1977) to distinguish mathematically two series elastic components; a force dependent and force independent compliance. For all isometric conditions a typical force-stiffness curve was found, where stiffness increased with force, and this increase levelled off at higher forces. Stiffness in dynamic shortening and lengthening contractions is related to force in a completely different way than in isometric condition. An increase in temperature caused a decrease in muscle stiffness for a given force, and the effects of muscle length, activation level, and prestretch were small. It was concluded that the series elastic component of skeletal-muscle-tendon complex is probably located in more than two morphologically identifiable elements. Furthermore, we concluded that using a single series elastic element in muscle modelling is not appropriate to describe muscle behaviour under all conditions that occur during in vivo activation.

Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance

Continuous stochastic position perturbations are an attractive alternative to transient perturbations in muscle and reflex studies because they allow efficient characterization of system properties. However, the relevance of the results obtained from stochastic perturbations remains unclear because they may induce a state change in muscle properties. We addressed this concern by comparing the force and stiffness responses of isolated muscles of the decerebrate cat elicited by stochastic perturbations to those evoked by "step" stretches of similar amplitudes. Muscle stiffness during stochastic perturbations was found to be predominantly linear and elastic in nature for a given operating point, showing no evidence of instantaneous amplitude-dependent nonlinearities, even during large movements. In contrast, force responses evoked by step stretches were found to be mainly viscous in nature and nonlinear for larger stretches, with only a small maintained (elastic) component. Stiffness magnitude decreased with displacement amplitude for both stochastic and step perturbations. Our results are largely consistent with the crossbridge theory of muscle contraction, indicating that transient and continuous displacements evoke different, although functionally relevant, aspects of muscle behavior. These differences have several implications for the neural control of posture and movement, and for the design of perturbations appropriate for its study.

Myofibrillar ATPase activity and mechanical performance of skinned fibres from rabbit psoas muscle

1. The relationship between energy turnover and mechanical performance was investigated in chemically skinned single fibres from rabbit psoas muscle at 15 degrees C, pH = 7.1, with MgATP, 5 mM; free Mg2+, 1 mM; ionic strength, 200 mM and sarcomere length, 2.4 microns by measuring force production and myofibrillar ATP turnover during isometric contractions as well as during repetitive changes in length. ATP hydrolysis was stoichiometrically coupled to the breakdown of NADH, which was measured photometrically via the absorption of near UV light at 340 nm. 2. Force and ATPase activity were measured during square-wave length changes of different amplitudes (1-10% of the fibre length, Lo) and different frequencies (2.5-167 Hz). The average force during the length changes was less than the isometric value and decreased with increasing amplitude and frequency. At full activation (pCa 4.5), the isometric ATP turnover rate (+/- S.E.M.) was 2.30 +/- 0.05 s-1 per myosin head. ATP turnover increased monotonically with increasing amplitude as well as with increasing frequency until saturation was reached. The greatest increase observed was 2.4 times the isometric value. 3. Force and ATPase activity were also determined for ramp shortenings followed by fast restretches. The average force decreased with increasing shortening velocity in a hyperbolic fashion. The ATP turnover increased with ramp velocity up to 0.5 L0 s-1 and stayed almost constant (at 2.2 times the isometric value) for larger velocities. 4. Isometric force and ATPase activity both decreased as the calcium concentration was decreased. They did not vary in proportion at low Ca2+ concentrations, but this could largely be accounted for by the presence of a residual, Ca(2+)-dependent, membrane-bound ATPase. At high calcium concentrations ATPase activity during square-wave length changes was higher than the isometric value, but at low calcium concentrations (pCa > 6.1), the ATPase activity during the length changes decreased below the isometric value and reached a minimum of 40% of the isometric level. 5. ATPase activity and average force obtained during changes in length show a high, movement protocol-independent correlation. During the length changes the rate of ATP turnover divided by the average force level (tension cost) was larger than the isometric tension cost. The largest value found, for 10% length changes at 23 Hz, was 17 times the tension cost under isometric conditions.(ABSTRACT TRUNCATED AT 400 WORDS)

Calcium modulates the influence of length changes on the myofibrillar adenosine triphosphatase activity in rat skinned cardiac trabeculae

The relationship between adenosine triphosphate (ATP) turnover and muscle performance was investigated in skinned cardiac trabeculae of the rat at different [Ca2+] and two different sarcomere lengths (1.8 microns and 2.2 microns) at 20 degrees C. ATP turnover was measured photometrically by enzymatic coupling of the regeneration of ATP to the oxidation of reduced nicotinamide adenine dinucleotide. The trabeculae were studied under isometric conditions and when the length was altered repetitively at a frequency of 23 Hz, with a square wave, by 5% of the initial length. The isometric ATPase activity amounted to 0.48 mM/s. Isometric ATP turnover and force were proportional at different [Ca2+]. During length changes at maximal activation (pCa 4.27) and 2.2 microns sarcomere length, ATPase activity increased to up to 162% whereas at low [Ca2+], ATPase activity decreased with respect to the isometric value at that pCa. At pCa 5.5, ATPase activity was reduced to 33%. These results indicate that during the length changes the apparent cross-bridge detachment rate is increased and the apparent attachment rate is decreased. The findings suggest that the Fenn effect, i.e. the increase in energy turnover above the isometric value during shortening, is present in cardiac trabeculae at high levels of activation, but is absent or reversed at lower levels of activity.

Cross-bridge attachment and stiffness during isotonic shortening of intact single muscle fibers

Equatorial x-ray diffraction pattern intensities (I10 and I11), fiber stiffness and sarcomere length were measured in single, intact muscle fibers under isometric conditions and during constant velocity (ramp) shortening. At the velocity of unloaded shortening (Vmax) the I10 change accompanying activation was reduced to 50.8% of its isometric value, I11 reduced to 60.7%. If the roughly linear relation between numbers of attached bridges and equatorial signals in the isometric state also applies during shortening, this would predict 51-61% attachment. Stiffness (measured using 4 kHz sinusoidal length oscillations), another putative measure of bridge attachment, was 30% of its isometric value at Vmax. When small step length changes were applied to the preparation (such as used for construction of T1 curves), no equatorial intensity changes could be detected with our present time resolution (5 ms). Therefore, unlike the isometric situation, stiffness and equatorial signals obtained during ramp shortening are not in agreement. This may be a result of a changed crossbridge spatial orientation during shortening, a different average stiffness per attached crossbridge, or a higher proportion of single headed crossbridges during shortening.

Tension transients in skeletal muscle fibres of the frog at varied tonicity of the extracellular medium

Length steps (complete in 0.2 ms; amplitude < 2% of the fibre length) were applied during the tetanus plateau of intact frog muscle fibres (1.7-3.2 degrees C). The effects of varied tonicity on the early changes in tension in response to the length steps were studied. The solutions were made hypotonic by reduction of the NaCl concentration from 115.5 mM to 92.4 mM and hypertonic by addition of 98 mmol sucrose per litre of the normal Ringer fluid. In all solutions tested, the length step first caused tension to change simultaneously with the step reaching an extreme value T1. After completion of the length change, tension recovered quickly to an intermediate level T2 and, after a period with slowing or reversal of the recovery, it returned slowly to the steady-state value. The maximum isometric tension was significantly reduced by increases in tonicity. In contrast, there were only small effects of varied tonicity on the peak tension-change in response to a length step (the stiffness) and on the amplitude of the fast force recovery (T2-T1) after releases. The slope of the T2-curve (a plotting of T2 versus amplitude of the length step) was reduced for releases and increased for stretches when tonicity was raised. Furthermore, the T2-curve intersected the length axis for smaller releases at high tonicity levels. The reduced isometric tension to stiffness ratio at raised tonicity could be interpreted as a reduced average force per crossbridge. Simulations using the crossbridge model of Huxley and Simmons (1971) showed that the lack of change of the recovery amplitude (T2-T1) after releases and the changes in the T2-slope are in accordance with this interpretation. The shift of the T2 length intercept is consistent with the idea that the distance traversed by the crossbridges during the power-stroke is reduced by raised tonicity.

Determinants of velocity of sarcomere shortening in mammalian myocardium

Maximal unloaded velocity of shortening of cardiac muscle (Vo) depends on the level of activation of the contractile filaments. We have tested the hypothesis that this dependence may be caused by viscous resistance of the muscle to length changes. Twitch force (Fo) and sarcomere shortening were studied in trabeculae dissected from the right ventricle of rat myocardium, superfused with modified Krebs-Henseleit solution at 25 degrees C. Sarcomere length (SL) was measured by laser diffraction techniques; force was measured by a silicon strain gauge; velocity of sarcomere shortening was measured using the "isovelocity release" technique. Vo and Fo at slack SL were a sigmoidal function of [Ca2+]o, but Vo was more sensitive to [Ca2+]o (Km: 0.44 +/- 0.04 mM) than isometric twitch force (Km: 0.68 +/- 0.03 mM). At [Ca2+]o = 1.5 mM, Vo was independent of SL above 1.9 microns, but depended on SL at lower [Ca2+]o and always depended on SL < 1.9 microns. A constant relation was observed between Vo and Fo, irrespective whether Fo was altered by variation of [Ca2+]o or SL above slack length. Visco-elastic properties of unstimulated muscles were studied at SL = 2.0 microns by small linear length changes at varied velocities up to 40 microns/s. The force response to stretch, after correction for the contribution of static parallel elasticity, consisted of an exponential increase of force (tau = 4 ms) and an exponential decline after the stretch. This response would be expected from an arrangement of a viscous element in series with an elastic element. Viscous force increased in proportion to stretch velocity by 0.2-0.5% of Fo/micron/s up to 15 microns/s, while the calculated stiffness of the elastic component was 25-45 N.mm-3, suggesting that the most likely structural candidate for this visco-elastic element is titin. Dynamic stiffness at 500 Hz was proportional to instantaneous force during shortening and was 12% of stiffness at maximal twitch force when shortening occurred at Vo. This suggests that the number of active force generators, even at maximal activation, is strongly reduced during shortening at Vo. The observed relation between Vo and Fo could be explained by a model in which shortening velocity of the cardiac sarcomere depends on the level of activation and hence on the number of cross bridges supporting the viscous load.

An internal viscous element limits unloaded velocity of sarcomere shortening in rat myocardium

1. Peak twitch force (F0) and sarcomere length (SL) were measured in trabeculae that had been dissected from the right ventricle of rat heart and that were superfused with a modified Krebs-Henseleit solution at 25 degrees C. Sarcomere length was measured by laser diffraction techniques. Force was measured with a silicone strain gauge. Unloaded velocity of sarcomere shortening (V0) was measured by the 'isovelocity release' technique. 2. At [Ca2+]o = 1.5 mM and SL below 1.9 microns, V0 increased in proportion to SL, while V0 was independent of SL above 1.9 microns. At [Ca2+]o = 0.5 mM, V0 was proportional to SL up to 2.2 microns. At [Ca2+]o = 0.2 mM, V0 was proportional to SL up to 2.3 microns which is the longest SL that we were able to study in our trabeculae. 3. A unique relationship was observed between V0 and F0, irrespective of whether F0 was altered by variation of [Ca2+]o or sarcomere length above slack length. 4. Passive viscosity (Fv) was measured during the pause between contractions in the presence of 1.5 mM [Ca2+bdo and in the range SL = 2.0-2.1 microns by applying 0.1 micron stretches at various velocities up to v = 30 microns s-1. The force response to stretch, corrected for the contribution of parallel elastic force, showed viscoelastic characteristics with an exponential increase to a maximum (Fv) during stretch and an exponential decline after the end of the stretch. Fv increased, by 0.3%F0 microns-1 s-1, in proportion to v < 5 microns s-1; the increase of Fv was smaller at higher v, suggesting non-Newtonian viscous properties. 5. The time constant of the increase of force during the stretch decreased (tau rise congruent to 7 ms to tau rise congruent to 4 ms) with increases in v (congruent to 4 microns s-1 to v congruent to 10 microns s-1; P = 0.02). The time constant of decay of force at the end of the stretch also decreased with increases in v (tau decay congruent to 8 ms at v congruent to 4 microns s-1 to tau decay congruent to 3 ms at v congruent to 30 microns s-1; P < 0.001). Calculated stiffness of the elastic term of the viscoelastic element was independent of v, i.e. 45-50 N mm-3.(ABSTRACT TRUNCATED AT 400 WORDS)

Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading

A mathematical model for the regulation of mechanical activity in cardiac muscle has been developed based on a three-element rheological model of this muscle. The contractile element has been modeled taking into account the results of extensive mechanical tests that involved the recording of length-force and force-velocity relations and muscle responses to short-time deformations during various phases of the contraction-relaxation cycle. The best agreement between the experimental and the mathematical modeling results was obtained when a postulate stating two types of cooperativity to regulate the calcium binding by troponin was introduced into the model. Cooperativity of the first type is due to the dependence of the affinity of troponin C for Ca2+ on the concentration of myosin crossbridges in the vicinity of a given troponin C. Cooperativity of the second type assumes an increase in the affinity of a given troponin C for Ca2+ when the latter is bound by molecules neighboring troponin.

Tension as a function of sarcomere length and velocity of shortening in single skeletal muscle fibres of the frog

1. Simple measurements of muscle tension at fixed fibre or segment length produce a range of length-tension relationships, depending primarily on the duration of the interval between stimulation onset and tension measurement, in contradiction with the simple predictions of current models. This has been explained by non-uniformity in sarcomere lengths, leading to internal motion and, in turn, to increasing tension because the force-velocity relationship has a much greater slope for slow lengthening than for slow shortening. 2. Previous attempts to reduce the effect of internal motion have been focused on decreasing the initial extent of non-uniformity and measuring tension early in a contraction, when non-uniformities are at a minimum. An alternative approach that has not been attempted previously is to reduce the non-linearity of the force-velocity relationship by avoiding the discontinuity in slope at zero velocity. This is accomplished by imposing overall fibre shortening at velocities sufficient to ensure that all sarcomeres are shortening. 3. When the tension maintained during shortening was measured and plotted against sarcomere length for each release velocity used, linear length-tension relationships resulted that extrapolated to a common sarcomere length intercept. This was true whether the release was applied early in the tetanus or near the end of the 'creep phase' of tension rise. These observations were duplicated by computer simulation using a multisarcomere model of a muscle fibre. 4. These results provide strong support for the view that cross-bridges function as independent force generators and for the explanation of the creep phase of fibre or segment isometric tension as being due to internal motion. The results also imply that the force-velocity relationship scales with sarcomere length without changing shape. 5. Using this novel method for obtaining length-tension relationships, the sarcomere length at which active tension fell to zero was found, by extrapolation, to be 3.65 microns in semitendinosus fibres and 3.53 microns in tibialis anterior fibres from the frog (Rana temporaria).

The theory of sliding filament models for muscle contraction. III. Dynamics of the five-state model

The five-state model derived in the last paper is shown to provide a unified description of most dynamical behaviour of striated muscle, with a set of rate constants in accord with in-vitro values. It predicts several observed phenomena beyond the scope of older models. Rapid binding of M.ADP.Pi to actin generates a high-frequency tail in the Nyquist plot for AC stiffness, which is only weakly dependent on contraction velocity. Known effects of changes in Ca2+ level are predicted if Ca2+ activates only the phosphate-release step, e.g. in the relaxed-state there is substantial stiffness at high frequencies and weak stiffness at low frequencies. Under partial activation the tension drops with increasing extension speed, and Nyquist plots suggest that the reverse phosphate step should be unaffected by Ca2+. Lowering the phosphate level increases tension and also the first two loop amplitudes of the Nyquist plot. The model also yields an improved tension-velocity characteristic, acceptable length-step response, and simulates Brenner & Eisenberg's "stop and stretch" experiment which is shown to be closely related to isometric activation. Oscillatory length response to small tension steps is shown to be a general feature of any model whose AC stiffness can be fitted by a three-term Kawai formula. The model must be enlarged to include the rigor-state, and to describe the effects of variations in ATP and ADP levels correctly.