Stiffness and force in activated frog skeletal muscle fibers

Thick-Filament Extensibility in Intact Skeletal Muscle

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

Structural and functional impact of troponin C-mediated Ca2+ sensitization on myofilament lattice spacing and cross-bridge mechanics in mouse cardiac muscle

Acto-myosin cross-bridge kinetics are important for beat-to-beat regulation of cardiac contractility; however, physiological and pathophysiological mechanisms for regulation of contractile kinetics are incompletely understood. Here we explored whether thin filament-mediated Ca²⁺ sensitization influences cross-bridge kinetics in permeabilized, osmotically compressed cardiac muscle preparations. We used a murine model of hypertrophic cardiomyopathy (HCM) harboring a cardiac troponin C (cTnC) Ca²⁺-sensitizing mutation, Ala8Val in the regulatory N-domain. We also treated wild-type murine muscle with bepridil, a cTnC-targeting Ca²⁺ sensitizer. Our findings suggest that both methods of increasing myofilament Ca²⁺ sensitivity increase cross-bridge cycling rate measured by the rate of tension redevelopment (k_TR); force per cross-bridge was also enhanced as measured by sinusoidal stiffness and I_1,1/I_1,0 ratio from X-ray diffraction. Computational modeling suggests that Ca²⁺ sensitization through this cTnC mutation or bepridil accelerates k_TR primarily by promoting faster cross-bridge detachment. To elucidate if myofilament structural rearrangements are associated with changes in k_TR, we used small angle X-ray diffraction to simultaneously measure myofilament lattice spacing and isometric force during steady-state Ca²⁺ activations. Within in vivo lattice dimensions, lattice spacing and steady-state isometric force increased significantly at submaximal activation. We conclude that the cTnC N-domain controls force by modulating both the number and rate of cycling cross-bridges, and that the both methods of Ca²⁺ sensitization may act through stabilization of cTnC's D-helix. Furthermore, we propose that the transient expansion of the myofilament lattice during Ca²⁺ activation may be an additional factor that could increase the rate of cross-bridge cycling in cardiac muscle. These findings may have implications for the pathophysiology of HCM.

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

KEY POINTS

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

ABSTRACT

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

Torque response to external perturbation during unconstrained goal-directed arm movements

It is unclear to what extent control strategies of 2D reaching movements of the upper limbs also apply to movements with the full seven degrees of freedom (DoFs) including rotation of the forearm. An increase in DoFs may result in increased movement complexity and instability. This study investigates the trajectories of unconstrained reaching movements and their stability against perturbations of the upper arm. Reaching movements were measured using an ultrasound marker system, and the method of inverse dynamics was applied to compute the time courses of joint torques. In full DoF reaching movements, the velocity of some joint angles showed multiple peaks, while the bell-shaped profile of the tangential hand velocity was preserved. This result supports previous evidence that tangential hand velocity is an essential part of the movement plan. Further, torque responses elicited by external perturbation started shortly after perturbation, almost simultaneously with the perturbation-induced displacement of the arm, and were mainly observed in the same joint angles as the perturbation torques, with similar shapes but opposite signs. These results indicate that these torque responses were compensatory and contributed to system stabilization.

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

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

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

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

Spreading out muscle mass within a Hill-type model: a computer simulation study

It is state of the art that muscle contraction dynamics is adequately described by a hyperbolic relation between muscle force and contraction velocity (Hill relation), thereby neglecting muscle internal mass inertia (first-order dynamics). Accordingly, the vast majority of modelling approaches also neglect muscle internal inertia. Assuming that such first-order contraction dynamics yet interacts with muscle internal mass distribution, this study investigates two questions: (i) what is the time scale on which the muscle responds to a force step? (ii) How does this response scale with muscle design parameters? Thereto, we simulated accelerated contractions of alternating sequences of Hill-type contractile elements and point masses. We found that in a typical small muscle the force levels off after about 0.2 ms, contraction velocity after about 0.5 ms. In an upscaled version representing bigger mammals' muscles, the force levels off after about 20 ms, and the theoretically expected maximum contraction velocity is not reached. We conclude (i) that it may be indispensable to introduce second-order contributions into muscle models to understand high-frequency muscle responses, particularly in bigger muscles. Additionally, (ii) constructing more elaborate measuring devices seems to be worthwhile to distinguish viscoelastic and inertia properties in rapid contractile responses of muscles.

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

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

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

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

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

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

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

The cross-bridge stiffness can be used to estimate the number of S1 that are bound to actin during contraction, which is a critical parameter for elucidating the fundamental mechanism of the myosin motor. At present, the development of active tension and the increase in muscle stiffness due to S1 binding to actin are thought to be linearly related to the number of cross-bridges formed upon activation. The nonlinearity of total stiffness with respect to active force is thought to arise from the contribution of actin and myosin filament stiffness to total sarcomere elasticity. In this work, we reexamined the relation of total stiffness to tension during activation and during exposure to N-benzyl-p-toluene sulphonamide, an inhibitor of cross-bridge formation. In addition to filament and cross-bridge elasticity, our findings are best accounted for by the inclusion of an extra elasticity in parallel with the cross-bridges, which is formed upon activation but is insensitive to the subsequent level of cross-bridge formation. By analyzing the rupture tension of the muscle (an independent measure of cross-bridge formation) at different levels of activation, we found that this additional elasticity could be explained as the stiffness of a population of no-force-generating cross-bridges. These findings call into question the assumption that active force development can be taken as directly proportional to the cross-bridge number.

Reversal of the myosin power stroke induced by fast stretching of intact skeletal muscle fibers

Force generation and movement in skeletal muscle result from a cyclical interaction of overlapping myosin and actin filaments that permits the free energy of ATP hydrolysis to be converted into mechanical work. The rapid force recovery that occurs after a step release imposed on a muscle is thought to result from a synchronized tilting of myosin lever arms toward a position of lower free energy (the power stroke). We investigated the power stroke mechanism in intact muscle fibers of Rana esculenta using a fast stretch to detach forcibly cross-bridges. Stretches were applied either with or without a conditioning step release. Cross-bridge rupture tension was not significantly influenced by the release, whereas sarcomere elongation at the rupture point increased immediately after the release and returned to the prerelease condition within 15-20 ms, following a slower time course compared to the recovery of tension. These observations suggest that the rupture force of a bridge is unaltered by a conditioning release, but rupture must first be preceded by a power stroke reversal, which restores the prepower stroke state. The sarcomere extension at the rupture point indicates both the extent of this power stroke reversal and the time course of strained bridge replenishment.

Kinetics of force recovery following length changes in active skinned single fibres from rabbit psoas muscle: analysis and modelling of the late recovery phase

Redevelopment of isometric force following shortening of skeletal muscle is thought to result from a redistribution of cross-bridge states. We varied the initial force and cross-bridge distribution by applying various length-change protocols to active skinned single fibres from rabbit psoas muscle, and observed the effect on the slowest phase of recovery ('late recovery') that follows transient changes. In response to step releases that reduced force to near zero ( approximately 8 nm (half sarcomere)(-1)) or prolonged shortening at high velocity, late recovery was well described by two exponentials of approximately equal amplitude and rate constants of approximately 2 s(-1) and approximately 9 s(-1) at 5 degrees C. When a large restretch was applied at the end of rapid shortening, recovery was accelerated by (1) the introduction of a slow falling component that truncated the rise in force, and (2) a relative increase in the contribution of the fast exponential component. The rate of the slow fall was similar to that observed after a small isometric step stretch, with a rate of 0.4-0.8 s(-1), and its effects could be reversed by reducing force to near zero immediately after the stretch. Force at the start of late recovery was varied in a series of shortening steps or ramps in order to probe the effect of cross-bridge strain on force redevelopment. The rate constants of the two components fell by 40-50% as initial force was raised to 75-80% of steady isometric force. As initial force increased, the relative contribution of the fast component decreased, and this was associated with a length constant of about 2 nm. The results are consistent with a two-state strain-dependent cross-bridge model. In the model there is a continuous distribution of recovery rate constants, but two-exponential fits show that the fast component results from cross-bridges initially at moderate positive strain and the slow component from cross-bridges at high positive strain.

Force enhancement by PEG during ramp stretches of skeletal muscle

We have investigated the effects of a stronger actomyosin bond on force (Ps) during rapid stretch of active permeabilized rabbit psoas muscle fibers as a function of temperature from 5 to 30 degrees C. The strength of the actomyosin bond is enhanced by addition of polyethylene glycol (PEG), especially in pre-powerstroke states [Chinn et al. (2000) Biophys J 49: 437-451]. We have hypothesized that such states produce much of the force when activated muscles are stretched [Getz et al. (1998) Biophys J 75: 2971-2983]. Addition of PEG to activated fibers produced a small increase in isometric tension, Po (50-90 kN/m2), which was approximately independent of temperature. In contrast PEG produced a dramatic increase in Ps at low temperatures (200-300 kN/m2), but a modest increase at higher temperatures (70-90 kN/m2). We also measured Ps and Po in solutions containing the phosphate analog aluminum fluoride (AlF4) with and without PEG. In the absence of PEG, AlF4 reduced Po much more than Ps. Addition of PEG did not enhance Po, but enhanced Ps significantly. The contrasting effects of PEG on Ps and Po, and the effect of temperature can be explained by a model in which stretch force is produced by pre-powerstroke cross-bridges whose maximum distension is increased by PEG, and isometric force is produced by strongly bound cross-bridges whose bond strength is also enhanced by PEG, but to a lesser extent.

Elbow impedance during goal-directed movements

The mechanical properties and reflex actions of muscles crossing the elbow joint were examined during a 60-deg voluntary elbow extension movement. Brief unexpected torque pulses of identical magnitude and time-course (20-Nm extension switching to 20-Nm flexion within 30 ms) were introduced at various points of a movement in randomly selected trials. Single pulses were injected in different trials, some before movement onset and some either during early, mid, late or ending stages of the movement. Changes in movement trajectory induced by a torque pulse were determined over the first 50 ms by a nearest-neighbor prediction algorithm, and then a modified K-B-I (stiffness-damping-inertia) model was fit to the responses. The stiffness and damping coefficients estimated during voluntary movements were compared to values recorded during trials in which subjects were instructed to strongly co-contract while maintaining a static posture. This latter protocol was designed to help determine the maximum impedance a subject could generate. We determined that co-contraction increased joint stiffness greatly, well beyond that recorded under control conditions. In contrast, the stiffness magnitudes were quite small during routine voluntary movements, or when the subjects relaxed their limb. Furthermore, the damping coefficients were always significant and increased measurably at the end of movement. Reflex activity, as measured by EMG responses in biceps and triceps brachii, showed highly variable responses at latencies of 160 ms or greater. These reflexes tended to activate both elbow flexors and extensors simultaneously. These findings suggest that very low intrinsic muscle stiffness values recorded during point-to-point motion render an equilibrium point or impedance control approach implausible as a means to regulate movement trajectories. In particular, muscle that is shortening against inertial loads seems to exhibit much smaller stiffness than similarly active isometric muscle, although some degree of damping is always present and does not simply co-vary with stiffness. Although the limb muscles can be co-contracted statically or during movement with an observable increase in stiffness and even task performance, this control strategy is rarely utilized, presumably due to the greater energetic cost.

Effects of volatile anesthetics on elastic stiffness in isometrically contracting ferret ventricular myocardium

The effects of halothane, isoflurane, and sevoflurane on elastic stiffness, which reflects the degree of cross-bridge attachment, were studied in intact cardiac muscle. Electrically stimulated (0.25 Hz, 25 degrees C), isometrically twitching right ventricular ferret papillary muscles (n = 15) at optimal length (L(max)) were subjected to sinusoidal length oscillations (40 Hz, 0.25- 0.50% of L(max) peak to peak). The amplitude and phase relationship with the resulting force oscillations was decomposed into elastic and viscous components of total stiffness in real time. Increasing extracellular Ca(2+) concentration in the presence of anesthetics to produce peak force equal to control increased elastic stiffness during relaxation, which suggests a direct effect of halothane and sevoflurane on cross bridges.

Sarcomere tension-stiffness relation during the tetanus rise in single frog muscle fibres

The sarcomere stiffness was measured in single muscle fibres during the development of tetanic tension using a method insensitive to fibre inertia and viscosity. The stiffness was calculated by measuring the ratio between tension and sarcomere length during a period of fast sarcomere elongation at constant velocity. Tension changes were corrected for force truncation by the quick recovery mechanism. The results show that the relation between force and stiffness deviates from the direct proportionality less than previously reported. If the deviation is due to the presence of a linear myofilament compliance in series with the cross-bridges, our data suggest that myofilament compliance accounts for about 30% of the sarcomere compliance. This value is significantly smaller than 50-70% determined by X-ray diffraction measurements. These two different findings, however, may be reconciled by assuming that the myofilament compliance is non-linear increasing appropriately at low tension.

Myofilament compliance and sarcomere tension-stiffness relation during the tetanus rise in frog muscle fibres

The sarcomere stiffness was measured in single muscle fibres during the development of tetanic tension using a method insensitive to fibre inertia and viscosity. The stiffness was calculated as the ratio between tension changes and sarcomere length changes during a period of fast sarcomere elongation at constant velocity. The results show that, unlike previous measurements with step or sinusoidal length changes, the relation between relative force and relative stiffness on the tetanus rise is linear. Consequently, the development of stiffness upon stimulation is synchronous with the development of force. Since a substantial fraction of sarcomere compliance is localized in the myofilaments, this result can be accounted for by assuming that either myofilament compliance is highly non-linear or that crossbridges stiffness during the tetanus rise is not proportional to crossbridge tension.

ATP analogs and muscle contraction: mechanics and kinetics of nucleoside triphosphate binding and hydrolysis

The mechanical behavior of skinned rabbit psoas muscle fiber contractions and in vitro motility of F-actin (Vf) have been examined using ATP, CTP, UTP, or their 2-deoxy forms (collectively designated as nucleotide triphosphates or NTPs) as contractile substrates. Measurements of actin-activated heavy meromyosin (HMM) NTPase, the rates of NTP binding to myosin and actomyosin, NTP-mediated acto-HMM dissociation, and NTP hydrolysis by acto-HMM were made for comparison to the mechanical results. The data suggest a very similar mechanism of acto-HMM NTP hydrolysis. Whereas all NTPs studied support force production and stiffness that vary by a factor 2 or less, the unloaded shortening velocity (Vu) of muscle fibers varies by almost 10-fold. 2-Deoxy ATP (dATP) was unique in that Vu was 30% greater than with ATP. Parallel behavior was observed between Vf and the steady-state maximum actin-activated HMM ATPase rate. Further comparisons suggest that the variation in force correlates with the rate and equilibrium constant for NTP cleavage; the variations in Vu or Vf are related to the rate of cross-bridge dissociation caused by NTP binding or to the rate(s) of product release.

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.

Regulation of the cross-bridge transition from a weakly to strongly bound state in skinned rabbit muscle fibers

The regulation of cross-bridge transition from weakly attached to force-bearing states was studied at 10 degrees C in skinned muscle fibers by measuring the rate of force development after a quick release-restretch cycle (ktr), the rate of force decline (kPi) after photogeneration of Pi from caged Pi, and stiffness in the presence and absence of an inhibitor of strong cross-bridge formation, 2,3-butanedione monoxime (BDM). Both BDM and Pi suppressed force more than stiffness. However, reduction of Ca2+ suppressed force and stiffness in a parallel fashion. Both ktr and kPi were reversibly reduced (by 30-35%) in 3 mM BDM, but both were increased by increasing Pi concentration. Reduction of Ca2+ concentration to match the force seen in 3 mM BDM had no effect on kPi but decreased ktr by 85%. These results are inconsistent with cross-bridge models undergoing the transition from a weakly bound to a force-generating state in a single step but are consistent with a model having two steps, one of which is controlled by pCa.

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.

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.

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.

Tropomyosin. Does resolution lead to reconciliation?

New electron microscopic data provide direct evidence in support of the classic steric-blocking model for regulation of actin-myosin interactions by tropomyosin.

Muscle sound frequencies of the frog are modulated by skeletal muscle tension

The purpose of this study was to determine the relationships among muscle sound frequencies, muscle tension, and stiffness. Time-frequency transformations of nonstationary acoustic signals provided measures of resonant frequency during isometric contractions of frog (Rana pipiens) semitendinosus and gastrocnemius muscles. A mathematical expression for muscle transverse resonant frequency, elastic modulus and tension, based on elastic beam theory, was formulated by the Rayleigh method adapted for muscles. For thin muscles, the elastic modulus was found to have negligible influence on transverse muscle resonant frequency. Changes in muscle tension were the major determinants of changes in transverse resonant frequency. Consequently, for thin muscles, the time course of muscle tension, but not elastic modulus, can be monitored acoustically during the early phase of contraction when muscles give rise to sounds. Muscles were found to be anisotropic with a modulus of elasticity, EL, measured via length perturbations near 0.1% muscle length peak-to-peak, that was much larger than the modulus of elasticity, Eb, that resists the lateral bending that causes sound production. The elastic and resonant behavior of a thin muscle is similar to a tensioned fibrous cable with distributed mass.

The complex Young's modulus of skeletal muscle fibre segments in the high frequency range determined from tension transients

Stiffness measurements of muscle fibres are often based on application of a length change at one end of the muscle fibre and recording of the following tension change at the other end. In this study a method is developed to determine in the high frequency range (up to 40 kHz) the complex Young's modulus of skeletal muscle fibre as a function of frequency from the tension transient, following a rapid stepwise length change completed within 40 microseconds. For this purpose both a new mechanical moving part of the displacement generating system and a force transducer with a high natural frequency (70 kHz) had to be developed. In addition to stiffness measurements of a silk fibre to test the displacement generating system and the method of analysis, stiffness of skeletal muscle fibres in relaxed and rigor state have been measured. The complex Young's moduli of relaxed muscle fibres as well as muscle fibres in rigor state are frequency dependent. In both cases the complex Young's modulus increases smoothly with increasing frequency over a range of 250 Hz up to 40 kHz. The phase angles of the responses remained almost constant at a value of 0.3 radians for a fibre in rigor and 0.6 radians for a relaxed fibre. This leads to the conclusion that for muscle fibres in rigor state the recovery in the tension response to a step length change shows a continuous distribution of relaxation times rather than a few discrete ones. Results of our stiffness measurements are compared with results obtained from current viscoelastic models used to describe stiffness of muscle fibre in this frequency range.(ABSTRACT TRUNCATED AT 250 WORDS)

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 during steady lengthening of tetanized muscle fibres of the frog

1. Steady lengthenings at different velocities (0.02-1.6 microns/s per half-sarcomere, temperature 2.5-5.5 degrees C) were imposed on isolated frog muscle fibres at the plateau of the isometric tetanus (tension T0). When tension during lengthening had attained a steady value (Ti), which varied from about 1.5 to about 2 times T0 depending on lengthening velocity, tension transients were elicited by applying step length changes of different amplitudes. The change in length of a selected segment, close to the end of the fibre connected to the force transducer, was controlled by means of a striation follower. 2. The instantaneous plots of tension versus the length change during the step itself showed that at the high forces developed during steady lengthening, as at the plateau of isometric tetanus, the elasticity of the fibre was almost undamped in the whole range of lengthening velocities used. 3. The tension transient elicited by step length changes imposed in isometric conditions exhibited the characteristic four phases described previously: following the tension change simultaneous with the step (phase 1), there was a quick partial recovery (phase 2, the speed of which increased going from the largest step stretch to the largest step release), a subsequent pause or inversion in recovery (phase 3) and finally a slower approach to the tension before the step (phase 4). 4. In the region of small steps the plot of the extreme tension attained during the step (T1) versus step amplitude appeared more linear during steady lengthening than in isometric conditions and deviated progressively from linearity with increase in the size of step releases. The amount of instantaneous shortening necessary to drop tension to zero (Y0), measured by the abscissa intercept of the straight line drawn through T1 points for small steps, was about 4.1 nm per half-sarcomere in isometric conditions and 5.4 nm per half-sarcomere during lengthening at low speed (0.09 microns/s per half-sarcomere, Ti about 1.6 T0). Taken altogether this indicates, in agreement with previous work, that force enhancement during steady lengthening is due to increase in both number and extension of attached cross-bridges. During lengthening at high speed (0.8 microns/s per half-sarcomere), further enhancement in steady force (Ti about 1.9 T0) was accompanied by increase of Y0 to 6.3 nm per half-sarcomere, indicating that increase in lengthening velocity exclusively produces increase in cross-bridge extension.(ABSTRACT TRUNCATED AT 400 WORDS)

Short-time-scale left ventricular systolic dynamics. Evidence for a common mechanism in both left ventricular chamber and heart muscle mechanics

Based on the premise that short-time-scale, small-amplitude pressure/volume/outflow behavior of the left ventricular chamber was dominated by dynamic processes originating in cardiac myofilaments, a prototype model was built to predict pressure responses to volume perturbations. In the model, chamber pressure was taken to be the product of the number of generators in a pressure-bearing state and their average volumetric distortion, as in the muscle theory of A.F. Huxley, in which force was equal to the number of attached crossbridges and their average lineal distortion. Further, as in the muscle theory, pressure generators were assumed to cycle between two states, the pressure-bearing state and the non-pressure-bearing state. Experiments were performed in the isolated ferret heart, where variable volume decrements (0.01-0.12 ml) were removed at two commanded flow rates (flow clamps, -7 and -14 ml/sec). Pressure responses to volume removals were analyzed. Although the prototype model accounted for most features of the pressure responses, subtle but systematic discrepancies were observed. The presence or absence of flow and the magnitude of flow affected estimates of model parameters. However, estimates of parameters did not differ when the model was fitted to flow clamps with similar magnitudes of flows but different volume changes. Thus, prototype model inadequacies were attributed to misrepresentations of flow-related effects but not of volume-related effects. Based on these discrepancies, an improved model was built that added to the simple two-state cycling scheme, a pathway to a third state. This path was followed only in response to volume change. The improved model eliminated the deficiencies of the prototype model and was adequate in accounting for all observations. Since the template for the improved model was taken from the cycling crossbridge theory of muscle contraction, it was concluded that, in spite of the complexities of geometry, architecture, and regional heterogeneity of function and structure, crossbridge mechanisms dominated the short-time-scale dynamics of left ventricular chamber behavior.

Time-resolved changes in equatorial x-ray diffraction and stiffness during rise of tetanic tension in intact length-clamped single muscle fibers

We report the first time-resolved x-ray diffraction studies on tetanized intact single muscle fibers of the frog. The 10, 11, 20, 21, 30, and Z equatorial reflections were clearly resolved in the relaxed fiber. The preparation readily withstood 100 1-s duration (0.4-s beam exposure) tetani at 4 degrees C (less than 4% decline of force and no deterioration in the 10, 11 equatorial intensity ratio at rest or during activation). Equatorial intensity changes (10 and 11) and fiber stiffness led tension (t1/2 lead 20 ms at 4 degrees C) during the tetanus rise and lagged during the isometric phase of relaxation. These findings support the existence of a low force cross-bridge state during the rise of tetanic tension and isometric relaxation that is not evident at the tetanus plateau. In "fixed end" tetani lattice expansion occurred with a time course similar to stiffness during the tetanus rise. During relaxation, lattice spacing increased slightly, while the sarcomere length remained isometric, but underwent large changes after the "shoulder" of tension. Under length clamp control, lattice expansion during the tetanus rise was reduced or abolished, and compression (2%) of the lattice was observed. A lattice compression is predicted by certain cross-bridge models of force generation (Schoenberg, M. 1980. Biophys. J. 30:51-68; Schoenberg, M. 1980. Biophys. J. 30:69-78).

Muscle stiffness measured under conditions simulating natural sound production

Isolated whole frog gastrocnemius muscles were electrically stimulated to peak twitch tension while held isometrically in a bath at 4 degrees C. A quartz hydrophone detected vibrations of the muscle by measuring the pressure fluctuations caused by muscle movement. A small steel collar was slipped over the belly of the muscle. Transient forces including plucks and steady sinusoidal driving were applied to the collar by causing currents to flow in a coil held near the collar. The instantaneous resonant frequencies measured by the pluck and driving techniques were the same at various times during a twitch contraction cycle. The strain produced by the plucking technique in the outermost fibers was less than 1.6 x 10(-4%), a strain three orders of magnitude less than that required to drop the tension to zero in quick-length-change experiments. Because the pressure transients recorded by the hydrophone during plucks and naturally occurring sounds were of comparable amplitude, strains in the muscle due to naturally occurring sound must also be of the order 10(-3%). A simple model assuming that the muscle is an elastic bar under tension was used to calculate the instantaneous elastic modulus E as a function of time during a twitch, given the tension and resonant frequency. The result for Emax, the peak value of E during a twitch, was typically 2.8 x 10(6) N/m2. The methods used here for measuring muscle stiffness are unusual in that the apparatus used for measuring stiffness is separate from the apparatus controlling and measuring force and length.

Histochemical and physiological properties of Rana temporaria tibialis anterior and lumbricalis IV muscle fibres

Histochemical analysis was used to study the relationship between Rana temporaria tibialis anterior and lumbricalis IV fibre cross-sectional areas and concentrations of myosin ATPase and NADH reductase. Both tonic and twitch fibre types were histochemically identified in each muscle and the twitch fibres were subgrouped into types 1, 2, and 3. Fibres that had the largest cross-sectional areas were identified as the fibres which contained the highest myosin ATPase activity and the lowest NADH reductase activity (type 1 fibres). However, this relationship was more pronounced in the tibialis anterior muscle. In addition, single fibres from both muscles were isolated and injected with Ca2+ indicator aequorin. The fibres isolated from the tibialis anterior muscle were those with the largest cross-sectional areas relative to other fibres within a given muscle. The force responses and Ca2+ transients recorded from this group of single fibres were found to be fairly uniform, which may suggest that a single type of fibre was isolated. In contrast, the physiological properties of isolated lumbricalis IV fibres were highly variable and thus represented more than one fibre type.

Crossbridge activity monitored from the state of polarization of light diffracted by activated frog muscle fibres

The polarization properties of the first diffraction order have been measured when single frog fibres are illuminated by laser light. The relative difference in the amplitudes of the orthogonal electric field polarization components (differential field ratio) as well as their phase shift normalized by the pathlength (birefringence) have been obtained from fibres at rest and during fixed-end twitches and tetani. The differential field ratio decreased during contraction and the change during a single twitch averaged 69% of that during a companion tetanus. The birefringence of the first order averaged 2.80 +/- 0.59 x 10(-3) (mean +/- SD) at rest and the average decrease during a tetanus was 8.4% +/- 6.4%. The decrease in the differential field ratio upon activation was a decreasing function of sarcomere length, maximum at rest length and falling to zero at about 3.7 microns. Differences between the two first diffraction orders were observed for both the differentiated field ratio and the birefringence. At the time when force had risen to half the value reached at the end of the fast rise of tension, the change in the differential field ratio lead the tension by about 10-15 ms. The differential field ratio returned to its resting value after the fall of tension. The above results suggest that the differential field ratio is a sensitive indicator of intact fibre structure. The temporal lead in the differential field ratio with respect to tension rise supports models in which crossbridges initially attach in a non-force-producing state.

Changes in force and stiffness induced by fatigue and intracellular acidification in frog muscle fibres

1. Changes in force and stiffness were recorded simultaneously during 1 s isometric (fixed ends) tetani of single fibres isolated from the anterior tibialis muscle of Rana temporaria (temperature 1-3 degrees C; sarcomere length, 2.10 micron). Stiffness was measured as the change in force that occurred in response to a 4 kHz sinusoidal length oscillation of the fibre. Some experiments were performed in which stiffness was determined from a fast (0.2 ms) length step that was applied to a 'tendon-free' segment of the muscle fibre during the tetanus plateau. 2. A moderate degree of fatigue was produced by decreasing the time between tetani from 300 s (control) to 15 s. By this treatment the maximum tetanic force (Ftet) was reversibly reduced to 70-75% of the control value. Maximum tetanic stiffness (Stet) was related to Ftet according to the following regression (both variables expressed as percentage of their control values): Stet = 0.369 Ftet + 62.91 (correlation coefficient, 0.95; P less than 0.001). A 25% decrease in isometric force during fatigue was thus associated with merely 9% reduction of fibre stiffness. 3. Whereas the rate of rise of force during tetanus was markedly reduced by fatiguing stimulation, the rate of rise of stiffness was only slightly affected. 4. Intracellular acidification (produced by raised extracellular CO2 concentration) largely reproduced the contractile changes observed during fatigue. However, for a given decrease in tetanic force there was a smaller reduction in fibre stiffness during acidosis than during fatigue. 5. Caffeine (0.5 mM) added to the fibre after development of fatigue and intracellular acidosis greatly potentiated the isometric twitch but did not affect maximum tetanic force. This finding provides evidence that the contractile system was fully activated during the tetanus plateau both in the fatigued state and during acidosis. 6. The results suggest that the decrease in contractile strength after frequent tetanization (intervals between tetani, 15 s) is attributable to altered kinetics of cross-bridge function leading to reduced number of active cross-bridges and, most significantly, to reduced force output of the individual bridge. The possible role of increased intracellular H+ concentration in the development of muscle fatigue is discussed.

Muscle sounds are emitted at the resonant frequencies of skeletal muscle

The changes in mechanical resonant frequency of whole muscles during twitch and tetanic contractions were compared to changes in frequency components of the pressure wave produced by muscles during contraction. Resonant frequencies were determined by imposing sinusoidal length changes on a muscle and observing transverse standing waves when the frequency of length change matched the muscle's resonant frequency or a harmonic of the resonant frequency. Acoustic signal instantaneous frequency spectrums were calculated using time-frequency transformations including the Wigner transform and the exponential distribution. During a tetanic muscle contraction, the peak instantaneous frequency initially increased and then became constant as the force plateau was reached. The resonant frequencies determined during the force plateau and during relaxation spanned the same range as the peak instantaneous frequency of the acoustic signal. These results suggest that the acoustic signal may be useful as a non-invasive monitor of muscle resonant frequency during contraction.

Acoustic and surface EMG diagnosis of pediatric muscle disease

The ratio of acoustic myography (AMG) amplitude to surface electromyography (EMG) amplitude is proposed as a measure of mechanical output compared with electrical activity of the contractile system. AMG to EMG ratios were measured from 16 children with muscle disease diagnosed by clinical criteria, EMG, and/or muscle biopsy. These were compared with the ratios from 11 normal volunteers spanning the same age range (7-16 years). AMG to EMG ratios were significantly (P less than 0.01) different for the two populations. Using a linear discriminant function to define the normal range for AMG to EMG ratios yielded a sensitivity of 82% (13 of 16 abnormals diagnosed) and a specificity of 91% (10 of 11 normals). These findings suggest that surface recordings may provide significant diagnostic information in muscle disease. The accuracy may be improved further by using additional muscles (e.g., paraspinals) and evoked twitches.

Internal cell manipulation using infrared laser traps

The ability of infrared laser traps to apply controlled forces inside of living cells is utilized in a study of the mechanical properties of the cytoplasm of plant cells. It was discovered that infrared traps are capable of plucking out long filaments of cytoplasm inside cells. These filaments exhibit the viscoelastic properties of plastic flow, necking, stress relaxation, and set, thus providing a unique way to probe the local rheological properties of essentially unperturbed living cells. A form of internal cell surgery was devised that is capable of making gross changes in location of such relatively large organelles as chloroplasts and nuclei. The utility of this technique for the study of cytoplasmic streaming, internal cell membranes, and organelle attachment was demonstrated.

A model of force production that explains the lag between crossbridge attachment and force after electrical stimulation of striated muscle fibers

Whereas the mechanical behavior of fully activated fibers can be explained by assuming that attached force-producing crossbridges exist in at least two configurations, one exerting more force than the other (Huxley A. F., and R. M. Simmons. 1971. Nature [Lond.]. 233:533-538), and the behavior of relaxed fibers can be explained by assuming a single population of weakly binding rapid-equilibrium crossbridges (Schoenberg, M. 1988. Biophys. J. 54:135-148), it has not been possible to explain the transition between rest and activation in these terms. The difficulty in explaining why, after electrical stimulation of resting intact frog skeletal muscle fibers at 1-5 degrees C, force development lags stiffness development by more than 15 ms has led a number of investigators to postulate additional crossbridge states. However, postulation of an additional crossbridge state will not explain the following three observations: (a) Although the lag between force and stiffness is very different after stimulation, during the redevelopment of force after an extended period of high velocity shortening, and during relaxation of a tetanus, nonetheless, the plots of force versus stiffness in each of these cases are approximately the same. (b) When the lag between stiffness and force during the rising phase of a twitch is changed nearly fourfold by changing temperature, again the plot of force versus stiffness remains essentially unchanged. (c) When a muscle fiber is subjected to a small quick length change, the rate constant for the isometric force recovery is faster when the length change is applied during the rising phase of a tenanus than when it is applied on the plateau. We have been able to explain all the above findings using a model for force production that is similar to the 1971 model of Huxley and Simmons, but which makes the additional assumption that the force-producing transition envisioned by them is a cooperative one, with the back rate constant of the force-producing transition decreasing as more crossbridges attach.

The effects of temperature on relaxation in frog skeletal muscle: the role of parvalbumin

Isolated muscle fibers from Rana temporaria tibialis anterior muscles were microinjected with aequorin. The force responses and the Ca2+ transients associated with twitch and tetanic contractions were studied at several temperatures. The declines of the Ca2+ transients were well described by single exponential equations and the effects of temperature were complex (multi-exponential). To determine if these temperature effects on the Ca2+ transients were influenced by the Ca2+ indicator itself, samples of the injected aequorin were studied in vitro using a Gibson stopped-flow apparatus. The quenching of aequorin luminescence with either EGTA or de-calcified Rana temporaria parvalbumin were mono-exponential. These overall quenching reactions had single exponential temperature dependencies. The effects of temperature on the declines of the single fiber Ca2+ transients did not appear to be influenced by the kinetics of the aequorin reaction. The disparity in the effects of temperature on the single fiber Ca2+ transients versus the in vitro quenching of aequorin luminescence with parvalbumin, were interpreted to indicate that in twitch and tetanic contractions of these fibers, it was unlikely that soluble Ca2+ binding proteins played a major role in the regulation of myoplasmic Ca2+.

Stiffness of frog muscle fibres during rise of tension and relaxation in fixed-end or length-clamped tetani

Stiffness measurements were performed during the rise, the plateau and the relaxation of tetanic contractions both in whole single muscle fibres and in tendon-free fibre segments under either fixed-end or length-clamp conditions. Fibres were isolated from the tibialis anterior muscle of the frog. Experiments were performed at 2-6 degrees C. Changes in length of tendon-free fibre segments were monitored by means of a "striation follower", an opto-electronic device which, during contraction, measured sarcomere displacement at the level of two selected regions of a fibre. Fast length perturbations imposed at one tendon end of a fibre during the plateau of tetanic contractions distribute uniformly along its length. During the tetanus rise stiffness led isometric tension in whole fibres under fixed conditions as well as in tendon-free fibre segments under length-clamp conditions. It was confirmed that a significant part of the unlinearity of T1 relations is determined by tendon compliance. During the isometric phase of relaxation in fixed-end tetani, the decline of tension led that of stiffness both in whole fibres and in tendon-free fibre segments. It is concluded that the shift observed between stiffness and tension during tetanus rise and relaxation represents a true specific event in the contractile process.

The time course of the contractile force measured during a twitch under fixed sarcomere length

A sarcomere length-controlled feedback system was constructed utilizing the laser diffraction technique of Haugen & Sten-Knudsen (1976) to detect sarcomere length changes. The system allowed the sarcomere length to be kept constant within 0.02% during an isometric twitch. The contractile force developed approximates closely to the force exerted by the crossbridges when their translatory movements are prevented. Thus, the force developed under this condition should correspond to the intensity of the active state as defined by A. V. Hill (1949). The time course of the twitch under constant sarcomere length differs substantially from that of the active state curves obtained using quick stretches and quick releases. Thus, the force does not rise quickly to its maximum but rather resembles the fixed-end twitch curve by leading it only slightly (5 ms at 5 degrees C). Its peak value does not reach the level of the tetanic plateau, but is only 9% higher than the maximum fixed-end twitch tension. The force remains above the curve of the fixed-end twitch during its entire course. It is shown that the quick-stretch procedure which results in active state curves as those obtained by A.V. Hill (1949) led to a considerable elongation of the sarcomeres. It is concluded that the slow rise of the contractile force under ordinary isometric conditions is due to properties inherent in the contractile machinery other than those resulting from the extension of series elastic components.