Sinusoidal Length Changes Research Articles

Effect of fusimotor stimulation on ia discharge during shortening of cat soleus muscle at different speeds.

1. In barbiturate-anaesthetized cats, the L7 and S1 dorsal and ventral roots were dissected to isolate functionally single afferents identified as primary endings of soleus muscle spindles, and motor filaments which exerted a fusimotor action on the afferents with limited action on extrafusal muscle. Up to seven filaments, with an action on a given primary ending, could be isolated and each was classified as exerting either a predominantly dynamic or static action.2. Combined stimulation of these filaments, at rates up to 200 impulses/s could maintain afferent firing during muscle shortenings at speeds up to 200 mm/s.3. Fusimotor stimulation could also maintain afferent firing at a target frequency of 100 impulses/s during muscle shortenings up to 200 mm/s. The timing, in relation to the onset of shortening, and the rates of fusimotor stimulation were found to be critical in achieving the target frequency.4. Sinusoidal modulation of the frequency of fusimotor stimulation was used to study the conditions required to achieve constant afferent firing in the face of imposed sinusoidal length changes.5. For given depths of modulation, the phase advance of fusimotor stimulation needed to produce minimum modulation of afferent firing (best compensation) increased with increasing frequency of the sinusoids. The compensation deteriorated with an increase in the frequency of the sinusoids and a change in the mean muscle lengths, although in some cases it could be restored by adjustments to the depth of modulation of fusimotor rate. This suggests that for movements of varying speeds and amplitudes, settings which are appropriate for shortening at a given velocity and mean muscle length, do not apply if either of these two variables are altered.6. These findings demonstrate that the fusimotor system is potentially capable of eliciting constant afferent firing as envisaged in the ;servo-assistance' hypothesis (Matthews, 1964, 1972; Stein, 1974). This, and the fact that constant afferent firing is not seen during normal unobstructed shortenings at velocities greater than 0.2 resting length/s (Prochazka, 1981), are used to argue that it is by choice rather than necessity that ;servo-assistance' (as defined above) is not employed during normal movements. However, servo-assistance of a different form (involving modulated spindle afferent feed-back from both agonists and antagonists) remains a viable alternative.

Substrate-concentration of dependences of tension, shortening velocity and ATPase activity of glycerinated single muscle fibers.

Tension P0 and ATPase activity J0 of glycerinated single muscle fibers under isometric concentration as well as the velocity V0 of unloaded shortening were measured as a function of substrate concentration [S]. The stiffness of fibers with sinusoidal length changes at 1 kHz was used as a qualitative measure of the amount of rigor complex. P0 is an increasing function of [S] at low substrate concentrations and has a broad maximum at about 10-40 micrometers MgATP. In this concentration range, 10-40 micrometers, V0 still has a very small value. Then it increases and finally reaches at a plateau at about 1 mM MgATP. J0 increases as P0 does. However, it reaches at a saturated level at about the same concentration as V0. Either 0.5 mM 8-BrATP or 1 mM PPi was added to the substrate solutions to reduce the amount of rigor complex at low substrate concentrations. The addition of PPi of 8-BrATP decreases P0 dominantly at low concentrations of substrate and shifts the maximum to about 100 micrometers MgATP. 8-BrATP considerably increases V0 at low substrate concentrations while V0 is decreased by added PPi. The temperature coefficients, Q10 values were obtained for P0, J0, and V0. The values are essentially constant, 2.1-2.4, in the cases of P0 and J0, and about the same values were found for V0 at very low substrate concentrations. However, they become about 3.3 in the concentration range from 34 micrometers and 2.3 mM. The P-V relation was obtained at 11 micrometers and 2.3 micrometers MgATP. The normalized P-V relation at 11 micrometers was unchanged when 8-BrATP was added. The results are discussed in connection with the mechanism of actomyosin-ATPase activity as well as that of the elementary cycle of the motive force generation.

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

1. The length changes of a central segment of a frog muscle fibre were measured during and after a quick shortening was applied to the end of the fibre, by attaching two markers an using a spot follower apparatus. In this way it was shown that the stiffness of tetanized single frog fibres as mounted in our apparatus was located predominantly in the sarcomeres, and that the ends were comparatively stiff. 2. The stiffness of tetanized frog single fibres at 0 degrees was measured by applying a small 4 kHz sinusoidal length change, and measuring the resultant tension change. This was done during the first few milliseconds after a quick release, and while the fibre was shortening at constant velocity. 3. The stiffness during the fast tension transient after a quick release was always less than the stiffness before release, supporting the idea that the fast recovery is not due to attachment of extra cross-bridges. 4. The stiffness during the steady shortening was always less than when isometric. A line fitted to this stiffness-tension plot, when extended, intercepted the stiffness axis at less than half the isometric value. 5. The slope of the stiffness-force plot during the fast tension transient was consistently and significantly less than the slope of the stiffness-force plot during steady shortening, further supporting the conclusion that only a small part of the decrease seen during shortening could be due to non-linear end compliance. 6. Possible ways of reconciling these results with recent reports of X-ray diffraction suggesting little if any change in the position of myosin heads during steady shortening are discussed.

An analysis of receptor potential and tension of isolated cat muscle spindles in response to sinusoidal stretch.

In isolated cat muscle spindles the receptor potential responses of primary and secondary endings as well as tension responses to sinusoidal length changes in the steady state have been analysed. 1. At a given stimulus frequency, receptor potential per unit length change (receptor potential gain) in both primary and secondary endings is constant when displacement is less than about 10 micrometer. With larger stretches, receptor potential gain decreases approximately as a power function of displacement, the gain of primary endings decreasing more rapidly with increasing displacement than that of secondary endings. Tension per unit length change (tension gain) shows a similar constant range above which it also decreases as a power function of displacement. 2. In spite of the large reduction in gain at high displacement amplitudes, response wave forms remained essentially sinusoidal. The gain reduction results principally from a displacement-dependent non-linearity which has a rapid onset and slow decay. 3. Receptor potential and tension responses to small amplitude sinusoidal stretch depend, in a parallel manner, on the initial length of the preparation. 4. Both receptor potential and tension responses are highly dependent on frequency of sinusoidal stretch. In primary endings receptor potential gain increased as a power function of frequency over the range 0 . 01 to about 40 Hz, above which frequency the gain decreased; phase advance remained relatively constant up to 10 Hz then decreased to become a phase lag at higher frequency. In secondary endings receptor potential gain remained fairly constant between 0 . 01 and 1 Hz then rose as a power function of frequency but less steeply than in primary endings. 3. The possible mechanisms underlying these findings are discussed.

Transient tension responses of heart muscle in Ba2+ contracture to step length changes.

To characterize mechanical properties of activated heart muscle, kitten papillary muscles in Ba2+ contracture were stretched or released stepwise, and the transient tension responses were analyzed. Various amplitudes of step length change (0.1-1.0% of Lmax) were tested from different initial lengths and at different temperatures. The tension response to either stretch or release showed four different phases, which were nearly symmetric when the input length change was 0.1% of Lmax. When the length changes was 1%, the second phase of stretch response became shorter, whereas that of release became longer. The third phase of stretch response was prolonged, whereas that of release response became obscure. The peak tension (F1) in the first phase was linearly related to the amplitude, whereas those in the second and third phase were not. Increasing temperature markedly decreased F1 and shortened the second and third phase independently of initial muscle length. These results were consistent with those properties of heart muscle in Ba2+ contracture previously characterized with sinusoidal length changes.

Activation of the contractile system of insect fibrillar muscle at very low concentrations of Mg2+ and Ca2+.

The mechanical properties of single fibres and fibre bundles of glycerinated dorsal longitudinal muscle from lethocerus maximus were investigated in ATP-salt solutions containing only trace concentrations of free Ca2+ (pCa>9). A reduction in the magnesium concentration (pMg ∼ 7) resulted in an increase in the instantaneous stiffness of glycerinated insect flight muscle fibres, though very little accompanying tension was developed. Stiffness was measured either using small amplitude sinusoidal length changes of high frequency (1 kHz) or rapid rectangular form length changes. The ratio of stiffness to tension in solutions free of added magnesium and calcium was equal to or greater than that obtained from the tissue in the rigor state, and much larger than that obtained in the presence of both magnesium and calcium. Extrapolation of the linear part of the change-tension relationship (obtained during rapid length changes completed within 0.3 ms) back to zero tension indicated that the elastic elements of attached crossbridges were less extended under conditions of Mg2+-deprivation than during Ca-activation in Mg2+-rich solution. Following a quick stretch a delayed tension development similar to that obtained in the presence of magnesium and calcium ions was observed. The rise in tension was delayed with respect to the accompanying rise in stiffness and reached a peak value after about 2 s. Similar tension transients followed a subsequent release. The possibility that an unusually slow corss-bridge cycle might be responsible for these slow transients was suggested by the finding that the fibres showed a very low ATPase activity under these conditions which could be slightly activated by stretches. On increasing the free Ca2+ concentration during magnesium deprivation, the time course of the stretch induced tension transients became faster, while stiffness and the steady state tension rose to reach a ‘high tension state’ at aboutpCa 6.5.

Mechanical properties of succinylcholine activated muscle fibers in the inferior oblique muscle of the cat.

To determine the mechanical properties of the multi-innervated fibres in inferior oblique muscle of the cat, these fibers were selectively activated by means of an intravenous injection of succinylcholine chloride (Sch). For small sinusoidal length changes (+/- 1 mm) of low frequency, tension in the Sch activated muscle exhibited a component that was sensitive to the direction of stretch but was independent of the velocity. At higher frequencies of length change (16 Hz) a form of negative friction was observed. Negative friction had not been previously noted in mammalian muscles, although a similar friction was observed both in the muscles of insects and amphibians. These properties were expressed in the form of a simple mechanical model.

Responses of primary and secondary endings of isolated mammalian muscle spindles to sinusoidal length changes.

1. Responses of primary and secondary endings of isolated cat spindles to sinusoidal length changes have been recorded before and after block of impulse activity by tetrodotoxin. 2. Primary endings may discharge with each cycle of sinusoidal stretch at 25-50 Hz, with stretch amplitudes applied to the spindle poles as small as 1 micron. Thresholds are higher at lower frequencies. 3. In primary endings, amplitude of the receptor potential varies with frequency and magnitude of sinusoidal stretch. At a given stretch amplitude, the receptor-potential response increases markedly between 1 and 10 Hz. At a fixed frequency, for example, at Hz, the response to graded amplitude of sinusoidal stretch is highly nonlinear, sensitivity decreasing with large amplitudes. 4. Secondary endings show a much higher threshold than primary endings to sinusoidal stretch. Thus, at 25 Hz, secondary endings required stretch amplitudes of 50-100 micron to evoke discharge. Relatively large amplitudes of stretch were also required to evoked detectable receptor potentials. Over the range studied, the receptor potential varied more linearly with stretch amplitude in secondary than in primary endings.

Dependence of energy transduction in intact skeletal muscles on the time in tension

In intact single crayfish muscle fibers and frog semitendinosus muscles we have studied the tension response to sinusoidal length changes in the frequency range of 0.25-133 Hz. By this method we have resolved three processes in the interaction of myosin cross-bridges with actin in fully activated preparations. They are (A) a low-frequency phase advance, (B) a middle-frequency delay, and (C) a high-frequency advance. These processes can be used as probes to study the chemomechanical coupling of contractility. Process (B) represents net power output from the muscle preparation (oscillatory work). With maximal K or caffeine activation of crayfish muscle at 20 degrees C, it decreases to zero in the initial 45 s of maintained tension. Similar results were obtained with frog semitendinosus whole muscles. We interpret this decrease of (B) with time as a gradual decrease in actomyosin ATP-hydrolysis rate.

The aortic arch baroreceptor response to static and dynamic stretches in an isolated aorta‐depressor nerve preparation of cats in vitro.

1. The aortic arch baroreceptors of cats were studied in an isolated aortic arch-depressor nerve preparation in vitro to analyse their transmission properties. 2. Sinusoidal length changes of varying amplitudes (0-34-1-2 mm) and frequencies (1-10 Hz) at a given pre-stretch were imposed on the isolated receptor zone to quantitate the velocity sensitivity of these receptors and to test the linearity of the system. 3. The receptor response was evaluated from the spike activity of single fibres of the depressor nerve in number of spikes per stimulus period, average discharge rate, instantaneous frequency, and phase angle between forcing function and instantaneous frequency. 4. The static response is characterized by a threshold, saturation range, and a relatively large linear part between these two non-linearities. 5. The aortic receptors exhibit rate sensitivity. Depending on the stimulus amplitude and frequency the phase angles between the forcing function and the instantaneous frequency ranged from -14 to -68 degrees. 6. The average discharge rate (spikes/sec) is sensitive to stimulus amplitude but not to stimulus frequency at near-threshold operation; in the linear part of the static response curve, the receptor response becomes independent of the stimulus mode. 7. The baroreceptors of the aorta share many properties with other mechanoreceptors of different species and organ systems, particularly with those of the rest of the circulation. They exhibit static and to some degree rate sensitivity and operate physiologically near their thresholds, i.e. the afferent arc of the baroreflexes is highly non-linear.

Variation of muscle stiffness with force at increasing speeds of shortening.

Single frog skeletal muscle fibers were attached to a servo motor and force transducer by knotting the tendons to pieces of wire at the fiver insertions. Small amplitude, high frequency sinusoidal length changes were then applied during tetani while fibers contracted both isometrically and isotonically at various constant velocities. The amlitude of the resulting force oscillation provides a relative measure of muscle stiffness. It is shown from an analysis of the transient force responses observed after sudden changes in muscle length applied both at full and reduced overlap and during the rising phase of short tetani that these responses can be explained on the basis of varying numbers of cross bridges attached at the time of the length step. Therefore, the stiffness measured by the high frequency legth oscillation method is taken to be directly proportional to the number of cross bridges attached to thin filament sittes. It is found that muscle stiffness measured in this way falls with increasing shortening velocity, but not as rapidly as the force. The results suggest that at the maximum velocity of shortening, when the external force is zero, muscle stiffness is still substantial. The findings are interpreted in terms of a specific model for muscle contraction in which the maximum velocity of shortening under zero external load arises when a force balance is attained between attached cross bridges somr interpretations of these results are also discussed.

A one-dimensional viscoelastic model of cat heart muscle studied by small length perturbations during isometric contraction.

To develop a model of heart muscle, we studied cat papillary muscle contracting in a quasi-isometric condition under a fixed inotropic state. The properties of resting muscle were determined by using a step stretch of less than 1.2% of Lmax for initial lengths from 85 to 100% Lmax. The passive force response suggested the model of the passive branch (Fig. 1). All five parameters were small at muscle lengths below 95% of Lmax but increased markedly at longer lengths. The properties of contracting muscle were studied with a sinusoidal length change (amplitude less than 0.15% of Lmax, frequency 0.1-35.0 Hz). The frequency response of active (total minus passive) stiffness suggested the model of the active branch (Fig. 1). We determined the dependency of the elastic elements (K, Ks) and the viscous element (C) on length and time by recording the frequency response at various combinations of length and time Ks varied linearly with active force (FA). K and C exhibited time courses that paralleled FA up to 0.6tmax, and they maintained their values until 1.4tmax. K then fell toward zero, whereas C exhibited a secondary rise before it fell toward zero. K was dependent of length up to 95% of Lmax and then began to decline, but C varied in proportion to muscle length.

The afferent discharge pattern of atrial mechanoreceptors in the cat during sinusoidal stretch of atrial strips in situ.

1. The differences in spike discharge from atrial mechanoreceptors in vivo suggest the existence of different receptor types. To test this possibility, and to see how atrial receptors compare with other mechanoreceptors, their response was studied under comparable stimulus conditions.2. Sinusoidal length changes, with frequencies from 1 to 10 Hz and amplitudes of 1.5-5.0 mm at a given static extension, were imposed in situ on strips of atrial receptor areas of cats.3. The receptor response was evaluated from functional single fibres in terms of number of spikes per stimulus period, average discharge rate, instantaneous spike frequency, and phase angle between forcing function and instantaneous frequency.4. Irrespective of the fibre type, atrial fibres appear to originate from identical mechanoreceptors which sense length at low stimulus frequency and low stimulus amplitudes, but also sense velocity in the high frequency range and with large stimulus amplitudes.5. The difference in the discharge pattern and in the functional behaviour of the atrial fibres in vivo can be explained on the basis of identical receptors.6. The difference in the temporal occurrence of the atrial burst is still open to debate, but probably is related to the site of the receptor.

Influence of temperature on the mechanical properties of cardiac muscle.

The influence of temperature on contractile performance, total myocardial stiffness, and the elastic and viscous components of stiffness was studied in intact hearts (dog) and isolated cardiac muscle (cat). In 12 dogs on whole-heart bypass, stiffness (Δ P /Δ V ) was determined by inducing sinusoidal 0.5-ml volume changes in paced, isovolumically contracting left ventricles and measuring the resultant pressure changes (Δ P ). In eight cat papillary muscles contracting isometrically at Lmax, stiffness (Δ T /Δ L ) was similarly determined from the changes in tension and length during sinusoidal length changes of 0.25% L max. Total stiffness was linearly related to ventricular pressure or muscular tension during both contraction and rest. As the temperature rose from 33° to 40°C in vivo and from 22° to 40°C in vitro, the slopes of the stiffness-pressure and stiffness-tension relationships and the intercept of the latter declined; therefore, stiffness is inversely related to temperature. Since both preparations responded as linear second-order systems, stiffness could be separated into its elastic and viscous components. The moduli of both components varied in the same direction as total stiffness during temperature changes; however, the viscous component was more sensitive to the influence of temperature.

Changes of stiffness of skeletal muscle during latency relaxation

Summary Changes of stiffness of muscle are measured during latency relaxation of frog toe muscle, using a piezo-electric device that imposes sinusoidal length changes of small amplitude and high frequency (kHz) on the muscle. It is shown that a decrease in stiffness is associated with the beginning of latency relaxation and that there is an increase in stiffness before the onset of the contractile force development.

The effects of fibre length and calcium ion concentration on the dynamic response of glycerol extracted insect fibrillar muscle.

1. The property of insect fibrillar muscle which enables it to oscillate continuously when it is connected to a resonant load is the delayed activation by stretch of contractile activity. The dynamic response has been measured at different fibre lengths and at different calcium ion concentrations, to see what effects these conditions have on the magnitude and rate constant of the delayed tension.2. Bundles of ten fibres of the dorsal longitudinal muscle of the water bug, Lethocerus cordofanus, which had been in glycerol for less than 5 days were used. Graded activation was obtained with buffered calcium ion concentrations between 10(-7) and 10(-5)M.3. A computer-controlled apparatus was used to measure the dynamic mechanical properties of the muscle fibres. This allowed many measurements to be made on the same preparation. Further computer programs analysed the Nyquist plots produced by the experiment.4. When the mean length of a fibre bundle was increased, the magnitude of the delayed tension was increased (for a constant amplitude of sinusoidal length change), the rate constant was unaltered, and the stiffness of the fibres was increased. When the calcium ion concentration was raised, the magnitude of the delayed tension was increased, the rate constant increased, and the stiffness of the fibres fell. Calcium activation and stretch activation are thus clearly separable in their effects, and so the mechanisms must be separate.5. The various different effects of calcium cannot be explained by any simple model of activation, for example, an on-off switch mechanism controlling the number of bridges in action.6. The stretch-induced activity is proportional to a power of the length of two or greater and this non-linearity aids the efficient operation of the oscillatory mechanism.

An Interpretation of the Effects of Fiber Length and Calcium on the Mechanical Properties of Insect Flight Muscle

Insect fibrillar flight muscle has many properties in common with vertebrate skeletal muscle. However, it is not capable of the constant velocity shortening at constant load which is the mechanical characteristic of vertebrate striated muscles, but is adapted to produce rapid oscillatory contractions of small amplitude. Consequently, the classical type of mechanical study, involving the measurement of force-velocity diagrams and the fitting of a hyperbola to them, is not suitable for investigations of the properties of insect flight muscle. Instead, periodic length changes must be used. The result of forcing a sinusoidal length change of low amplitude on insect flight muscle is that, over a certain range of frequencies, the resulting sinusoidal tension changes lag behind the length changes (Machin and Pringle, 1960; Jewell and Ruügg, 1966). It is this delay which allows the muscle to deliver work continuously to a resonant load without neural control. One possible way of...

Stretch activation and myogenic oscillation of isolated contractile structures of heart muscle.

Glycerinated or freeze-dryed fibre bundles of heart muscles (papillary and trabecular muscles of rabbit or guinea pig) show in ATP-salt solution with about 10−6M Ca2+ an active, delayed tension increment after quick or sinusoidal stretching. The active tension increase is completely different from the passive tension increment caused by stretching of the elastic structures of the muscle; this well known length dependence of tension is also in phase with the length changes (or the tension-phase preceeds the length-phase in visco-elastic bodies). On the other hand, the active tension increase is delayed with respect to the length change; this can be observed very well after rectangular changes in length. The delayed activation of the contractile bonds at stretch and the delayed deactivation at shortening induce the muscle-during sinusoidal length changes in a characteristic frequency range-to produce power output. The frequency range corresponds to the heart beat frequency of the living muscle. Temperature rise and inorganic phosphate accelerate, Mg-ions and ADP retard the contraction speed. Ca-ions influence only the amount of the isometric tension, but not the contractile velocity.

Mechanical activation of the contractile system in skeletal muscle.

Fibre bundles of frogs m. semitendinosus and rabbit psoas were extracted with glycerol and then suspended in ATP-salt solution at varying levels of free calcium. Abrupt stretch by 0.2–0.5% of the fibre length caused a (transient) delayed rise in tension and a quick release often produced a delayed tension fall. Consequently the extracted fibre system was able to oscillate since during sinusoidal length changes (0.5% at 5–10 c/sec) the sinusoidal tension changes lagged behind, as in myogenic oscillation of insect flight muscle.

Mechanical properties of glycerinated fibres from the tymbal muscles of a Brazilian cicada.

1. Some of the properties of glycerinated fibres from the synchronous tymbal muscles of the cicada Fidicina rana have been investigated.2. In the presence of suitable concentrations of ATP and calcium ions, the fibres are able to perform oscillatory work when subjected to small sinusoidal length changes in the frequency range 2-30 c/s.3. When subjected to abrupt changes in length, active fibres show a delayed increase in tension after a stretch and a delayed decrease in tension after release.4. The muscle fibres therefore show the mechanical properties characteristic of glycerinated fibres from asychronous insect flight muscles. Some implications of this finding in relation to the evolution of asynchronous muscles are discussed.