Superimposing noise linearizes the responses of primary muscle spindle afferents to sinusoidal muscle stretch

Experiments were conducted in anaesthetized and spinalized cats to measure the extent to which the non-linear response of Ia afferent fibers to sinusoidal muscle stretch as expressed by the peristimulus-time-histograms, PSTHs, can be transformed into a linear one by means of the superposition of random stretch ("mechanical noise"). The gastrocnemius muscles of one hind leg were stretched and the response to sinewave muscle stretch (amplitudes between 0.01 and 4.0 mm, frequencies between 0.1 and 20 Hz) were investigated while band-limited mechanical noise was superimposed on the sinewave stretch. The random stretch upper cut-off frequency was varied between 60 and 300 Hz; the displacements were normally distributed. The noise amplitude sigma, i.e. the standard deviation of the displacement distributions, was varied systematically between 0.002 and 0.4 mm. Mechanical noise was very effective in raising the mean discharge rate. Added to the sinusoidal stretch it prevented the cessation of firing during the release phase of the stretch cycle, or at least reduced the duration of discharge pauses, i.e., a linearization occurred. In general, the larger the noise amplitude, the more the amplitude of the fundamental harmonic component was attenuated and the phase lead reduced. Apart from this rule the particular combination of superimposing small noise (sigma less than 0.02 mm) on small sinewave stretch (A less than 0.02 mm) could enhance the depth of sinusoidal modulation of cycle histograms (compared with responses to pure sinusoids). Linearizing the sinewave response by additional noise allowed the estimation of frequency response characteristics in the otherwise non-linear range of amplitudes (sinewave amplitude 0.5-1.0 mm).(ABSTRACT TRUNCATED AT 250 WORDS)     

Spike discharges of skeletomotor neurons during random noise modulated transmembrane current stimulation and muscle stretch

 Spike discharges of skeletomotor neurons innervating triceps surae muscles elicited by white noise modulated transmembrane current stimulation and muscle stretch were studied in decerebrated cats. The white noise modulated current intensity ranged from 4.3 to 63.2 nA peak-to-peak, while muscle stretches ranged from 100 μm to 4.26 mm peak-to-peak. The neuronal responses were studied by averaging the muscle length records centered at the skeletomotor action potentials (peri-spike average, PSA) and by Wiener analysis. Skeletomotor spikes appeared after a sharp peak in PSA of the injected current, preceded by a longer-lasting smaller wavelet of either depolarizing or hyperpolarizing direction. The PSA amplitude was not related to the injected current amplitude nor showed any differences related to the motor unit type. The PSA amplitudes were virtually independent of the stretching amplitude σ, after an initial increase with stretching amplitudes in the range of 15–40 μm (S.D.), or 100–270 μm peak-to-peak.Analyses of cross-spectra indicated a small or absent increase in gain with frequency in response to injected current, but about 20 dB/decade in the range 10–100 Hz in response to muscle stretch. The peaks of both Wiener kernels in response to current injection appear to decrease with the amplitude of injected current, but this decrease was not statistically significant. The narrow first-order kernels suggest that the transfer function between the current input and spike discharge is lowpass with a wide passband, i.e. there is very little change in dynamics. The values of the second-order kernels appear to be nonzero only along the main diagonal. This is characteristic of a simple Hammerstein type cascade, i.e. a zero memory nonlinearity followed by a linear system. Small values of second-order kernels away from the origin and narrow first-order kernels suggest that the linear cascade contributes very little to the overall dynamic response.In contrast to Wiener kernels found in response to current injection, the Wiener kernels in response to stretch showed a decreasing trend with stretch amplitude. The size of the second-order kernels decreased to a somewhat larger extent with input amplitude than that of the first-order kernels, indicating an amplitude-dependent nonlinearity. Overall, the transformation between length and spike output was described as an LNNL cascade with second-order nonlinearities. Received: 1 April 1993/Accepted in revised form: 24 March 1994     

Analysis of the coding of a periodic movement of stretch receptors of an insect

A study has been made of the input-output relationships of the in situ stretch receptor organs at the tibio-femoral joint of the locust. Sinusoidal deformations of variable amplitudes and frequencies were applied at different angular levels of the tibia. Three units were mainly recorded with silver electrodes on the lateral femoral nerve of the insect. The experimental conditions for which the discharge was periodically abolished are described. The shape and the amplitude of the impulse frequency modulation signal were studied also in relation to the stimulus gradation applied at the input. This response was highly temperature dependent. A graphical representation of the gain is given by a Bode plot (1·7 dB/octave), but over the range of stimulus cycle frequencies the phase-advance of impulse frequency modulation was constant. In successive cycles, there was no phase relation for each spike, except when the response was limited to a single one. In this condition, the response seemed locked in phase over a small range of relatively high frequencies.     

Cerebellar cortical activity during stretch of antagonist muscles

Single unit activity was recorded from the anterior lobe of the cerebellum during ramp and hold stretches of limb muscles in chloralose anesthetized cats. The activity of 95 "phasic" units showed a transient response during dynamic stretch of at least one muscle usually lasting for less than 350 ms following the stimulus onset. The activity of 59 phasic-tonic units was modified not only during dynamic stretch but also during the 1 s of maintained muscle length. All Purkinje cells, identified by their complex spikes, that responded to muscle stretch demonstrated exclusively phasic changes in discharge. Fourteen of 25 Purkinje cells (56%) responded to stretch of both antagonist muscles and these responses were always similar rather than reciprocal. From the 129 units without complex spikes, 70 demonstrated phasic discharge patterns whereas 59 had tonic responses. Seventy-five (59%) of these unidentified units revealed convergent responses to stretch of both antagonists, compared with 54 which responded to stretch of one muscle only. Of the unidentified units receiving convergent afferents from antagonist muscles, 62 (83%) had similar responses and only 13 (17%) had reciprocal reactions. There appeared to be no evidence that muscle afferents alone can induce reciprocal discharge patterns in Purkinje neurons of the cerebellar cortex. The firing frequency of some phasic-tonic units was correlated with both the velocity and amplitude of muscle stretch. No Purkinje cells were found with activity related to either velocity or amplitude of muscle stretch. One phasic and seven phasic-tonic unidentified units were activated at fixed latencies following trains of electrical stimulation applied to the thoracic spinal cord at frequencies exceeding 200 Hz, implying they were terminal portions of mossy fibers originating from direct spinocerebellar tracts. A few recordings of compound potentials were presumed to arise from the cerebellar glomeruli. The changing form of one of these potentials suggested that the glomerulus might be a site at which somatosensory peripheral information is modified by the cerebellar cortex.     

The cerebellum and initiation of movement: the stretch reflex

Studies of the stretch reflex in decerebrate cats indicate a phase advance of peak sinusoidal tension in steady-state cycles between 0.1 and 10 Hz. This phase advance is reduced in acute and chronic cerebellectomy, as shown in previous investigations. Also, the augmentation of muscle peak tension in initial sinusoidal stretch cycles at 0.5-5 Hz has been found to be reduced during the time of reflex and motor instability in the several months following cerebellar ablation. This report shows the increased amplitude and phase lead of integrated electromyographic activity in initiating sinusoidal stretch cycles in the decerebrate cat. These reflex aspects are demonstrated in relation to the discharge of neurons in the dorsal spinocerebellar tract and of cerebellar cortical Purkinje cells in initial sinusoidal cycles. The intensity and phase advance of the discharge in dorsal spinocerebellar tract neurons is altered little, but these features are usually increased in Purkinje cells during initial stretches compared to continuous cycling. In terms of overall motor control, these findings are compatible with concepts of movement control, modulated by the cerebellum, in which the discharge of antagonist motor neurons is regulated in concert with that of agonist muscles upon initiation and termination of movement.     

History-dependence of isometric muscle force: effect of prior stretch or shortening amplitude

It is well-recognised that steady-state isometric muscle force is decreased following active shortening (force depression, FD) and increased following active stretch (force enhancement, FE). It has also been demonstrated that passive muscle force is increased following active stretch (passive FE). Several studies have reported that FD increases with shortening amplitude and that FE and passive FE increase with stretch amplitude. Here, we investigate whether these trends continue with further increases in shortening or stretch amplitude. Experiments were performed using in situ cat soleus muscles (n=8 for FD; n=7 for FE and passive FE). FD, FE and passive FE were measured after shortening or stretch contractions that covered as wide a range of amplitudes as practically possible without damaging the muscles. FD increased approximately linearly with shortening amplitude, over the full range of amplitudes investigated. This is consistent with the hypothesis that FD arises from a stress-induced inhibition of crossbridges. FE increased with stretch amplitude only up to a point, and then levelled off. Passive FE, and the transient increase in force at the end of stretch, showed relationships to stretch amplitude that were qualitatively very similar to the relationship for FE, increasing only until the same critical stretch amplitude had been reached. We conclude that FE and passive FE do not increase with stretch amplitude under all circumstances. This finding has important consequences for determining the mechanisms underlying FE and passive FE because any mechanism that is proposed to explain them must be able to predict it.     

Does residual force enhancement increase with increasing stretch magnitudes?

It is generally accepted that force enhancement in skeletal muscles increases with increasing stretch magnitudes. However, this property has not been tested across supra-physiological stretch magnitudes and different muscle lengths, thus it is not known whether this is a generic property of skeletal muscle, or merely a property that holds for small stretch magnitudes within the physiological range. Six cat soleus muscles were actively stretched with magnitudes varying from 3 to 24 mm at three different parts of the force–length relationship to test the hypothesis that force enhancement increases with increasing stretch magnitude, independent of muscle length. Residual force enhancement increased consistently with stretch amplitudes on the descending limb of the force–length relationship up to a threshold value, after which it reached a plateau. Force enhancement did not increase with stretch amplitude on the ascending limb of the force–length relationship. Passive force enhancement was observed for all test conditions, and paralleled the behavior of the residual force enhancement. Force enhancement increased with stretch magnitude when stretching occurred at lengths where there was natural passive force within the muscle. These results suggest that force enhancement does not increase unconditionally with increasing stretch magnitude, as is generally accepted, and that increasing force enhancement with stretch appears to be tightly linked to that part of the force–length relationship where there is naturally occurring passive force.     

Tonic inhibitory influences of locus coeruleus on the response gain of limb extensors to sinusoidal labyrinth and neck stimulations

Previous experiments had shown that in decerebrate cats activation of limb extensor motoneurons during side-down roll tilt of the animal or side-up neck rotation depends on both an increased discharge of excitatory vestibulospinal (VS) neurons and a reduced discharge of inhibitory reticulospinal (RS) neurons of the medulla, thus leading to disinhibition of limb extensor motoneurons. The present experiments were performed to find out whether the locus coeruleus (LC) complex keeps under its tonic inhibitory control the medullary inhibitory RS neurons and, if so, whether this structure intervenes in the gain regulation of the vestibular and neck reflexes acting on the limb extensor musculature. In precollicular decerebrate cats with good postural rigidity of the four limbs, the amplitude of modulation and thus the response gain of the first harmonic component of multiunit EMG responses of limb extensors to sinusoidal stimulation of labyrinth and neck receptors (at 0.15 Hz, +/- 10 degrees) were quite small in forelimb muscles (triceps brachii) and almost negligible or absent in hindlimb muscles (triceps surae). Electrolytic lesion limited to the LC complex decreased the tonic contraction of limb extensors, but greatly increased in the forelimbs (and brought to the light in the hindlimbs) the response modulation of extensor muscles to the same parameters of labyrinth or neck stimulation. Correspondingly, the response gain increased, but no change in the phase angle of the responses was observed. Both changes in posture, as well as in response gain of the limb extensors to labyrinth and neck stimulation, fully developed some time after the LC lesion. This increase in response gain of the vestibular and neck reflexes acting on the limb extensor muscles did not depend on the decrease in postural activity following the LC lesion, since it was still obtained when an increased static stretch of the extensor muscle following passive flexion of the limb compensated for the reduced EMG activity. Moreover, the slope of the regression line relating the gain of the multiunit EMG response of the triceps brachii to animal tilt with the base frequency greatly increased following lesioning of the LC, thus indicating that for the same background discharge of the muscle the amplitude of modulation, and thus the response gain, increased significantly. The effects described above involved mainly, but not exclusively, the limbs ipsilateral to the side of the lesion.(ABSTRACT TRUNCATED AT 400 WORDS)     

Observations on phase-locking within the response of primary muscle spindle afferents to pseudo-random stretch

In order to uncover encoder properties of primary muscle spindle afferent fibers, time coupling (phase-locking) of action potentials on cyclic muscle stretch was studied by means of pseudo-random noise. In cats Ia action potentials were recorded from dorsal root filaments and the gastrocnemius muscles of one hind leg were stretched. The stimulus time course was a determined sequence of randomly varying muscle length which could be applied repeatedly (sequence duration 0.6 or 20 s). The noise amplitude (standard deviation of displacements) was varied between 5 and 300 m, the upper cut-off frequency of noise f _c was varied between 20 and 100 Hz. The responses to the consecutive pseudo-random noise cycles were displayed as raster diagrams and cycle histograms. Phaselocking characterized the responses at all noise amplitudes outside the near threshold range (>10 m). The higher and f _c , the stronger was the phase-locking of impulses on the stretch. When and f _c were selected to achieve high mean stretch velocities of about 500 mm/s, phase-locking was as precise as 0.15 ms, measured as the variability of spike occurrences with respect to stretch. The rasters obtained with low noise amplitudes (<40 m) showed a loose phase-locking and this gave insight into underlying mechanisms: The elicitation of action potentials caused by dynamic stretch can be prevented by a post-spike depression of excitability. This disfacilitation was very effective in counteracting weak stretch components within the random sequence and less effective or even missing when relatively strong stretch components could force the spike elicitation. This led to the reestablishment of phase-locked patterns. The results were discussed in relation to the known encoder models.     

Neural response to very low-frequency sound in the avian cochlear nucleus

Recordings were made in the chick cochlear nucleus from neurons that are sensitive to very low frequency sound. The tuning, discharge rate response and phase-locking properties of these units are described in detail. The principal conclusions are: 1. Low frequency (LF) units respond to sound frequencies between 10-800 Hz. Best thresholds average 60 dB SPL, and are occasionally as low as 40 dB SPL. While behavioral thresholds in this frequency range are not available for the domestic chick, these values are in good agreement with the pigeon behavioral audiogram (Kreithen and Quine 1979). 2. About 60% of the unit population displays tuning curves resembling low-pass filter functions with corner frequencies between 50-250 Hz. The remaining units have broad band-pass tuning curves. Best frequencies range from 50-300 Hz. 3. Spontaneous discharge rate was analyzed quantitatively for LF units recorded from nucleus angularis. The distribution of spontaneous rates for LF units is similar to that seen from higher CF units (300-5000 Hz) found in the same nucleus. However, the spontaneous firing of LF units is considerably more regular than that of their higher CF counterparts. 4. Low frequency units with low spontaneous rates (SR's less than 40 spikes/s) show large driven rate increases and usually saturate by discharging once or twice per stimulus cycle. Higher SR units often show no driven rate increases. 5. All LF units show strong phase-locking at all excitatory stimulus frequencies. Vector strengths as high as 0.98 have been observed at moderate sound levels. 6. The preferred phase of discharge (relative to the sound stimulus) increases with stimulus frequency in a nearly linear manner. This is consistent with the LF units being stimulated by a traveling wave. The slope of these phase-frequency relationships provides an estimate of traveling wave delay. These delays average 7.2 ms, longer than those seen for higher CF auditory brainstem units. These observations suggest that the peripheral site of low frequency sensitivity is the very distal region of the basilar papilla, an area whose morphology differs significantly from the rest of the chick basilar papilla. 7. LF units are described whose response to sound is inhibitory at frequencies above 50 Hz.     

Effect of the amplitude and frequency of sinusoidal stimulation on the harmonic distortion of the response of sensory terminations of muscle spindles

Harmonic distortion (HD) from 1,055 responses of muscle spindles sensory endings to sinusoidal stretches (frequency range 0.0008 to 0.8333 Hz, amplitude range 0.019 to 3.09 mm) has been studied in the cat soleus muscle. Sixty-six per cent were primary afferents (Ia) and 34% secondary (II). HD mean value (0.28) did not show any significant differences between both types of endings. Analysis of variance for HD versus stimulation amplitude showed a greater HD when stretch amplitudes were beyond 1.599 mm or less than 0.031 mm on primary afferents (p less than 0.001) and less than 0.070 mm on secondary (p less than 0.001). The effect of stimulus frequency was also significant (p less than 0.01 Ia and p less than 0.001 II), however only at 0.8333 Hz and in secondary endings HD was significantly higher. The silent period in the response, at release of stretch, caused by half wave rectification could explain about 50% of measured HD.     

The relative sensitivity of Renshaw cells to orthodromic group Ia volleys caused by static stretch and vibrations of extensor muscles.

1. Activity of Renshaw cells monosynaptically excited by ventral root stimulation and disynaptically excited by electric stimulation of the group Ia afferents in the gastrocnemius-soleus (GS) nerve, was recorded in precollicular decerebrate cats. The response of these units to prolonged vibration applied longitudinally to the deefferented GS muscle was then compared with that elicited by static stretch of the homonymous muscle, for comparable frequencies of discharge of the group Ia afferents. 2. Small-amplitude vibration of the GS muscle at 200/sec for one second produced a sudden increase in the discharge rate of Renshaw cells, which gradually decreased within the first 100 msec of vibration to reach steady albeit lower level than that obtained during the first part of vibration. The response of the Renshaw cells during the first 100 msec of vibration (phasic response) and that elicited during the last 500 msec of vibration (tonic response) were evaluated for different frequencies of sinusoidal stretch. The mean increase in the firing frequency per imp./sec in the Ia afferents was also calculated using the total one-second period. 3. The response of Renshaw cells to muscle vibration increased with the frequency of vibration and, over the value of 10/sec, appeared to be linearly related to the frequency of the input, at least up to the frequency of 150/sec. Since vibration was of sufficient amplitude to produce driving of all the primary endings of muscle spindles, the responses were expressed as mean increases in the discharge rate of Renshaw cells per average impulse/sec in the Ia afferents. The discharge of the Renshaw cell increased on the average by 2.90 and 1.08 imp./sec per each imp./sec in the Ia afferents during the phasic and the tonic component of the response respectively, while the response calculated during the whole period of vibration corresponded on the average to 1.45 imp./sec per each imp./sec in the Ia afferents. 4. The Renshaw cells tested above responded also with increasing frequencies of discharge to increasing levels of static extension of the GS muscle. In particular the discharge frequency of Renshaw cells was on the average linearly related to muscle extension, at least for values ranging from 0 to 8 mm. The mean increase in discharge rate as a function of the static extension corresponded on the average to 0.89 imp./sec/mm. Since the discharge rate of the primary endings of muscle spindles recorded from the deefferented GS muscle increased by 2.62 imp./sec/mm, it appears that the mean increase in the discharge rate of Renshaw cells as a function of static extension corresponded to 0.34 imp./sec per each imp./sec in the Ia afferents.     

Spike generation by spinal neurons evoked by sinusoidal depolarization in cats

Dynamic characteristics of transformation of cell membrane depolarization by spinal neurons into spike discharge frequency were investigated in anesthetized cats. Neurons were activated by sinusoidally modulated currents passed through an intracellular microelectrode. Frequency analysis of this transformation for motoneurons was carried out within a modulation frequency range of 0.2–10 Hz. Frequency characteristics were determined with respect to parameters of the first harmonic of the evoked firing rate; the region of values of current fluctuations was chosen on the linear part of the current intensity versus firing rate characteristic curve. Changes in amplitude characteristics did not exceed 5 dB in absolute terms; at the same time the phase lead of the output signal increased with a rise of frequency. At a frequency of 0.2 Hz phase shifts were virtually absent, but at frequencies of 1, 5, and 10 Hz they amounted to 32, 50, and 83° on average respectively. Transformation of membrane depolarization by neurons into spike discharge frequency is characterized by essentially nonlinear properties, due in particular to the absence of a dynamic component of the response to a negative rate of change of depolarizing current. The frequency characteristics of spike activity of neurons of the motor system are discussed from the standpoint of possible correction of dynamic properties of the whole system at the single unit level.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Dnepropetrovsk State University. Translated from Neirofiziologiya, Vol. 14, No. 1, pp. 35–42, January–February, 1982.     

Neuromuscular transmission in some hindlimb muscles of piglets with congenital myofibrillar hypoplasia (splayleg).

Seventeen new-born piglets of hybrid stock were tested for defects of neuromuscular transmission by stimulation electromyography (EMG). Nine of these displayed extreme symptoms of muscle weakness (splayleg), while the others were their clinically normal littermates. Muscles from four different functional groups were investigated, including the gastrocnemius, tibialis anterior, knee flexors and thigh adductors. Repetitive stimulation of muscle nerves at 3 Hz gave comparable peak-to-peak amplitudes of the EMG response in splayleg and control piglets (mean values from 5 to 10 mV). The lowest mean EMG response values at this stimulation frequency were found in splayleg adductor muscles of the thigh which were not, however significantly different from the controls. Higher frequencies of stimulation (30, 50 and 100 Hz), in general, led to a less pronounced decrease of EMG amplitude in splayleg piglet muscles than in the controls, with the exception of knee flexors. Neither splayleg nor control muscles exhibited post-activation exhaustion or post-tetanic potentiation. It is being concluded from these results that congenital myofibrillar hypoplasia is not primarily a myasthenia-like syndrome, but that either excitation-contraction coupling or the contractile mechanism itself are primarily affected.     

Cyclic stretch induced MAPK phosphorylation stronger than static stretch.

The environment for living organism in space has microgravity and/or hypergravity and/or any kind of mechanical stresses. Cellular response may differ from the variety of mechanical stress. Mitogen-activated protein kinases (MAPKs) pathway is related to various cellular events. In the present study it was investigated the serial measurement of MAPK phosphorylation using western-blotting analysis following with three types of cyclic stretch, static, 0.1 Hz and 0.25 Hz. The result was that induction of MAPK phosphorylation had peaks within 2 to 4 hours and attenuated, while induction of p38 phosphorylation in 0.1 Hz stretch had a peak at 6 hours later and the strongest. Thus, there might be differential cellular response depends upon the frequency of cyclic stretch .     

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch

The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input-output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener's white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0∶0.47∶0.26.     

The effects of cold-induced muscle spindle secondary activity on monosynaptic and stretch reflexes in the decerebrate cat.

The effects of muscle spindle secondary ending activity on the stretch reflex were studied in unanesthetized decerebrate cats. Activation of secondary endings was accomplished by reducing the muscle temperature. This has been shown to cause a sustained asynchronous discharge from secondary endings. Cooling of the medial gastrocnemius or lateral gastrocnemius-soleus muscles caused an increase in the phasic and tonic components of their stretch reflexes. Cooling of the relaxed medial gastrocnemius muscle caused similar increases in the components of the stretch reflex of the synergistic lateral gastrocnemius-soleus muscle and an increase in its monosynaptic reflex. It was concluded that the facilitatory autogenetic and synergistic effects of muscle cooling on the stretch and monosynaptic reflexes were brought about by activity in group II afferents from muscle spindle secondary endings and could not be ascribed to any other type of muscle receptor. These results support the concept of an excitatory role for the secondary endings of the muscle spindle in the stretch reflex of the decerebrate cat.     

Critical sarcomere extension required to recruit a decaying component of extra force during stretch in tetanic contractions of frog skeletal muscle fibers

29 single frog skeletal muscle fibers were stretched during fused tetanic contractions. The force increase during stretch exhibited a breakpoint at a critical length change (average: 16.6 nm per one-half sarcomere) that was independent of velocity of stretch and of sarcomere length between 1.8 and 2.8 microns. After stretch there was an early decaying force component with a force-extension curve similar to that during stretch, which disappeared over approximately 2 s. This component was removed by a small, quick release, leaving a longer- lasting component. The critical amplitude of release required to produce this result was found by clamping the fiber to a load at which there was zero velocity of shortening. This amplitude increased with time up to the angle in the force record during stretch, was constant for the remainder of the stretch, and decreased with time after the end of stretch; it was consistently less than the critical amplitude of stretch required to reach the breakpoint of force enhancement during stretch but was also independent of sarcomere length. The force drop accompanying the critical release showed a small increase up to an optimum magnitude at 2.4--2.7 microns sarcomere length, with a decrease at longer lengths.     

Information transmission by isolated frog muscle spindle

Transmission of sensory information was calculated for the isolated frog muscle spindle receptor, using Shannon's information measure. Sinusoidal movements, random noise stretches, and sinusoids with superimposed auxiliary noise were applied as stimuli. In addition, the static prestretch level of the intrafusal muscle bundle was adjusted between resting length (L0) and L0 + 600 micron, so that the analysis of the information transmission properties covered the entire dynamic range of the sensory receptor organ. Sinusoidal stretches below 2 Hz evoked smoothly modulated cycle histograms, which were approximately linearly related to the stimulating sinewave. The transinformation rates under these conditions were generally low (5-17 bit X s-1), regardless of the amplitude of the applied movement. Increasing prestretch enhanced the modulation depth of the cycle histograms considerably, but increased the transinformation rates by less than 10 bit X s-1. By contrast, sinusoids above 2 Hz evoked clearly nonlinear cycle histograms, because each action potential was firmly phase-locked to a small segment of the stretch cycle. Under these conditions the transinformation rates grew larger with increasing stimulus frequency and approached 130 bit X s-1 at 60 Hz. Small amplitude sinusoidal stretches, however, evoked considerable transinformation rates in the high frequency region only then, when the spindle receptor was extended to higher prestretch levels. Random stretches evoked transinformation rates between 5 and 30 bit X s-1 depending on both the prestretch level and the intensity of the noise stimulus. The linear response components carried only about 25% of the transinformation rates transmitted by both the linear and nonlinear response components. Auxiliary noise stimuli greatly improved the information transmission of sinusoidal stretches. For example, a pure sinusoid evoked 5 bit X s-1. Adding a noise signal with equal energy to the sinusoidal movement elicited 20 bit X s-1. This facilitation effect of auxiliary noise was restricted to low frequency sinusoidal stimuli. The present results are discussed with respect to the information transmission properties of various sensory systems evaluated by either the same or different information processing procedure as that used in the present study. The functional significance of high transinformation rates sent by the muscle spindle to the central nervous system is discussed with respect to motor control.     

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch

 The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input–output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener’s white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0 : 0.47 : 0.26. Received: 15 November 1994/Accepted in revised form: 23 May 1995