tion) to identify the type(s) of intrafusal fiber activated by the stim- ulation of single static axons was tested in Peroneus tertius muscle spindles of anesthetized ...
Testing the Classification of Static g Axons Using Different Patterns of Random Stimulation JULIEN PETIT, ROBERT W. BANKS, AND YVES LAPORTE Laboratoire de Physiologie de la Perception et de l’Action. Colle`ge de France, 75005 Paris, France Petit, Julien, Robert W. Banks, and Yves Laporte. Testing the classification of static g axons using different patterns of random stimulation. J. Neurophysiol. 81: 2823–2832, 1999. The possibility of using randomly generated stimulus intervals (with a Poisson distribution) to identify the type(s) of intrafusal fiber activated by the stimulation of single static g axons was tested in Peroneus tertius muscle spindles of anesthetized cats. Three patterns of random stimulation with different values of mean intervals [20 6 4.47, 30 6 8.94, and 40 6 8.94 (SD) ms] were used. Single static g axons activating, in single spindles, either the bag2 fiber alone or the chain fibers alone or both types of intrafusal fiber were prepared. Responses of spindle primary endings elicited by the stimulation of g axons were recorded from Ia fibers in cut dorsal root filaments. Cross-correlograms between stimuli and spikes of the primary ending responses, autocorrelograms, interval histograms of responses, and stimulations were built. The characteristics of cross-correlograms were found to be related not only to the type of intrafusal muscle fibers activated but also to the parameters of the stimulation. Moreover some cross-correlograms with similar characteristics were produced by the activation of different intrafusal muscle fibers. It also was observed that, whatever the type of intrafusal muscle fiber activated, cross-correlograms could exhibit oscillations after an initial peak, provided the extent in frequency of the primary ending response was small; these oscillations arise in part from the autocorrelation of the primary ending responses. Therefore, cross-correlograms obtained during random stimulation of static g axons cannot be used for unequivocally identifying the type(s) of intrafusal muscle fiber these axons supply.
INTRODUCTION
Histophysiological studies as well as direct observation of isolated spindles have shown that individual static g axons (gs) may innervate, in single spindles, the bag2 fiber alone or the chain fibers or both these types of fiber together (see review by Banks 1994a). Although this much generally is agreed, the question of the degree of specificity of static g axons, by which is meant their tendency to innervate the same type of intrafusal fiber in all the spindles each one supplies, is disputed (Banks 1991, 1994b; Barker et al. 1973; Boyd 1986; Brown and Butler 1973; Celichowski et al. 1993, 1994; Dickson et al. 1993; Emonet-De´nand et al. 1998; Taylor et al. 1998; Wand and Schwartz 1985). In a correlated histological and physiological study of the cat tenuissimus, which allows individual spindles to be located, Banks (1991) concluded that although there is only a single type of static g neuron, some differential distribution to bag2 and chain fibers according to axonal conduction velocity is The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked ‘‘advertisement’’ in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
observed. Celichowski et al. (1994) since have developed generally applicable physiological tests based on known contractile properties of bag2 and chain fibers to determine the types of intrafusal muscle fiber activated by single gs axons. With these tests, they studied the distribution of single gs axons to the intrafusal muscle fibers of all spindles supplied by each g axon in two cat muscles with different g to spindle ratios (Boyd and Davey 1968): the Peroneus tertius and the Peroneus longus muscles. In the tertius, the ratio of which is low, they found only 13% of specific axons as compared with 45% in the longus, the ratio of which is much larger (Celichowski et al. 1994; Emonet-De´nand et al. 1998). Durbaba et al. (1993) and Taylor et al. (1994, 1998) reported that another test intended to determine the fiber-type distribution of static g axons can be used to assess the relative contribution of chain and bag2 contractions in mixed effects. This test is based on the inspection of cross-correlograms between the response of a primary ending and a train of stimuli, the successive interval values of which were generated at random and followed a Poisson distribution. Studying the distribution of gs axons in single gastrocnemius spindles with this test, they concluded that the incidence of specific axons is greater than would be expected by chance. In the present study of the responses of primary endings to similar random trains of stimuli, we have especially studied the influence of the distribution of stimulus intervals on the responses by using several trains of stimuli with different Poisson distributions (Poisson stimulation). The characteristics of the cross-correlograms between response and Poisson stimulation proved to be related not only to the type of intrafusal muscle fiber activated (previously determined by Celichowski et al.’s technique) but also to the parameters of the stimulation to such an extent as to cast serious doubts on the possibility of correctly identifying the type(s) of muscle fiber activated in a spindle with this kind of stimulation. METHODS
The experiments were carried out on the left peroneus tertius muscles of two adult cats (4.6 and 5.8 kg) anesthetized with pentobarbital sodium (Nembutal, 35 mg/kg ip), supplemented intravenously as required. Most of the techniques used in this study have been described fully in previous papers, especially in that on the distribution of peroneus tertius static g axons (Celichowski et al. 1994). Static g axons were identified by the typical changes their repetitive stimulation elicited in the response of primary endings to ramp stretch (Crowe and Matthews 1964; Emonet-De´nand et al. 1977). Identification of intrafusal muscle fibers activated by the g axons was made with the method developed by Celichowski et al. (1994), which rests on cross-correlograms between stimuli at 100 Hz and Ia afferent
0022-3077/99 $5.00 Copyright © 1999 The American Physiological Society Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
2823
2824
J. PETIT, R. W. BANKS, AND Y. LAPORTE
impulses, and on the features of primary-ending responses during stimulation at 30 Hz. Ramp stimulation, as introduced by Boyd and Ward (1982), also was used; the frequency increased linearly from 10 to 150 Hz in 2.5 s. Poisson stimulation was produced using three different trains of stimuli in which the values of the intervals between successive stimuli were generated using MapleV software. They were designed so that two shared the same mean but had a twofold difference in standard deviation and two had the same standard deviation but twofold differences in mean. The Poisson distribution has the following formula: P(x) 5
e 2bbx x!
where x is a random variable and p(a) is the probability that the variable x has the value a. The mean value of x is b, and its standard deviation is =b. Because x is obviously an integer, the Poisson distribution is a discrete distribution; however, it may be approximated by a continuous distribution using the gamma function, thus allowing nonintegral values of time intervals to be computed with distributions having known means and standard deviations. Three series of 1,000 interval values were generated; then each series was divided into five subseries of 200 values. The interval distributions of the series had means of 20 6 4.472, 20 6 8.94, and 40 6 8.94 (SD) ms. For simplicity, we shall use ‘‘Poisson distribution’’ to describe all three time-interval distributions, even though they are all nonintegral and in two of them either the standard deviation or the mean has been rescaled. We note that Taylor et al. (1998) rescaled the output from a radioactive source to generate stimulus trains with two different means but unknown standard deviations, and that they also described these as Poisson-distributed. Static g axons were stimulated using trains of 200 stimuli triggered by the subseries just described with a minimal delay between two trains of stimulation of 30 s to avoid fatigue of the chain fibers. Three cross-correlograms between the randomly distributed stimuli and the primary-afferent discharge were built, one for each of the different distributions (results obtained using subseries with the same mean interval and SD were pooled). For the same periods of stimulation, the three autocorrelograms of the afferent discharges and the interval histograms of the stimulation and of the afferent response also were built. For the correlograms, selecting a binwidth of 1 ms ensured that no more than one spike could be added to each bin during each triggered sweep. The cross-correlograms were normalized by dividing the number of spikes obtained in each bin by the number of stimuli. Because the cross-correlograms were triggered by the stimuli, they
then could be taken to represent the probability that a sampling bin with a given delay after each stimulus will contain a spike. Thus if a spike was always to occur in the nth bin after each stimulus, there would be the same number of spikes in bin n of the correlogram as there were stimuli, and the normalized ordinate of the bin would be 1. The arrangement therefore conforms with the formal definition of probability, in that the ordinate in any bin cannot exceed 1. In addition the interval histograms of the stimulation and of the afferent response were built for the same periods of stimulation. RESULTS
The action of 10 static g axons on the discharges of primary endings (11 Ia fibers prepared) was studied in two experiments: three activated one spindle, three activated two spindles, three activated three spindles, and one activated four spindles. The intrafusal fibers innervated by each g axon in each spindle were determined with the method described by Celichowski et al. (1994). Responses of a primary ending when chain fibers alone are activated The evidence that only chain fibers were activated in a given spindle rested on the tests shown in Fig. 1. The response of the primary ending to a stimulation at 30 Hz of the single g axon (Fig. 1A) shows a typical 1:1 driving, a single spike being generated by each stimulus. The cross-correlogram between the afferent discharge and stimulation at a constant frequency of 100 Hz (Fig. 1B) exhibits a peak at 4.5 ms with a probability of 1 of observing a spike between 14 and 16 ms poststimulus. To take account of the conduction time of the g axon and of the Ia fiber one stimulation period (10 ms), this value has to be added to the observed delay. In this particular example, 1:1 driving was especially well marked, occurring over virtually the whole range of a linearly increasing stimulus frequency above the primary afferent’s resting discharge (Fig. 1C). Unlike the bag2 fiber, the chain fibers have very rapid contractions that are not completely fused at 100 Hz. A peak in the cross-correlogram such as the one in Fig. 1B indicated the contraction of these fibers. At 30 Hz, the primary-afferent discharge mimicked the stimulation. There was no obvious sign of bag2 activation and the minimal instantaneous frequency of the dis-
FIG. 1. Tests for demonstrating that intrafusal chain fibers are activated alone in a spindle by the stimulation of a single static g axon. A: response, in instantaneous frequency, of the primary ending (top) during the stimulation at 30 Hz of the single g axon (top horizontal bar). B: cross-correlogram between the primary ending response and the stimulation at a constant frequency of 100 Hz of the static g axon. C: response, in instantaneous frequency, of the primary ending (dots) during the ramp frequency stimulation (triangles) of the single g axon from 7 to 147 Hz. Response and stimulation superposed almost exactly above ;30 Hz, so that triangles are visible only ,30 Hz.
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
STATIC g AXONS AND POISSON STIMULATION
2825
FIG. 2. Activation of chain fibers alone by Poisson stimulation of a single g axon (same axon as in Fig. 1). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 20 6 4.47 (SD) ms. A: interval histogram of stimuli. B: spike interval histogram of the primary ending response to the static g axon stimulation. C: cross-correlogram between the stimuli and the primary ending response to the static g axon stimulation. D: autocorrelogram of the primary ending response to the static g axon stimulation. Ordinate axis is aligned with the 1st peak in the cross-correlogram (- - -). Peak with 0 lag and an amplitude of 1 was omitted.
charge during stimulation was not above the frequency of stimulation (see Celichowski et al. 1994); therefore, chain fibers could be considered as having been activated alone. In the present study, five instances of chain fibers activated alone in a spindle by a single g axon were observed. During the Poisson stimulation, a nearly perfect 1:1 driving was preserved as indicated by the close similarity of the interval histogram of the spikes (Fig. 2B) with the interval histogram of the stimuli (Fig. 2A). The interval histogram was approximately Gaussian with a mean interval of 20 6 4.47 (SD) ms (the minimal and maximal intervals were 8 and 36 ms, respectively). This was confirmed by the cross-correlogram between the stimulation and the afferent discharge (Fig. 2C), which exhibits a large peak with a latency of 16 –17 ms. The probability that a spike occurred between 14 and 20 ms (sum of the values in bins between these 2 times) was almost 1 thus confirming the totally driven nature of the Ia response. Oscillations that were observed after the main peak in the cross-correlogram (Fig. 2C) exactly corresponded to oscillations in the autocorrelogram of the response (Fig. 2D). The reason for the similarity of the oscillations is clearly the perfect 1:1 driving, as in this case, single spikes occurred with an almost constant delay after each of the successive stimuli. Therefore the probability of observing a spike x ms after the stimulus (where x . latency of the 1st peak) then would be expected to equal the probability of observing a spike y ms after each spike located in the peak (where y 5 x minus the 1st peak latency), which is the definition of the autocorrelation function. Therefore the autocorrelogram of the response was built and shifted, in Fig. 2D, by an amount equal to the latency of the first peak observed in the cross-correlogram of Fig. 2C. The first oscillation in the autocorrelogram extended between 10 and 30 ms, the maximum being at 20 ms, which precisely corresponded to the features of the interval histogram in Fig. 2B. This has to be expected because if the range of the spike intervals in the afferent response is not too wide, the latency of the first peak in the autocorrelogram is equal to the modal interspike interval.
It was likely that the marked oscillations observed in the cross-correlogram of Fig. 2C were due to the limited range of intervals in the response. Therefore we increased the range of intervals by using a stimulation with the same mean of time intervals, 20 ms, but a larger SD. The interval histogram of this stimulation (Fig. 3A), asymmetrical as expected from a Poisson distribution, shows that intervals spread from 2 to 50 ms. The corresponding histogram of the afferent response (Fig. 3B) was approximately the same but with a larger proportion of short and long intervals. Nevertheless 1:1 driving persisted as confirmed by the occurrence of a large peak in the cross-correlogram between the stimuli and the afferent response (Fig. 3C). In this case, only that part of the autocorrelogram between 0 and 20 ms (Fig. 2D) was similar to the cross-correlogram of the afferent response (Fig. 3C) because the spread of the spike intervals in the response (Fig. 3B) was too wide compared with the mean interval to allow separate oscillations to occur. To confirm the importance of the ratio between the range and the mean of spike intervals in the generation of oscillations in the cross-correlogram, we used a third stimulation pattern, with a mean interval of 40 6 8.94 (SD) ms. The interval histogram of the afferent response (Fig. 4B) was similar to the stimulus interval histogram (Fig. 4A): both spread from 20 to 60 ms. A sharp peak (delay 17–18 ms) was present in the cross-correlogram between stimuli and afferent response (Fig. 4C). Again because the response was an almost perfect 1:1 driving, the second part of the cross-correlogram was almost exactly the autocorrelogram of the afferent response (Fig. 4D). The delay of the maximum of the first oscillation in the autocorrelogram (;40 ms) corresponded to the mean spike and stimulus intervals. It should be noted that the delay of the peak in the crosscorrelogram was 14.5 ms in Fig. 1B, 16 –17 ms in Fig. 2C, and 17–18 ms in Fig. 4C. Dickson et al. (1993) and Celichowski et al. (1994) already noted that the peak delay is longer for low frequencies of stimulation than for high frequencies. This observation is confirmed in the present study because the frequency of stimulation was 100 Hz (constant frequency) for
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
2826
J. PETIT, R. W. BANKS, AND Y. LAPORTE
FIG. 3. Activation of chain fibers alone by ‘‘Poisson random’’ stimulation of a single g axon. (same axon as in Fig. 1). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 20 6 8.94 (SD) ms. A–D: same as in Fig. 2.
Fig. 1B, ;50 Hz (Poisson stimulation) for Fig. 2C, and ;25 Hz (Poisson stimulation) for Fig. 4C. The peak in the crosscorrelogram of Fig. 3C was wider than corresponding peaks in the other cross-correlograms because of the wider range of stimulation frequencies (from 25 to 250 Hz) that was responsible for rather different delays in spike generation. This explains the relatively small amplitude of the peak but because the total area of the peak was close to 1, the response of the primary ending during that stimulation of the g axon also was dominated by 1:1 driving. The characteristics of the responses of the primary ending to the contraction of chain fibers described in Fig. 1 to 4 are the consequence of a perfect 1:1 driving and were observed only once. Usually, during contraction of chain fibers alone, primary-ending responses may exhibit 1:1 driving only over a limited range of frequencies of stimulation. Therefore some
spikes in the afferent response are not so closely correlated to the stimuli which leads to a constant level in the cross-correlogram between response and stimuli, on which peaks might be superimposed. More precisely, the cross-correlograms have the same shape as those described in Figs. 2– 4, but no bins are empty. An example of such an activation is shown in Fig. 5. The cross-correlograms in Fig. 5, C and D, are indistinguishable from those obtained during the stimulation of both chain and bag2 fibers (see following text). Responses of a primary ending to the concomitant contraction of bag2 and chain fibers The responses of another primary ending to stimulation of another static g axon, the intrafusal distribution of which was identified by the Celichowski et al. (1994) tests as supplying
FIG. 4. Activation of chain fibers alone by Poisson stimulation of a single g axon (same axon as in Fig. 1). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 40 6 8.94 (SD) ms. A–D: same as in Fig. 2.
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
STATIC g AXONS AND POISSON STIMULATION
2827
FIG. 5. Top: tests for demonstrating that intrafusal chain fibers are activated alone in a spindle by the stimulation of a single static g axon. A: response, in instantaneous frequency, of the primary ending (top) during the stimulation at 30 Hz of the single g axon (top horizontal bar). B: cross-correlogram between the primary ending response and the stimulation at a constant frequency of 100 Hz of the static g axon. Bottom: cross-correlograms between the randomly generated stimuli and the primary ending response to the static g axon stimulation. C: Poisson distribution with mean of 20 6 4.47 (SD) ms. D: Poisson distribution with mean of 20 6 8.94 (SD) ms.
both bag2 and chain fibers, are presented in Fig. 6. The crosscorrelogram (Fig. 6B) between the afferent discharge and the stimulation (constant frequency 100 Hz) exhibited a peak that had a delay of 18.5 ms (because the measured conduction time in the Ia fiber and in the g axon was .8.5 ms, the latency of the peak was 8.5 ms plus the stimulus period of 10 ms). The existence of this peak indicates the activation of chain fibers but in this case there was also coactivation of bag2 fibers because during stimulation at a constant frequency of 30 Hz (Fig. 6A) the minimal afferent discharge frequency was well above the frequency of stimulation (see Celichowski et al. 1993). The responses of the primary ending to the ramp frequency stimulation showed that 1:1 driving was limited to a small range of frequencies of activation; this is consistent with both bag2 and chain activation (Fig. 6C). There were eight instances of such activations in this study. To compare responses of primary endings to the concomitant contraction of bag2 and chain fibers with those obtained during activation of chains alone, we used the same three random stimulation patterns. In Fig. 7 (same stimulation as for
Fig. 2), it can be seen that the interval histogram of the afferent response to the stimulation of a chain-bag2 axon (Fig. 7) was different from the stimulus interval histogram (Fig. 7A). The mean stimulus interval was higher than the mean spike interval, there being approximately twice as many spikes as stimuli. In this case, the cross-correlogram between the stimuli and the response (Fig. 7C) also presented a sharp peak (delay 16 ms) followed by oscillations that had the same delays as those observed in the autocorrelogram of the response (Fig. 7D). However, features in the cross-correlogram not observed with strongly driving gs should be noted: on both sides of the sharp peak no bins were empty, that is, a constant level of probability due to spikes uncorrelated with the stimulus was present (compare with Fig. 2C); and the shape of the oscillations observed after the peak in the cross-correlogram were slightly different from those in the autocorrelogram. This was expected because the amplitude of the oscillations in the cross-correlogram is a function of the height of the first peak, which was much smaller in this case than the peak illustrated in Fig. 2C (at the limit, when no primary peak is present in the cross-correlo-
FIG. 6. Tests for demonstrating that chain fibers and the bag2 fiber are activated concomitantly in a spindle by the stimulation of a single static g axon. A: response, in instantaneous frequency, of the primary ending (top) during the stimulation at 30 Hz of the single g axon (top horizontal bar). B: cross-correlogram between the primary ending response and the stimulation at a constant frequency of 100 Hz of the static g axon. C: response, in instantaneous frequency, of the primary ending (dots) during the ramp frequency stimulation (triangles) of the single g axon from 7 to 147 Hz.
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
2828
J. PETIT, R. W. BANKS, AND Y. LAPORTE
FIG. 7. Concomitant activation of chain fibers and bag2 fiber by Poisson stimulation of a single g axon (same fibers as in Fig. 6). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 20 6 4.47 (SD) ms. A: interval histogram of stimuli. B: spike interval histogram of the primary ending response to the static g axon stimulation. C: crosscorrelogram between the stimuli and the primary ending response to the static g axon stimulation. D: autocorrelogram of the primary ending response to the static g axon stimulation. Ordinate axis is aligned with the 1st peak in the cross-correlogram (- - -). Peak with 0 lag and an amplitude of 1 was omitted.
gram, there can be no subsequent oscillations due to the autocorrelogram). We also used a stimulation pattern with a mean interval of 20 ms but with a wide SD (Fig. 8). The afferent-dischargeinterval histogram (Fig. 8B) was different from the stimulusinterval histogram (Fig. 8A), again with about twice as many spikes as stimuli. The cross-correlogram between response and stimuli (Fig. 8C) still exhibited a sharp main peak, followed by a smaller subsidiary peak corresponding to the autocorrelogram (Fig. 8D). This cross-correlogram was similar to that shown Fig. 3C except for the presence of a constant level of probability due to spikes uncorrelated with the stimuli. Finally we used a third stimulation pattern which had a mean
interval of 40 ms. The interval histogram of the response (Fig. 9B) was strikingly different from the stimulus-interval histogram (Fig. 9A). The number of spikes was about three times the number of stimuli, and the cross-correlogram (Fig. 9C) exhibited a small and wide peak with a delay of ;18 ms. In spite of the small size of the peak, oscillations with delays similar to the strong oscillations of the autocorrelogram (Fig. 9D) could be seen, added to a constant level of probability. The cross-correlogram of Fig. 9C is very different from that of Fig. 4C in contrast with the similarity of the cross-correlograms of Figs. 7C and 2C and of the cross-correlograms of Figs. 8C and 3C. In Fig. 9 the Poisson stimulation had a mean frequency of 25 Hz with a range of 15–35 Hz. In this range of
FIG. 8. Concomitant activation of chain fibers and bag2 fiber by Poisson stimulation of a single g axon (same axon as in Fig. 6). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 20 6 8.94 ms. A–D: same as in Fig. 6.
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
STATIC g AXONS AND POISSON STIMULATION
2829
FIG. 9. Concomitant activation of chain fibers and bag2 fiber by Poisson stimulation of a single g axon (same axon as in Fig. 7). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 40 6 8.94 ms (see METHODS). A–D: same as in Fig. 7.
frequencies, the contraction of the bag2 fiber is partially fused, eliciting a rather strong activation of the primary ending (see Fig. 10), whereas the contraction of the chain fibers is unfused. Consequently the driving at low frequencies of the afferent discharge by chain oscillations hardly is depicted in the afferent response and the first peak in the cross-correlogram is small. Conversely, in Figs. 7 and 8, high frequencies are present in the stimulation, which does not increase the activation of the bag2 fiber (fusion frequency for this fiber is ;60 –70 Hz) but which increases noticeably the contribution of the driving of the primary ending to the response by chain fibers. Therefore the peak in the cross-correlogram becomes significant. The striking differences in the correlograms that are related to the different patterns of Poisson stimulation show that a correlogram, on its own, cannot be a valid test to
determine the type of intrafusal muscle fibers activated by the stimulation of a single g axon. Responses of a primary ending when the bag2 fiber alone is activated The identification by Celichowski et al. (1994) tests of a g axon activating the bag2 fiber alone in another spindle is illustrated by Fig. 10. Stimulation at 30 Hz of the axon elicited a large increase in frequency well above the frequency of stimulation (Fig. 10A) and the cross-correlogram between the stimulation at a constant frequency of 100 Hz and the afferent response presented no significant peak (Fig. 10B). As expected, the afferent response to the ramp stimulation presented no sign of 1:1 driving. However, Dickson et al. (1993) and Celichowski et al. (1994) already noted that in some instances the
FIG. 10. Tests for demonstrating that the intrafusal bag2 fiber is activated alone in a spindle by the stimulation of a single static g axon. A: response, in instantaneous frequency, of the spindle primary ending (top) during the stimulation at 30 Hz of the single g axon (top horizontal bar). B: cross-correlogram between the primary ending response and the stimulation at a constant frequency of 100 Hz of the static g axon. C: cross-correlogram between the primary ending response and the stimulation at a constant frequency of 30 Hz of the static g axon. D: autocorrelogram of the primary ending response to the static g axon stimulation. Ordinate axis is aligned with the first peak in the cross-correlogram (dotted line). E: response, in instantaneous frequency, of the primary ending (dots) during the ramp frequency stimulation (triangles) of the single g axon.
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
2830
J. PETIT, R. W. BANKS, AND Y. LAPORTE
FIG. 11. Activation of the bag2 fibers alone by Poisson stimulation of a single g axon (same axon as in Fig. 10). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 20 6 8.94 ms. A: interval histogram of stimuli. B: spike interval histogram of the primary ending response to the static g axon stimulation. C: cross-correlogram between the stimuli and the primary ending response to the static g axon stimulation. D: autocorrelogram of the primary ending response to the static g axon stimulation. Ordinate axis is aligned with the 1st peak in the cross-correlogram (- - -). Peak with 0 lag and an amplitude of 1 was omitted.
partially fused contraction of the bag2 at comparatively low frequencies of stimulation may elicit some entrainment or partial driving of the afferent discharge. This is the case in the present example because the cross-correlogram between the stimulation at 30 Hz and the primary-ending discharge (Fig. 10C) exhibited a small peak (delay 14 ms). The other oscillations, present during the period of 33 ms, were due to the autocorrelogram of the response which is shown Fig. 10D (It should be remembered that for a stimulation with a constant frequency the cross-correlogram is periodic). As expected, when the random stimulation with a mean interval of 20 ms was used, the cross-correlogram between the stimuli and the response presented no significant peak as shown in Fig. 11C obtained using the stimulation with a wide SD (see Fig. 11A). Therefore no correspondence between the autocorrelogram (Fig. 11D) and the cross-correlogram (Fig. 11C) could be observed. When the Poisson stimulation with a mean interval of 40 ms was used (Fig. 12), a small peak (delay 14 ms) in the cross-
correlogram between the stimuli and the afferent response was observed. This could be expected because the range of stimulation frequencies used was 15–35 Hz and because a peak already had been observed in the cross-correlogram with the stimulation at a steady 30 Hz (Fig. 10C). The small peak and the strong oscillations in the autocorrelogram of the response (Fig. 12D) explained the subsequent oscillations that occurred after the small primary peak in the cross-correlogram. DISCUSSION
The main finding of this study is that the characteristics of cross-correlograms between a random Poisson stimulation of single static g axons and the responses elicited in primary endings depend on the parameters of the random stimulation as well as on the mechanical properties of the activated intrafusal muscle fibers. Therefore it should be examined whether the main characteristics of such cross-correlograms can serve to
FIG. 12. Activation of the bag2 fibers alone by Poisson stimulation of a single g axon (same axon as in Fig. 10). Randomly generated intervals between stimuli had a Poisson distribution with a mean of 40 6 8.94 ms. A–D: same as in Fig. 11.
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
STATIC g AXONS AND POISSON STIMULATION
identify, with a reasonably high degree of confidence, the types of intrafusal muscle fiber activated by single gs axons. Occurrence of peaks in cross-correlograms The first peak is known to be due to spikes elicited by oscillations in the unfused contractions of intrafusal fibers (Bessou and Page`s 1975; Boyd 1986; Boyd et al. 1985). A peak can be ascribed either to the contraction of a bag2 fiber or to that of chain fibers depending on the chosen parameters of the Poisson stimulation. Thus in the present experiments, when the bag2 fiber alone was activated, there was a barely visible peak in the cross-correlogram (Fig. 11C) when the mean and the SD of the Poisson distribution were 20 ms (50 Hz) and 8.9 ms, respectively. This is because, during such a stimulation, most values of intervals between stimuli (Fig. 11A) ranged between 25 and 10 ms and in the corresponding range of frequencies (40 –100 Hz) the contraction of this fiber is either completely or partially fused. However, when the mean stimulus interval was 40 ms (25 Hz), an early small peak was visible in the crosscorrelogram (Fig. 12C) because bag2 contraction was unfused. Therefore a first peak can be ascribed specifically to the contraction of chain fibers only if the Poisson distribution of the stimulus intervals does not include intervals above ;25 ms (40 Hz). Furthermore this distribution should not include intervals ,5 ms (200 Hz) because the contraction of chain fibers is almost fused near that frequency and consequently spikes elicited during such high rates of stimulation are no longer correlated with the stimulation. Including such small intervals in the stimulation would only result in decreasing the amplitude of the first peak. Among the three patterns of stimulation we used (see METHODS), the second type (mean 20 ms and wide SD) fulfilled these conditions. The height and shape of the first peak in the cross-correlogram cannot readily be related to the type of intrafusal muscle fiber activated because they are influenced by the combination of three parameters: relationship between the delay of the spike and the values of the intervals between stimuli (see Figs. 1B, 2C, and 4C), distribution of the stimulus intervals and range of frequencies in which the primary ending is driven. It is only if an adequate range of stimulation frequencies (above ;50 Hz and below ;150 Hz) is selected that the presence of a first peak in the cross-correlogram is a valid proof of the contraction of chain fibers. Consequently, when this range is used, the absence of a peak proves that the primary ending activation elicited by the stimulation of single g axons is due to the contraction of the bag2 fiber alone. Oscillations after the first peak Using three patterns of random stimulation that differed by the means and SD of their interval distributions, we have shown that these oscillations arise in part from the autocorrelation of the primary-ending response. They are present when intrafusal chain fibers are activated either alone or with the bag2 fiber as shown by the similarity of cross-correlograms in Figs. 2C and 7C and of correlograms in Figs. 3C and 8C, respectively, obtained by activating chain fibers alone (Figs. 2C and 3C) and chain fibers and bag2 together (Figs. 7C and 8C). It is clear that the existence of oscillations and of troughs in the cross-correlogram on both sides of the first peak is very
2831
dependent on the pattern of stimulation and therefore cannot provide proof that the bag2 fiber is activated concomitantly with the chain fibers as proposed by Taylor et al. (1994, 1998). However, if stimulations with low mean frequencies (25 Hz in our experiments) are used, the cross-correlogram obtained during activation of chain fibers (Fig. 4C) is different from that obtained during the concomitant activation of bag2 and chain fibers (Fig. 9C). In the latter case, the peak is rather small and most spikes are uncorrelated with the stimuli. The features of cross-correlograms elicited by Poisson stimulation of chain fibers alone or together with bag2 fibers very much depend not only on the mean stimulus intervals but also on the standard deviation of these intervals, as clearly shown by Figs. 2–9. There is no indication of SD value in Taylor et al. (1998), which suggests that data collected from several stimulations with different parameters were pooled, which makes the interpretation of such correlograms hazardous. If the parameters of stimulation are defined properly and if the activated intrafusal muscle fibers already are identified, the characteristics of a cross-correlogram certainly can be interpreted. However, for the reasons given earlier the reverse is not true. From the characteristics of a cross-correlogram it is not possible to unequivocally identify the type of intrafusal muscle fibers activated by single g static axons. Nearly all the observations of Taylor et al. (1998) were done on one spindle-one axon couples because in the large muscle they used (cat gastrocnemius) gs axons activating more than one spindle were seldom prepared. This difficulty led them to calculate three probabilities: that the bag2 was innervated alone, that the chain fibers were innervated alone, and that the chain and the bag2 fibers were innervated together. Such a calculation initially was done by Celichowski et al. (1994), who also found that the innervation of the intrafusal fibers in individual Peroneus tertius spindles was slightly different from random. This appears to be a general feature of all muscle spindles, possibly related to the number of gs entering the spindle or its separate poles (Banks 1994b). However this feature, on its own, cannot give an indication on the way an axon is distributed to intrafusal muscle fibers in all the other spindles it may supply. Precisely in that study on Peroneus tertius spindles, it was observed that for 35 of 42 gs axons supplying more than three spindles (83%), the distribution varied from one spindle to the other (Celichowski et al. 1994). The distribution of static g axons is most likely not the same in all muscles, a view supported by recent work of EmonetDe´nand et al. (1998) on Peroneus longus spindles, in which most gs axons were observed to activate only one or two spindles. In the longus, whose ratio of the number of static g axons to the number of spindles is much larger than in the tertius (Boyd and Davey 1968), nearly half of the static g axons (45%) were found to be specifically distributed as compared with the 17% of specific axons found in the tertius. In the longus study, a statistical analysis of experimental data based on the binomial distribution (see Emonet-De´nand et al. 1998) had to be used to estimate the number of spindles supplied by individual gs axons and the proportion of gs axons that actually supplied only one spindle, among axons that were observed to activate only one. This analysis made it possible to classify a certain number of those axons as specifically distributed (either to bag2 or to chain fibers). Without such an analysis, axons observed to activate either the bag2 alone or chains alone in
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
2832
J. PETIT, R. W. BANKS, AND Y. LAPORTE
only one spindle cannot be classified as specific because the possibility that they supplied a different intrafusal fiber in another spindle(s) could not be excluded. Possibly in Gastrocnemius there is a fair proportion of specific gs axons as in Peroneus longus, but for the reasons developed in this study, the evidence presented by Taylor et al. (1998) does not convincingly support this view. The authors thank S. de Saint Font for help in the preparation of the manuscript. This work was supported by the Association Franc¸aise contre les Myopathies and the Fondation pour la Recherche Me´dicale. Y. Laporte is an Honorary Professor at Colle`ge de France. Present address: R. W. Banks, Dept. of Biological Sciences, University of Durham, Durham DH1 3LE, UK. Address for reprint requests: J. Petit, L.P.P.A., Colle`ge de France, 11 Place Marcelin Berthelot, 75231 Paris Ce`dex 05, France. Received 13 November 1998; accepted in final form 3 February 1999. REFERENCES BANKS, R. W. The distribution of static g axons in the tenuissimus muscle of the cat. J. Physiol. (Lond.) 442: 489 –512, 1991. BANKS, R. W. The motor innervation of mammalian muscle spindles. Prog. Neurobiol. 43: 323–362, 1994a. BANKS, R. W. Intrafusal motor innervation: a quantitative histological analysis of tenuissimus muscle spindles in the cat. J. Anat. 185: 151–172, 1994b. BANKS, R. W., HARKER, D. W., AND STACEY, M. J. A study of mammalian intrafusal muscle fibers using a combined histochemical and ultrastuctural technique. J. Anat. Lond. 123: 783–786, 1977. BARKER, D., EMONET-D´ENAND, F., LAPORTE, Y., PROSKE, U., AND STACEY, M. J. Morphological identification and intrafusal distribution of the endings of static fusimotor axons in the cat. J. Physiol. (Lond.) 230: 405– 427, 1973. BESSOU, P., LAPORTE, Y., AND PAGES, B. Similitude des effets (statiques ou dynamiques) exerc´es par des fibres fusimotrices uniques sur les terminaisons primaires de plusieurs fuseaux chez le chat. J. Physiol. Paris. 58: 31–39, 1966. BESSOU, P. AND PAGES, B. Cinematographic analysis of contractile events produced in intrafusal muscle fibres by stimulation of static and dynamic fusimotor axons. J. Physiol. (Lond.) 252: 397– 427, 1975. BOYD, I. A. Two types of static g axons in cat muscle spindles. Q. J. Exp. Physiol. 71: 307–327, 1986.
BOYD, I. A. AND DAVEY, M. R. Composition of Peripheral Nerve. London: Livingstone, 1968: BOYD, I. A., MURPHY, P. R., AND MANN, C. The effect of chain fibre ‘‘driving’’ on the length sensitivity of primary sensory endings in the tenuissimus, peroneus tertius and soleus muscles. In: The Muscle Spindle, edited by I. A. Boyd and M. H. Gladden. Macmillan: London, 1985, p. 195–199. BOYD, I. A. AND WARD, J. The diagnosis of nuclear chain intrafusal fibre activity from the nature of group Ia and group II afferent discharge of isolated cat muscle spindles. J. Physiol. (Lond.) 329: 17–18P, 1982. BROWN, M. C. AND BUTLER, R. G. Studies on the site of termination of static and dynamic fusimotor fibres within muscle spindles of the tenuissimus muscle of the cat. J. Physiol. (Lond.) 233: 553–573, 1973. CELICHOWSKI, J., EMONET-D´ENAND, F., LAPORTE, Y., AND PETIT, J. Indirect identification of intrafusal muscle fibres activated by static g axons in peroneus tertius spindles of anaesthetised cats (Abstract). J. Physiol. (Lond.) 467: 198P, 1993. CELICHOWSKI, J., EMONET-D´ENAND, F., LAPORTE, Y., AND PETIT, J. Distribution of static g axons in cat peroneus tertius spindles determined by exclusively physiological criteria. J. Neurophysiol. 71: 722–732, 1994. CROWE, A. AND MATTHEWS, P.B.C. The effects of stimulation of static and dynamic fusimotor fibres on the response to stretching of the primary endings of muscle spindles. J. Physiol. (Lond.) 174: 109 –131, 1964. DICKSON, M., EMONET-D´ENAND, F., GLADDEN, M. H., PETIT, J., AND WARD, J. Incidence of non-driving excitation of Ia afferents using ramp frequency stimulation of static g axons in cat hindlimbs. J. Physiol. (Lond.) 460: 657– 673, 1993. DURBABA, R., TAYLOR, A., RODGERS, J. F., AND FOWLE, A. J. Subclasses of fusimotor action on muscle spindles of the anaesthetised cat revealed by crosscorrelation of firing with random stimulation (Abstract). J. Physiol. (Lond.) 473: 206P, 1993. EMONET-D´ENAND, F., LAPORTE, Y., MATTHEWS, P.B.C., AND PETIT, J. On the subdivision of static and dynamic fusimotor actions on the primary ending of the cat muscle spindle. J. Physiol. (Lond.) 268: 827– 861, 1977. EMONET-D´ENAND, F., LAPORTE, Y., AND PETIT, J. Comparison of static fusimotor innervation in cat peroneus tertius and longus muscles. J. Neurophysiol. 80: 249 –254, 1998. TAYLOR, A., DURBABA, R., AND RODGERS, J. F. Correlation methods in identifying intrafusal muscle fibre activity. In: Alpha and Gamma Motor Systems, edited by A. Taylor, M. H. Gladden, and R. Durbaba. Plenum Press: New York, 1994, p. 280 –283. TAYLOR, A., ELLAWAY, P. H., AND DURBABA, R. Physiological signs of the activation of bag2 and chain intrafusal muscle fibers of gastrocnemius muscle spindles in the cat. J. Neurophysiol. 80: 130 –142, 1998. WAND, P. AND SCHWARTZ, M. Two types of cat static fusimotor neurones under separate central control? Neurosci. Lett. 58: 145–149, 1985.
Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (191.101.064.103) on January 11, 2018. Copyright © 1999 American Physiological Society. All rights reserved.
