Laboratoire de Physiologie de la Perception et de l'Action. Collège de France, 75005 Paris, France
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ABSTRACT |
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Petit, Julien,
Robert W. Banks, and
Yves Laporte.
Testing the classification of static axons using different patterns
of random stimulation. 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
axons was tested in Peroneus tertius muscle spindles of
anesthetized cats. Three patterns of random stimulation with different
values of mean intervals [20 ± 4.47, 30 ± 8.94, and
40 ± 8.94 (SD) ms] were used. Single static
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
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
axons cannot be used for unequivocally identifying the type(s) of
intrafusal muscle fiber these axons supply.
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INTRODUCTION |
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Histophysiological studies as well as direct
observation of isolated spindles have shown that individual static axons (
s) 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
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-Dénand 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
neuron, some differential distribution to
bag2 and chain fibers according to axonal conduction
velocity is 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
s
axons. With these tests, they studied the distribution of single
s
axons to the intrafusal muscle fibers of all spindles supplied by each
axon in two cat muscles with different
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-Dénand 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
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
s 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.
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METHODS |
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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 axons (Celichowski
et al. 1994
). Static
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-Dénand et al. 1977
).
Identification of intrafusal muscle fibers activated by the
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 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:
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Static 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.
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RESULTS |
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The action of 10 static 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
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 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
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).
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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 discharge 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 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 ± 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.
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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 = 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).
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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 ± 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.
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It should be noted that the delay of the peak in the cross-correlogram
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 Fig.
1B, ~50 Hz (Poisson stimulation) for Fig. 2C,
and ~25 Hz (Poisson stimulation) for Fig. 4C. The peak in
the cross-correlogram 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
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).
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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 axon, the intrafusal distribution of which was identified by
the Celichowski et al. (1994)
tests as supplying both bag2 and chain fibers, are presented in Fig.
6. The cross-correlogram (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
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.
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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
s 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-correlogram, there can be no subsequent oscillations due to the autocorrelogram).
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We also used a stimulation pattern with a mean interval of 20 ms but with a wide SD (Fig. 8). The afferent-discharge-interval histogram (Fig. 8B) was different from the stimulus-interval 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.
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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.
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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 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 axon.
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Responses of a primary ending when the bag2 fiber alone is activated
The identification by Celichowski et al.
(1994) tests of a
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 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.
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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.
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DISCUSSION |
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The main finding of this study is that the characteristics of
cross-correlograms between a random Poisson stimulation of single static 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 identify, with a reasonably high
degree of confidence, the types of intrafusal muscle fiber activated by
single
s 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 Pagès 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 cross-correlogram (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 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 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 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)
s 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
s 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
s axons supplying more than three spindles (83%),
the distribution varied from one spindle to the other
(Celichowski et al. 1994
).
The distribution of static axons is most likely not the same in all
muscles, a view supported by recent work of Emonet-Dénand et al. (1998)
on Peroneus longus spindles, in which most
s
axons were observed to activate only one or two spindles. In the
longus, whose ratio of the number of static
axons to the number of
spindles is much larger than in the tertius (Boyd and Davey
1968
), nearly half of the static
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-Dénand et al. 1998
) had to be used to
estimate the number of spindles supplied by individual
s axons and
the proportion of
s 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 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 s
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.
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ACKNOWLEDGMENTS |
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The authors thank S. de Saint Font for help in the preparation of the manuscript.
This work was supported by the Association Française contre les Myopathies and the Fondation pour la Recherche Médicale. Y. Laporte is an Honorary Professor at Collège de France.
Present address: R. W. Banks, Dept. of Biological Sciences, University of Durham, Durham DH1 3LE, UK.
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FOOTNOTES |
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Address for reprint requests: J. Petit, L.P.P.A., Collège de France, 11 Place Marcelin Berthelot, 75231 Paris Cèdex 05, France.
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.
Received 13 November 1998; accepted in final form 3 February 1999.
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REFERENCES |
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