Departments of 1Surgery (Otolaryngology-Head and Neck Surgery) and 2Neurobiology, Pharmacology and Physiology, University of Chicago, Chicago, Illinois 60637
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ABSTRACT |
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Brichta, Alan M. and
Jay M. Goldberg.
Responses to Efferent Activation and Excitatory
Response-Intensity Relations of Turtle Posterior-Crista
Afferents.
J. Neurophysiol. 83: 1224-1242, 2000.
Multivariate
statistical formulas were used to infer the morphological type and
longitudinal position of extracellularly recorded afferents. Efferent
fibers were stimulated electrically in the nerve branch interconnecting
the anterior and posterior VIIIth nerves. Responses of bouton (B) units
depended on their inferred position: BP units (near the planum
semilunatum) showed small excitatory responses; BT units (near the
torus) were inhibited; BM units (in an intermediate position) had a
mixed response, including an initial inhibition and a delayed
excitation. Calyx-bearing (CD-high) units with an appreciable
background discharge showed large per-train excitatory responses
followed by smaller post-train responses that could outlast the shock
train by 100 s. Excitatory responses were smaller in calyx-bearing
(CD-low) units having little or no background activity than in CD-high
units. Excitatory response-intensity functions, derived from the
discharge during 2-s angular-velocity ramps varying in intensity, were
fit by empirical functions that gave estimates of the maximal response
(rMAX), a threshold velocity
(vT), and the velocity producing a
half-maximal response (v1/2). Linear gain is
equal to rMAX/vS,
vS = v1/2 vT.
vS provides a measure of the velocity range
over which the response is nearly linear. For B units,
rMAX declines by as much as twofold over the
2-s ramp, whereas for CD units, rMAX
increases by 15% during the same time period. At the end of the ramp,
rMAX is on average twice as high in CD as in
B units. Thresholds are negligible in most spontaneously active units,
including almost all B and CD-high units. Silent CD-low units typically
have thresholds of 10-100 deg/s. BT units have very high linear gains
and vS < 10 deg/s. Linear gains are
considerably lower in BP units and vS > 150 deg/s. CD-high units have intermediate gains and near 100 deg/s
vS values. CD-low units have low gains and
vS values ranging from 150 to more than 300 deg/s. The results suggest that BT units are designed to measure the
small head movements involved in postural control, whereas BP and CD
units are more appropriate for monitoring large volitional head
movements. The former units are silenced by efferent activation,
whereas the latter units are excited. This suggests that the efferent
system switches the turtle posterior crista from a "postural" to a
"volitional" mode.
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INTRODUCTION |
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In the preceding paper (Brichta and
Goldberg 2000), we characterized the discharge properties of
labeled bouton, calyx, and dimorphic afferents in the turtle posterior
crista, including their discharge regularity and their responses to
0.3-Hz sinusoidal head rotations. The behavior of bouton (B) units
varied with their longitudinal position in each hemicrista: units
located near the planum were regularly discharging and had small gains
and small phase leads re angular head velocity; other units, located
near the torus, were irregular, and had large gains and large phase leads; and still other units, found in midportions of the hemicrista, had intermediate properties. Because calyx and dimorphic units had
similar discharge properties, they were placed into a single calyx-bearing (CD) category. CD units have an irregular discharge resembling bouton units near the torus, but the gains and phases of the
CD units are similar to those of bouton units located in midportions of
the hemicrista. Almost all B units had an appreciable background
discharge as did many CD units. Other CD units could be silent or
nearly silent at rest and many of their other discharge properties were
distinctive. From these data we developed multivariate statistical
formulas that reliably distinguished between B and CD units and
accurately predicted their locations within a hemicrista.
In the present paper, we used these formulas to classify
extracellularly recorded units and then studied two other aspects of
their discharge. One of these was the response to electrical stimulation of efferent fibers. In mammals (Goldberg and
Fernández 1980; McCue and Guinan 1994
) and
in the toadfish (Boyle and Highstein 1990
;
Highstein and Baker 1985
), efferent activation excites
afferents. More heterogeneous responses are observed in the posterior
crista (Bernard et al. 1985
; Rossi et al.
1980
; Sugai et al. 1991
) and other vestibular
organs of anurans (Sugai et al. 1991
). In the present
study, heterogeneous responses were found in afferents innervating the
turtle posterior crista. As in anurans, some turtle afferents are
excited by efferent activation, whereas others are inhibited. In an
attempt to understand the functional significance of the heterogeneity,
we compared efferent responses in the several afferent groups.
The second discharge property studied was the relation between
excitatory response magnitude and stimulus intensity. We became interested in response-intensity relations for three reasons. First,
there is an 200-fold variation in the linear (near-threshold) gains
of individual afferents (Brichta and Goldberg 2000
). The variation is 20 times larger than seen in mammals (Baird et al. 1988
; Lysakowski et al. 1995
). One notion is
that the most sensitive fibers monitor small head movements and that
progressively less sensitive fibers monitor progressively larger head
movements. To evaluate such a recruitment scheme, we needed to
determine how the sensitivity of afferent groups was related to their
maximal response rates and the stimulus ranges over which their sensory coding was linear. Second, it has been suggested that one function of
type I hair cells and calyx endings is to increase the linearity of
vestibular transduction (Baird et al. 1988
;
Goldberg 1996
) To test the suggestion, we compared
response-intensity functions obtained from B and CD units. The third
reason concerned our efferent results. A comparison of the linear
stimulus ranges and efferent responses of individual afferents led to
the hypothesis that efferent activation switches the turtle posterior
crista from a "postural" to a "volitional" mode.
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METHODS |
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Tissue preparation
Methods were similar to those described in previous papers
(Brichta and Goldberg 1998a, 2000
). In brief, we
used male and female red-eared turtles [Pseudemys (Trachemys)
scripta elegans] weighing 200-400 g and having carapace
lengths of 11-14 cm. After decapitation, the head was sectioned in the
midsagittal plane, and one of the two half-brains was blocked at the
levels of the trigeminal nerve rostrally and the glossopharyngeal nerve
caudally. In most instances, the left half-head was chosen. Pivoting
the brain stem exposed the dorsal surface of the posterior division of
the VIIIth nerve, including the fibers innervating the posterior crista. The isolated half-head was placed on its lateral surface in a
recording chamber that was bolted to the superstructure of a
computer-controlled rotating device. Extracellular recordings were made
with glass micropipettes filled with 3 mM NaCl and having impedances of
20-40 M
.
Physiological testing
As described elsewhere (Brichta and Goldberg
2000), rotations were used to identify posterior-crista (PC)
fibers. For all PC units, a 5-s sample of background discharge was
recorded, as was the response to a 0.3-Hz sinusoidal head rotation. The
coefficient of variation (cv*), normalized to a standard mean interval
of 50 ms, provided a measure of discharge regularity (Brichta
and Goldberg 2000
; Goldberg et al. 1984
). A
Fourier analysis was used to extract the fundamental components of the
response and the angular-velocity signal from the servo's tachometer.
Gains were calculated as the ratio of the fundamental components of the
response (in spikes/s) and the angular velocity (in deg/s). Phases were calculated as the difference (in deg) between the response phase and
the angular-velocity phase; positive phases correspond to response
phase leads. During testing, the posterior canal was tilted 45° from
the horizontal plane of rotation. As a result, reported gains should be
multiplied by 1/cos(45°) =
to get their maximal
values. Phases are unaffected (Brichta and Goldberg
1998a
).
Classification of units
Extracellularly recorded units were assigned to the CD or B
categories based on their quadratic discriminant scores, g
(Brichta and Goldberg 2000). The coefficients of the
discriminant formulas were set so a unit with a positive score was
assigned to the B group, whereas one with a negative score was assigned
to the CD group. A z score, z = g/SD, was obtained where SD is the pooled intragroup
standard deviation obtained from labeled B and CD units. From the
z score, a misclassification probability
(pM) was calculated based on the
assumption that B and CD units were equally probable (see
Brichta and Goldberg 2000
, Fig. 7D). In
addition, a linear regression was used to infer the normalized location
(
) of each afferent within a hemicrista (see Brichta and
Goldberg 2000
, Fig. 9).
Based on their values, B units were assigned to one of three
categories: BP (near the planum,
> 0.8), BM (midportions of
the hemicrista, 0.4
0.8), or BT (
< 0.4).
CD units were assigned to CD-high and CD-low categories depending on
their having background discharge rates >5 and <5 spike/s, respectively.
Efferent stimulation
All efferent fibers destined for the posterior crista travel in
the nerve bundle connecting the anterior and posterior branches of the
VIIIth nerve (Fayyazuddin et al. 1991) (Fig.
1A). A Teflon-coated chlorided
silver wire with a 0.5-mm exposed tip was placed on the nerve bundle. A
second Ag-AgCl electrode was placed on the skull. Electrical stimuli
consisted of trains of 100-µs constant-current shocks delivered from
a World Precision Instrument 1850A stimulus isolator to the two
electrodes. The first electrode was the cathode. To record afferent
activity during repetitive shocks, the associated artifacts were
canceled by a computer program written in Microsoft C5.0 for a PC
computer. On a first pass, an average shock artifact was computed. On
subsequent passes, whenever a shock was issued by the program, an
inverted version of the average was produced on-line by a DAC and was
summed in an operational-amplifier with the raw record. The procedure
reduced the artifact by
40 dB (Fig. 1B). The program also
collected voltages and spike times and stored them on disk, provided
on-line displays, and generated voltages to control devices.
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Response-intensity relations
These were obtained from the discharge during 2-s ramps of angular velocity that were the leading edges (up ramps) of velocity trapezoids. Only excitatory ramps were analyzed. For the left half-head, which was used most often, the excitatory direction is counterclockwise (as viewed from above). Maximum ramp amplitudes were 320 deg/s in early experiments and 640 deg/s in later experiments. To achieve the larger velocities, the chair first was rotated in the inhibitory direction to 320 deg/s and kept there until unit discharge returned to its background value. Maximal (640 deg/s) rotations reached 320 deg/s in the excitatory direction at the end of the ramp. Typically, responses were obtained as amplitude was increased in 6-dB steps, usually starting at 10 or 20 deg/s. If the maximum amplitude was reached while the unit remained isolated, a descending series was done, starting 3 dB below maximum and continuing in 6-db steps. At the lowest intensities, responses to several identical ramps sometimes were averaged.
Rates were calculated for each 0.5 s of the ramp and responses
(actual rate minus background rate) were plotted against stimulus velocity. Responses were fit by the formula
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(1) |
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Estimates of rMAX, vT, and vS were obtained by nonlinear regression (Levenberg-Marquardt method). If the estimated value of vT was positive and significantly different from zero (P < 0.05), these values of the three parameters were used. Otherwise, a second regression with vT constrained to zero provided new values of rMAX and vS. Reliable estimates of the parameters required that the maximum velocity, vMAX, exceed vS. So as not to bias the samples toward low values of vS, we did a post hoc analysis to determine an adequate vMAX that would exceed vS for all units in each class. For the last 0.5 s of the 2-s ramp, values of vMAX (in deg/s) for the various unit categories are followed (in parentheses) by the number of qualifying units over the total number: BP, 450 (8/17); BM, 160 (6/7); BT, 40 (17/17); CD-high, 320 (31/32); and CD-low, 640 (9/24). Linear gains and thresholds could be estimated even when vMAX < vS.
In analyzing how response-intensity functions change with elapsed time
during the ramp, it became important to predict how response dynamics
would affect gV(0). To accomplish this, we
used a simple linear model of canal dynamics
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(2) |
Unless otherwise stated, means are presented ±SE.
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RESULTS |
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Responses to electrical activation of efferent fibers
For every unit, we first obtained a sample of its background
discharge and a response to 0.3-Hz sinusoidal head rotations. The
discharge regularity and rotational responses were used to assign the
unit to the B or CD categories and to infer its normalized location
() within a hemicrista (see Brichta and Goldberg
2000
);
= 0 corresponds to the torus and
= 1 to the planum. The central zone of the hemicrista extends from
= 0.4 to
= 0.8. On the basis of their presumed locations, B
units were called BT, BM, or BP (see METHODS for details).
CD units were distinguished into those with background discharges >5
spikes/s (CD-high) or <5 spikes/s (CD-low). Efferent responses were
collected for a standard train consisting of 20 shocks delivered at a
rate of 200/s. Discernible responses were seen at shock strengths of
10-40 µA. Except where noted, responses were obtained with shock
amplitudes two to four times threshold and were found to be nearly
maximal. Only responses obtained in the absence of head rotations were
studied in any detail.
Units differed in their responses to the standard efferent shock train. This was so even in units obtained in a single preparation. Responses from eight units recorded from one half-head are seen in Fig. 2; the units are presented in the order in which they were encountered. Six of the units (Fig. 2, A, B, D, E, G, and H) are excited, whereas two show a mixed response including an inhibition during the shock train and a post-train excitation (Fig. 2, C and F). Excitatory responses can be small (Fig. 2, B, E, and H) or large (Fig. 2, A, D, and G). Although not seen in this particular preparation, in some units an inhibitory response during the shock train was not followed by a post-train excitation (see, for example, Fig. 7, A-C).
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Relation between unit type and efferent response
The efferent responses shown by units are related to their
head-rotation responses and, by inference, to their morphological types
and longitudinal positions in the crista. Figure
3 illustrates the relation between the
cv*, rotational gain, and rotational phase for units distinguished by
their efferent responses. Included in the figure are discriminant
curves separating units into B and CD categories (see Brichta
and Goldberg 2000, Fig. 7). Table 1 presents the mean locations for B and
CD units showing different kinds of efferent responses.
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Both B and CD units showed excitatory efferent responses (Fig. 3,
A and B). On the basis of their regular
discharge, small rotational gains, and phases, the excited B units were
categorized as BP (and less frequently as BM) units. Excitatory
responses, measured during the first 100 ms after the standard efferent
shock train, were considerably smaller in BP and BM units than in CD units. Mean excitatory responses were 9.9 ± 2.4 spikes/s for 22 B
units as compared with 28.8 ± 1.8 spikes/s for 65 CD units. One
of the B units was probably misclassified. It had a z score of 0.097 and a misclassification probability,
pM > 0.4. In addition, the unit had a
large excitatory efferent response of 57 spikes/s, which was unlikely
to have been drawn from the same population as the responses seen in
the other B units (P 0.001). Removing the atypical unit
reduced the mean excitatory response of the B units to 7.6 ± 0.9 spikes/s.
There was a difference in excitatory-response size between CD-high units (30.1 ± 2.0 spikes/s, n = 58) and CD-low units (17.6 ± 2.1 spikes/s, n = 7). The difference between the two kinds of CD units may be more substantial than indicated by these statistics because they were compiled only for CD-low units with definite efferent responses. In our best preparations, almost all CD-high units showed large excitatory responses, whereas many CD-low units were unresponsive. The lack of responsiveness of CD-low units was not merely due to their being silent. Many CD-low units with background rates of 1-5 spikes/s were unresponsive, and many silent CD-low units remained unresponsive in the presence of activity produced by excitatory rotations.
Inhibited units, whether their responses were purely inhibitory or inhibitory-excitatory, had a background discharge and this was abolished during the efferent shock train (Fig. 2, C and F; see Fig. 7). Most (50/57) inhibited afferents were B units (Table 1). Of the 75 CD units studied, 7 (9.3%) were inhibited during the shock train; each of the 7 inhibited units had a misclassification probability, pM > 0.10, consistent with the possibility that they were actually B units. From their irregular discharge, large rotational gains, and phases, inhibited B units were classified most often as BT units and less often as BM units. Units showing purely inhibitory responses had mean longitudinal positions nearer the torus than did those showing inhibitory-excitatory responses and both groups were nearer the torus than were excited B units (Table 1). There was only a small degree of overlap in the presumed longitudinal positions of B units having inhibitory, inhibitory-excitatory, and excitatory efferent responses (Fig. 4).
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Excited units
Responses are shown for six excited afferents in Fig. 5, including three B units with small responses (<15 spikes/s, Fig. 5, A-C) and three CD-high units with large responses (>30 spikes/s, Fig. 5, E-G). Responses begin shortly after the start of the shock train and persist for 500-1,000 ms after the train is terminated. In most excited units, the response shows a single peak, occurring early in the post-train period. In a few CD units, the excitatory response consists of two peaks, one during the shock train and the other in the post-train period (see, for example, Fig. 5H). Units with two peaks were not placed in a separate category.
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The presence of two peaks suggests that per-train and posttrain excitation might reflect separate mechanisms. Figure 5D illustrates a variant of the typical excitatory response that also suggests the presence of a distinct posttrain excitation. Here there is no significant response during the shock train, but an excitatory response is seen in the post-train period. Such "delayed excitation" was observed in two B and three CD units. The two B units had near-zero z scores suggesting that they might be CD units. Among the three CD units with delayed excitation, one was highly unlikely to have been misclassified (pM < 0.001).
Longer (10-s) shock trains were used in several CD units. In some of them, shock frequency was varied. Results for one such unit are presented in Fig. 6, left. Per-stimulus responses are seen down to 20 shocks/s. At higher rates (Fig. 6, A and B), there is a response decline during the shock train and a posttrain undershoot. This is followed by a slow response of 10-15 spikes/s that takes 30 s to reach its peak and almost another 100 s to return to the baseline. A slow response is seen down to 10 shocks/s, a rate at which fast, per-stimulus responses are no longer observed. Most (26/29) CD-high units tested with 10-s trains had slow responses, as did 6/9 CD-low units. As was the case for fast (per-stimulus) responses, slow (poststimulus) responses were generally larger in CD-high than in CD-low units. Both fast and slow excitatory responses commonly were seen at shock rates as low as 20/s and occasionally were observed down to 5/s. In all cases, slow responses outlasted the shock train by 50-100 s. The peak post-train response could occur immediately after the train or, as exemplified by Fig. 6 (left), be delayed.
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Slow responses also were seen in two of three BP units tested with 10-s shock trains. In the two positive cases, responses peaked immediately after the train and had durations of 20-30 s, shorter than those of CD units.
Inhibited units
Responses of three units with purely inhibitory responses are shown in Fig. 7, A-C. For the first two units, the inhibition outlasts the shock train by 2,000 ms. Post-train inhibition is shortened to 500 ms in the third unit and to 150-250 ms in three other units in which a per-train inhibition is followed by a post-train excitation (Fig. 7, D-F).
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A simple interpretation of the post-train excitation is that it represents an adaptive rebound from the preceding inhibition. We now present evidence that the excitation cannot be explained in this way. The mixed inhibitory-excitatory response of a BT unit to our standard efferent shock train is seen in Fig. 7F. Longer (10-s) shock trains varying in shock rate were studied in the same unit (Fig. 8). For rates of 100/s and 50/s (Fig. 8, A and B), inhibition persists throughout the shock train and is immediately followed by a post-train excitatory response of 60 spikes/s, which declines to background rates over the next 20-30 s. At 20 shocks/s, inhibition lasts for 2.5 s and is replaced by a small (3 spikes/s) excitatory response (Fig. 8C). Even though inhibition has ceased 7.5 s previously, there is still a large post-train excitation of 40 spikes/s lasting 10 s. It would be even more difficult to ascribe the post-train excitation seen with 10 shocks/s to the consequences of inhibition. Here, the small per-train response consists of a gradually increasing excitation without any sign of a net inhibition (Fig. 8D). Despite this, there is a 15 spikes/s post-train excitation.
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An alternative explanation for the post-train excitation would envision that each shock evokes both an excitatory and an inhibitory process (see DISCUSSION). The two processes could arise from the convergence of separate excitatory and inhibitory inputs or could represent separate processes in the hair cells and/or afferent fiber triggered by activity in individual efferent fibers. Were separate inputs involved, one might expect that the balance between excitation and inhibition would be altered as shock intensity was raised and as successive inputs were recruited. Such an effect was not seen in three units in which it was sought. The unit shown in Fig. 8 illustrates the point. Shocks were delivered at 20/s, while current strength was varied between a near-threshold 12 µA (Fig. 8H) and 50 µA (Fig. 8E). Even though there was a large variation in response amplitude, the same response pattern was seen throughout the intensity range. During the shock train, there was a relatively brief inhibition, followed by a more prolonged, but weaker excitation. This was followed by a post-train excitation.
It might be expected that units showing purely inhibitory efferent responses would show relatively simple responses as shock frequency is lowered. Consider the unit (Fig. 7B) whose response to the standard efferent shock train showed a prolonged inhibition with only a hint of a post-train excitation. The unit was tested with 10-s shock trains (Fig. 6, E-H). As shock rate was varied, only inhibition was seen during the train. Note that there is still a clear inhibitory response at a shock rate of 5/s. A post-train excitation is seen. It differs from that observed in units with mixed (inhibitory-excitatory) responses in being smaller, of shorter duration, and in reflecting the magnitude and duration of the preceding inhibition. These are properties that would be expected of a postinhibitory rebound.
Response-intensity functions
As in our efferent studies, the background discharge and responses to 0.3-Hz head rotations were used to classify afferents into several classes. After this preliminary testing, response-intensity functions were determined for each of the four consecutive 0.5-s intervals (designated t1-t4) in 2-s velocity ramps.
General features of the functions and their fit by Eq. 1 are illustrated in Fig. 9, A and B, based on t4 data from a BP unit. The function is plotted in both semilogarithmic (Fig. 9A) and double logarithmic coordinates (Fig. 9B). Equation 1 provides an excellent fit; rMAX is denoted by the thick horizontal lines and v1/2 = vS by the thick vertical lines. The function in semilogarithmic coordinates is sigmoidal with an inflection point at vS. Departures from linearity are better illustrated in the double-logarithmic plot. Because the threshold is zero, the low-intensity points in Fig. 9B are fit by a unity-slope (- - -) line. Data for a BM unit with a nonzero threshold is seen in Fig. 9, C and D. As a result of the nonzero threshold, the double-logarithmic plot (Fig. 9D) is concave downward even near threshold.
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Figure 10 includes results for four
units illustrative of the relations for the several unit classes. In
Fig. 10, A-D, response rates are plotted as a function of
time within the ramp and are compared with linear extrapolations, which
for each unit were calculated from the expressions,
gV(0)(v vT), separately calculated for the
four periods,
t1-t4.
Companion response-intensity functions are presented for the four
periods (Fig. 10, A1-D1). Response-intensity functions for
the t4 period are plotted for units of
each particular class in Fig. 11 and
mean values of the t4 and (when
available) the t1 parameters of
Eq. 1 are included in Table 2.
Unless otherwise stated, parameters cited in the text are for the
t4 period. The exception is
vT, which was more accurately
estimated from the lower velocities obtaining during
t1.
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BP units
These units have modest values of
rMAX, combined with small values of
linear (near-threshold) gain, gV(0). As a
result, vS is relatively large,
approaching 200 deg/s (Table 2). Each of the 17 BP units in the sample
had an appreciable background discharge and only one of them had a
statistically significant t1
threshold. Based on their responses to sinusoidal head rotations
(Brichta and Goldberg 2000, Fig. 14), BP units can be
described as approximately velocity sensitive with k
0 in Eq. 2. Reflecting these response dynamics, linear gains
re head velocity change only slightly with elapsed time during velocity
ramps. The mean (±SE) ratio between the
t1 and
t4 linear gains was 0.99 ± 0.06 (
, Fig. 14A).
The large values of vS imply that the responses of BP units remain approximately linear for large stimulus amplitudes. In addition, the units are nearly velocity sensitive. These two features can be seen in the ramp responses of an individual BP unit (Fig. 10A). For the ramp to a final velocity of 40 deg/s, responses increase almost linearly with time, more or less paralleling angular velocity. The responses to the 80 and 160 deg/s ramps show a partial saturation that becomes prominent for t3 and t4. As the final velocity reaches 320 or 640 deg/s, the response is linear only during t1 and reaches a nearly constant value of 70-80 spikes/s during t2-t4.
The t4 response-intensity functions for BP units show large linear stimulus ranges, with vS values typically being between 120 and 240 deg/s (Fig. 11, C and F).
BT units
Linear (near-threshold) gains of BT units are much higher than
those of BP units and are associated with small values of
rMAX and especially small values of
vS (Table 2). All 17 BT units had
background rates >5 spikes/s; only 4 of them had a statistically significant t1 threshold, the largest
of which was 0.24 deg/s. From their responses to sinusoidal head
rotations between 0.1 and 1 Hz, BT units can be approximated by
Eq. 2 with a fractional exponent, k 0.7 (Brichta and Goldberg 2000
, Fig. 14), closer to
acceleration (k = 1) than to velocity
(k = 0). As a consequence of the partial acceleration
sensitivity of BT units, responses to small-amplitude (1 deg/s) ramps
reach nearly constant values from t2
onward (Fig. 10B) even though head velocity continues to grow. As a result, there is a time-dependent decrease in
gV(0). The mean ratio of the linear
velocity gains for t1 and
t4 is 2.9 ± 0.4 (n = 17)
(
, Fig. 14A).
Because of their small vS values, BT units have very small linear stimulus ranges. This can be seen in the responses of the unit in Fig. 10B. Responses are nearly linear for a ramp with a final velocity of 1 deg/s. For ramps to 5 deg/s, responses are close to linear for the first 0.5 s but then become saturated. At higher intensities (20-320 deg/s), even the early response falls short of linearity. rMAX declines with time, from 134 spikes/s for t1 to 57 spikes/s for t4 (Fig. 10B1).
Response-intensity functions for several BT units are presented in Fig. 11A. Typically, responses become nonlinear for head velocities of 5 deg/s and saturate between 10 and 50 deg/s.
BM units
There were only a few BM units and a disproportionate number of them (4/7) had low background rates (<5 spikes/s). Two of the low-rate units had nonzero t1 thresholds. rMAX and vS values for BM units were intermediate between those for BT and BP units (Table 2 and Fig. 11B). Misclassification probabilities (pM) are high, ranging from 0.10 to 0.49 and suggesting that some of the units may have been misclassified.
CD units
Linear (near-threshold) gains are intermediate between those of BT
and BP units (Table 2). vS values
overlap those of BM and BP units and are considerably higher in CD-low
than in CD-high units. CD units have distinctively high
t4
rMAX values, 1.5 to 3 times those of B
units. Correlated with the difference in their background rates, 21/24
CD-low units, but only 1/32 CD-high units had statistically significant
nonzero t1 thresholds. Thresholds of
five CD-low units were so high that they did not respond or only
responded at the very highest intensity during
t1. For this reason, we could not
compute a t1 threshold or linear gain.
These five "very insensitive" units were compared with other CD-low units during t4. Thresholds ranged
from 37 to 102°/s for the five units (Fig.
12) and from 0 to 67°/s for the other
19 CD-low units. In addition to their high-thresholds, the very
insensitive CD-low units had distinctively low linear gains, with a
mean (in spikes · s1/deg · s
1) of 0.37 ± 0.11 as compared with
1.21 ± 0.15 for the other CD-low units and 0.67 ± 0.09 for
BP units (Fig. 12).
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Responses of individual CD units are illustrated in Fig. 10,
C and D. Time profiles of responses to
low-velocity ramps fall between those of BP and BT units, consistent
with CD response dynamics being between those of the other two groups
(Brichta and Goldberg 2000, Fig. 15). Unlike the
responses of BT units, those of CD units continue to grow during
velocity ramps. At the same time, and unlike the situation in BP units,
the increase falls short of the linear growth in stimulus velocity.
Response-intensity curves for t4 are shown for several CD-high (Fig. 11, D and F) and CD-low units (Fig. 11, E and F). As can be seen in Table 2, CD-low units have vS values during t4 that are higher than those of BP units and considerably higher than those of CD-high units. None of the aforementioned very insensitive units were tested with velocities that allowed us to estimate vS or rMAX, so they are not included in Fig. 11, E and F, or Table 2. As can be seen in Fig. 12, responses of the very insensitive units remain approximately linear to 280 deg/s, the highest velocity tested in them. The figure also includes the mean response-intensity functions for BP and CD-low groups, other groups with large values of vS. Clearly, the very insensitive fibers have smaller gains and considerably larger linear stimulus ranges than either of the other groups.
Changes in response-intensity functions with elapsed time
Response-intensity functions are shown in Fig. 10, A1-D1, for the four time periods, t1-t4. The functions for the BP unit at different times are almost superimposable (Fig. 10A1). In contrast, BT functions are shifted both horizontally and vertically with elapsed time (Fig. 10B1). CD units show horizontal shifts larger than those of BP units and smaller than those of BT units (Fig. 10, C1 and D1). Vertical shifts are not evident in CD units. In this section, we consider how time-related changes in response-intensity functions are affected by the choice of stimulus dimensions and by time variations in each unit's rMAX values.
There are three conditions required for response-intensity functions to
be superimposed as time progresses. First, the stimulus dimension,
x, has to be chosen so that the linear (near-threshold) gain, gx(0,t) = x(0), remains constant with time
(Fig. 13). The other two conditions are
that the threshold,
xT(t) =
T, measured in the x
stimulus dimension, and the maximal response,
rMAX(t) =
MAX, are both time invariant. The
constancy of
x(0) and
T assures the superimposition of the
linear (near-threshold) part of the function. In a similar way, the
constancy of
MAX and
x(0) assures the time invariance of
S =
MAX/
x(0). Finally, the constancy of
MAX
assures the time independence of the high-intensity portion of the
function. The entire function, when stated in terms of x, is
r(t,x) =
MAX(x
T)/[
S + (x
T)] and is
time invariant.
|
To examine whether these conditions held, we first determined that the
ratio between
gV(t1)
and
gV(t4)
reflected response dynamics, in particular, the transfer function,
HV (Eq. 2). Figure 14A plots the
gV ratio versus , the phase of the
response to 0.3-Hz rotational sinusoids. A semilogarithmic regression
provided a good fit (
, r = 0.83, n = 92) and was statistically indistinguishable from the relation predicted
from Eq. 2 (- - -). These results show that the transfer
function is sufficiently accurate to predict salient features of the
ramp response (see also Brichta and Goldberg 1998a
). The
conclusion is important because calculation of the appropriate stimulus
dimension is more easily done in the frequency domain rather than in
the time domain.1
|
For the response-intensity functions to be superimposable also requires that rMAX be independent of time. The condition is met only approximately by CD units (Fig. 14C). For these units, rMAX increases by 10-15% between t1 and t2 and then remains almost constant for the remainder of the ramp. An even larger discrepancy in the opposite direction is seen in BT units, where there is a twofold decrease in rMAX between t1 and t4, with most of the decrease occurring between t1 and t2 (Fig. 14B). Although rMAX for t1 could not be calculated for most other B units, for several of them we could calculate values for t2-t4. A decline in rMAX between t2 and t4 was seen in BP and BM, as well as BT, units. The ratio between the rMAX values for t4 and t2 for eight BP and BM units had a mean of 0.76 ± 0.08, compared with 0.70 ± 0.02 for 17 BT units. Both ratios are significantly different from unity (2-sided t-tests, P < 0.01) but not from each other.
Figure 15 depicts how response-intensity functions change with elapsed time for BP, BT, and CD-high groups. In the top row, the stimulus dimension is head velocity and the functions compare favorably with those for individual units (Fig. 10, A1-D1). On the bottom, the stimulus dimension appropriate to each kind of unit is used. Because the dimension was chosen so that the linear gains for the two times coincide, the low-intensity parts of the functions superimpose. The high-intensity portions diverge reflecting time-dependent changes in rMAX. So for BP and BT units, the high-intensity responses are higher for t1 than for t4. For CD-high units, there is a smaller effect in the opposite direction.
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DISCUSSION |
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Relation between sensory-coding and efferent-response properties
In mammalian vestibular organs (Goldberg and
Fernández 1980; McCue and Guinan 1994
) and
in the toadfish horizontal crista (Boyle and Highstein
1990
), efferent activation predominantly excites afferents.
More heterogeneous efferent responses are seen in the posterior crista
(Bernard et al. 1985
; Rossi and Martini 1991
; Rossi et al. 1980
; Sugai et al.
1991
) and other anuran vestibular organs (Sugai et al.
1991
). Reminiscent of the latter studies, some units in the
turtle posterior crista are excited, while others are inhibited when
efferent axons are stimulated. Furthermore units differing in the
polarity and magnitude of their efferent responses have distinctive
sensory coding properties. Using multivariate statistical formulas
(Brichta and Goldberg 2000
), we have been able to
distinguish extracellularly recorded units into B and CD categories, to
estimate the longitudinal position of either kind of unit in a
hemicrista and to relate the kind and location of an afferent with its
response to efferent activation.
In the turtle posterior crista, B units with small excitatory efferent responses are located near the planum and are regularly discharging, have small rotational gains, and near-zero rotational phases. B units with large inhibitory efferent responses are found near the torus and are irregularly discharging, have large rotational gains, and large phase leads. Still other B units have mixed efferent responses, consisting of an initial inhibition followed by an excitation. The sensory coding properties and inferred longitudinal positions of the units with mixed responses are intermediate between those of the excited and inhibited B units. Among CD units, those with an appreciable background discharge (CD-high units) have large excitatory efferent responses, whereas those with little or no resting activity (CD-low units) have smaller excitatory efferent responses or no efferent responses at all.
We now compare our findings concerning B units with those in anamniotes
(fish and amphibians), which lack CD units. B units located near the
planum (toadfish: Boyle et al. 1991; frog:
Honrubia et al. 1989
; Myers and Lewis
1990
; turtle: Brichta and Goldberg 2000
) have
excitatory efferent responses (toadfish: Boyle and Highstein
1990
; turtle: present study). In all species studied, such
units have a regular discharge together with low rotational gains and
phases. Efferent responses in these units are usually small; this may
explain why most regular fibers in anurans were described as
nonresponsive (Sugai et al. 1991
). B afferents located nearer the center of the crista or isthmus have higher rotational gains
and phases (toadfish: Boyle et al. 1991
; anurans:
Honrubia et al. 1989
; Myers and Lewis
1990
; turtles: Brichta and Goldberg 2000
). In
most species, these units have an irregular discharge, but in the
toadfish some of the units are regular (Boyle et al. 1991
). As compared with the fibers located near the planum,
those found near the isthmus have large efferent responses the polarity of which depends on species. Almost all isthmus units are excited in
the toadfish (Boyle and Highstein 1990
), about equal
numbers are excited or inhibited in anurans (Bertrand et al.
1985
; Rossi and Martini 1991
; Rossi et
al. 1980
; Sugai et al. 1991
) and almost all are
inhibited in the turtle (the present study). In the previous paper
(Brichta and Goldberg 2000
), we emphasized that in all
nonmammalian species there is a similar longitudinal gradient in the
sensory-coding properties of B units as one proceeds from the planum
toward the isthmus There are also gradients in efferent response
properties, but these vary across species.
Results in mammals resemble those in turtles in two ways. First,
regularly discharging mammalian afferents resemble comparable turtle
fibers in their sensory-coding properties (Baird et al. 1988; Lysakowski et al. 1995
) and in their small
excitatory efferent responses (Goldberg and Fernández
1980
). In terms of their structure, the mammalian regular
fibers differ from those in nonmammalian species in including
dimorphic, as well as bouton, fibers and in being distributed
throughout a peripheral zone that surrounds the central zone both near
the planum and at the base of the neuroepithelium (Baird et al.
1988
). Second, large excitatory efferent responses are obtained
from irregularly discharging mammalian afferents, which include calyx
and dimorphic fibers in the central zone. In their sensory-coding and
efferent-response properties, the centrally located mammalian units
resemble those of turtle CD-high units but not CD-low units. Mammals
may be unique in one way. Unlike turtles and anamniotes, they do not
have irregular B units with large rotational gains and phases and large
efferent responses. Rather all mammalian B units are regularly
discharging (Lysakowski et al. 1995
) and, so, may be
presumed to have small, excitatory efferent responses (Goldberg
and Fernández 1980
).
Mechanisms of efferent response heterogeneity
Some of the afferents innervating the turtle posterior crista are
excited by efferent activation, others are inhibited, and still others
show mixed responses. There are several mechanisms that could be
responsible for this response heterogeneity. In anurans, both the
efferent inhibition and the efferent excitation seen in irregular
fibers are mediated by presynaptic efferent inputs that modulate the
frequency of miniature excitatory postsynaptic potentials (mEPSPs)
arising in the hair cell and recorded in the postsynaptic fiber
(Bernard et al. 1985; Rossi et al. 1980
,
1994
; Sugai et al. 1991
). Rossi et al.
(1980
, 1994
) have found that efferent inhibition is mediated by
nicotinic receptors, whereas efferent excitation involves purinergic
transmission. In contrast, Bernard et al. (1985)
implicated nicotinic receptors for both kinds of efferent responses.
Efferent inhibition involves the entry of Ca2+
through nicotinic channels and the subsequent turning on of
Ca2+-activated K+
(KCa) channels that hyperpolarize the
hair cell (Fuchs and Murrow 1992a
,b
). Nicotinic channels
not linked to KCa channels should cause excitation both by depolarizing the hair cell and increasing intracellular Ca2+. There are also postsynaptic
efferent terminals on calyx endings (Lysakowski 1996
;
Lysakowski and Goldberg 1997
; Wersäll and
Bagger-Sjöbäck 1974
) and on afferent processes
terminating as boutons (Lysakowski and Goldberg 1997
;
Sans and Highstein 1984
). The large efferent excitation seen in turtle CD afferents and in CD afferents located in
the mammalian central zone is likely the result of postsynaptic efferent inputs. It is unclear whether the smaller excitation seen in
regularly discharging fibers involves presynaptic, postsynaptic, or
both kinds of efferent synapses.
A mixed efferent response consisting of per-train inhibition followed
by a post-train excitation is seen not only in the turtle posterior
crista but also in anuran vestibular organs (Rossi and Martini
1991; Sugai et al. 1991
) and in lateral-line
organs (Russell 1971a
; Sewell and Starr
1991
). Two of our observations suggest that the post-train
excitation is not merely a release from inhibition. First, by lowering
shock frequency, we could replace the per-train inhibitory response by
an excitatory response without abolishing the post-train excitation.
Second, the profile of the response did not change as shock intensity
and the number of efferent fibers recruited were altered. The results
suggest that an impulse in each efferent fiber gives rise to a fixed
sequence, f(t), of inhibition followed by
excitation. To explore this idea we set
f(t) = AE exp(
Et)
AI
exp(
It) and assumed that the responses to successive shocks summed linearly. To obtain a per-train inhibition followed by a
post-train excitation required that of the two rate constants,
E <
I. Keeping
AE and AI fixed
resulted in similar response profiles as shock frequency was changed.
For the particular values of AE and
AI used in Fig.
16A, the time at which
the response changed from inhibition to excitation increased only
slightly as shock rate was lowered. This is in contrast to observed
responses (Fig. 8, A-D), which consist almost entirely
of inhibition at high shock rates and of a brief inhibition followed by
a more prolonged excitation at low shock rates. As can be seen in Fig.
16B, these features can be reproduced by assuming that
AI increases with shock rate while
AE remains constant. The assumption is
equivalent to assuming that the inhibitory component shows facilitation
during repetitive activation of efferent synapses while the excitatory
component does not.
|
Excitatory efferent responses in mammalian afferents consist of fast
and slow response components (Goldberg and Fernández 1980). A slow excitatory response also has been seen in lateral lines after the fast inhibitory response is blocked pharmacologically (Russell 1971a
; Sewell and Starr 1991
).
We looked for slow responses in turtle posterior-crista afferents in
the period after 10-s shock trains. A slow excitatory response was
commonly seen in CD-high units and could take 30 s to reach its peak
and another 100 s to decline to zero. A smaller, shorter slow
response was seen in BP units. In BT and BM units showing mixed
inhibitory-excitatory responses, the posttrain excitatory response
could last
20 s and might qualify as a slow response. Even in units
showing purely inhibitory response to 100-ms shock trains, a small,
brief excitation was seen after 10-s shock trains. Here a distinction
between fast and slow responses could not be based on kinetics, which
was comparable for the per-train inhibition and the post-train
excitation. In general, distinctions based solely on kinetics are
likely to become obsolete as more is learned about the neurochemical
and cellular bases of the response components.
Excitatory response-intensity relations
The turtle vestibular system has to monitor a wide range of head
velocities. Postural control during quiet standing requires the
monitoring of small rotations, possibly 1 deg/s. In contrast, velocities of 200-600 deg/s occur during rapid forward extensions of
the head and neck or during diving behavior; the movements themselves
last 200-300 ms (J. Brannigan, A. M. Brichta, and R. A. McCrea, unpublished observations). Hence the velocities of natural head
movements match those used in our experiments, but natural
accelerations can be considerably higher than those we could produce.
As a result our velocities are relatively small at brief times.
One way of interpreting our results is that very sensitive BT units are
designed to monitor the small head rotations involved in postural
control, whereas less sensitive BP and CD units are more appropriate
for monitoring rapid, volitional movements. To illustrate the
situation, we first consider variations in
vS, the head velocity above threshold
leading to a half-maximal response. As such,
vS may be taken as a measure of the
range of angular head velocities over which unit response is
approximately linear. Even if we confine ourselves to B units,
vS varies almost 30-fold during
t4, from 5-10 deg/s in BT units to
150-200 deg/s in BP units. An even larger, possibly >100-fold
variation may occur for earlier times because
vS for BT units is 2.5 deg/s during t1, whereas the corresponding value of
vS for BP units is expected to be
>300°/s (Table 2).
There is an enormous difference in the linear stimulus ranges for BT
and BP units. But if we assume that all units operate in the same part
of their normalized response-intensity function, their differential
sensitivity, expressed as a Weber fraction, will be similar. To
see this, we can state stimulus velocities, v vT = fvS, as a fraction of
vS and assume that all units operate around a stimulus level,
vS, which
is a fixed fraction of vS. The Weber
fraction is defined as W =
s/s, where
s is the stimulus increment needed to produce a fixed response,
r.
Algebraic manipulation of Eq. 1 yields W =
r (1 +
)2/
rMAX,
inversely proportional to rMAX. The
results in Table 2 indicate that for either
t1 or
t4 there is less than a twofold variation in rMAX between BP and BT
units. Many sensory systems obey Weber's law, so that the
just-noticeable-difference (
s) is proportional to
stimulus magnitude (s) or, alternatively, the Weber fraction
(
s/s) is constant (see, for example,
Stevens 1951
). The presence of a variety of B units
allows the turtle posterior crista to maintain an almost constant Weber
fraction over a large dynamic range.
What about CD units? In previous papers (Baird et al.
1988; Goldberg 1996
), we suggested that type I
hair cells and calyx units are intended to extend the dynamic range of
vestibular transduction. The electrophysiology of type I and type II
hair cells is consistent with the suggestion. In particular, the input
impedance of type I hair cells is as much as 20-fold smaller than that
of many type II hair cells (Brichta et al. 1998
;
Rennie and Correia 1994
; Rüsch and Eatock
1996
). A smaller input impedance would serve to extend the
dynamic range of type I cells by reducing their receptor potentials. This is the first study to test the suggestion at the level of afferents. Results are equivocal and depend on elapsed time. Table 2
presents data for t4 and data or
extrapolations for t1. For the later time,
there is an overlap in the linear stimulus range for B and CD units.
The vS values of CD-high units are
intermediate between those of BT and BP units, whereas those of CD-low
units are only slightly larger than those of BP units. For the earlier time, BP units probably have the largest values of
v1/2 although this conclusion rests on the
unproven assumption that the decline in rMAX
with time is similar in BP units to the decline observed in BT units.
There is one group of presumed CD units that have high-thresholds
coupled with very low linear gains. These very insensitive CD units
extend the linear stimulus range beyond that reached by BP units. We
relied on a unit's background firing and its responses to modest head
rotations to detect its presence. As a result, we may have
underestimated the proportion of CD-low units, especially those that
were very insensitive. At the same time, one has to be suspicious of
such units when encountered in an in vitro preparation. Because of this
concern, we looked for (and found) such units in an intact,
barbiturate-anesthetized preparation (Brichta and Goldberg
2000), even though blood gases were maintained at normal concentrations by artificial respiration (Frankel et al.
1969
). We calculate for the very insensitive units a
vS=
rMAX/gV(0) + vT = 630 deg/s. In doing so, we have
used the mean values of gV(0) = 0.37 spikes · s
1/deg · s
1
and vT = 70 deg/s from the very
insensitive units (Fig. 12) and the mean value of
rMAX = 230 spikes/s from other CD-low
units (Table 2).
The situation in the turtle posterior crista can be compared with that
existing in mammals. In the latter, there are no units resembling BT
units in having large linear (near-threshold) gains and in becoming
saturated at relatively low excitatory head velocities. Nor are there
many silent units with low sensitivities. The highest discharge rates
seen in mammalian vestibular afferents are 400-600 spikes/s (J. M. Goldberg and C. Fernández, unpublished observations). Subtracting a background discharge of 50-100 spikes/s leaves an rMAX of 300-550 spikes/s. Linear gains in
mammals range from 0.2 to 2 spikes · s1/deg
· s
1 (Baird et al. 1988
;
Lysakowski et al. 1995
), so
vS is 150-275 deg/s in the most sensitive
units and 1,500-2,750 deg/s in the least sensitive fibers. This may be
compared with estimated vS values in the
turtle of 150-300 deg/s in BP and in many CD-low units and 600-650
deg/s in very insensitive CD-low units. These figures suggest that
canal units can have more than twice the dynamic range in mammals as
compared with turtles. Voluntary head movements, at least in humans, do
not reach 1,000 deg/s (Grossman et al. 1988
). This
implies that the least sensitive afferents in mammals will remain
linear for even the largest naturally occurring head movements. At the
same time, there are no afferents in mammals specialized to monitor the
small head movements involved in postural adjustments or silent, very
insensitive afferents seemingly specialized to extend the dynamic
range. In this sense, the turtle crista is more highly differentiated
than is that of mammals.
One difference between turtle B and CD units involves the time
dependence of their rMAX values. The values
for B units decline by as much a twofold from
t1 to t4, whereas
those for CD units show a slight increase over the same time period.
One result is that rMAX values of CD units
are two to four times higher than those of B units during
t4, but the difference is obscured during t1. As the time dependence is one of the few
differences seen between B and CD units, its cellular basis is of
interest. In the case of auditory afferents, comparisons between
hair-cell receptor potentials and afferent discharge have suggested
that the saturation of response-intensity functions occurs at later stages of transduction, possibly involving depletion of afferent neurotransmitter (Eatock et al. 1992; Smith
1985
). It is unclear whether a similar conclusion holds
for vestibular transduction. Assuming that it does, it is possible that
the persistently high values of rMAX for CD
units may reflect an unusual mode of synaptic transmission between them
and type I hair cells. In particular, it has been suggested that the
postsynaptic depolarization produced by the afferent neurotransmitter
is supplemented by the accumulation of K+ ions that are
released by the hair cell, accumulate in the synaptic cleft, and
depolarize the postsynaptic membrane (Goldberg 1996
). Accumulation is calculated to have slow kinetics (
100 ms); this may
explain the slight increase in rMAX between
t1 and t2.
Because the concentration of K+ ions in the cleft depends
almost entirely on the current entering the mechanoelectric transducer
channel, depolarization from this source may be expected to persist
even when neurotransmitter is depleted.
Functional interpretation
Results from the two parts of this paper suggest a specific function for efferent control in the turtle posterior crista. BT units are of particular interest. From their response-intensity functions, including their very large linear (near-threshold) gains and their limited rMAX values, these units have a limited dynamic range (<10 deg/s), which would make them useful in monitoring the small head movements involved in postural control but not in the guidance of larger, voluntary head movements. BT units are inhibited by activation of the efferent system. Most other afferents show efferent excitation (BP and CD-high units) or no efferent responses (many CD-low units).
To draw functional inferences, we need to consider the conditions
leading to efferent discharge. There is some suggestion that efferents
respond to voluntary head movements, either by an efference-copy
mechanism (Boyle and Highstein 1990; Roberts and
Russell 1972
; Russell 1971b
; Tricas and
Highstein 1990
, 1991
) or by a reafference mechanism
(Blanks and Precht 1976
; Dickman and Correia
1993
, Gleisner and Henriksson 1964
; Myers
et al. 1997
; Precht et al. 1971
; Schmidt
1963
). Many of the aforementioned studies show that the
efferent activation is not directionally specific in the sense that the
efferents going to a specific organ respond in anticipation of or as a
direct consequence of voluntary head movements that would activate any
vestibular organ. Such an efferent activation would silence the BT
units involved in postural control while at the same time exciting
other afferents involved in the guidance of voluntary movements. Were
the responses of BT units merely saturated by large-amplitude movements
the signals need not disrupt central processing. But we have seen that
the BT cells show time-dependent nonlinear distortions, which might
interfere with central processing and make it advantageous to silence
their discharge peripherally. The background discharge of excited units
would be increased, and this would serve to reduce inhibitory
silencing, especially in CD-high units with large efferent responses.
At the same time, excitatory dynamic ranges would be curtailed. This
may provide a rationale as to why the efferent responses in CD-low
units are so weak because these units seem specialized to ensure the
largest possible excitatory dynamic range.
Viewed more generally, the efferent system can be thought of as
switching the turtle posterior crista from a postural to a voluntary
mode. Three limitations of these ideas can be mentioned. First, we need
more detailed information on the physiological conditions leading to
efferent discharge. Second, the scenario depends on the efferent
inhibition of BT units, which are presumably specialized for the
monitoring of postural movements. But only in turtles are almost all
such cells inhibited. In other species, many of the comparable cells
are excited (Bernard et al. 1984; Boyle and
Highstein 1990
; Rossi et al. 1980
; Sugai
et al. 1991
). One suggestion is that nonlinear distortion is
less disruptive of central processing in these other species. Third,
the scenario presumes that efferent inhibition in the turtle abolishes
the responses of BT units to even intense head rotations. This last point has yet to be examined.
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ACKNOWLEDGMENTS |
---|
Drs. R. A. Eatock and A. Lysakowski made helpful comments on the manuscript.
This research was supported by National Institute on Deafness and Other Communication Disorders Grant DC-02508 (J. M. Goldberg, principal investigator).
Present address of A. M. Brichta: Discipline of Anatomy, Medicine and Health Sciences, University of Newcastle, Callaghan, NSW 2308 Australia.
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FOOTNOTES |
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Address for reprint requests: J. M. Goldberg, Dept. of Neurobiology, Pharmacology and Physiology, University of Chicago, 947 E. 58th St., Chicago, IL 60637.
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.
1 Let R(s) and V(s) be the Laplace transforms of the response and of the stimulus waveform expressed in terms of head velocity. Then R(s) = HV(s)V(s), where HV(s) is the transfer function re velocity. The appropriate stimulus dimension is defined by X(s) = HV(s)V(s), in which case the transfer function relating R(s) and X(s) is HX(s) = 1. It follows that the gain is constant in both the frequency and time domains.
Received 22 April 1999; accepted in final form 12 October 1999.
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REFERENCES |
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