Department of Neurobiology, Pharmacology and Physiology, University of Chicago, Chicago, Illinois 60637
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ABSTRACT |
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Belton, Timothy and
Robert A. McCrea.
Role of the Cerebellar Flocculus Region in Cancellation of the
VOR During Passive Whole Body Rotation.
J. Neurophysiol. 84: 1599-1613, 2000.
A series of studies were
carried out to investigate the role of the cerebellar flocculus and
ventral paraflocculus in the ability to voluntarily cancel the
vestibuloocular reflex (VOR). Squirrel monkeys were trained to pursue
moving visual targets and to fixate a head stationary or earth
stationary target during passive whole body rotation (WBR). The firing
behavior of 187 horizontal eye movement-related Purkinje (Pk) cells in
the flocculus region was recorded during smooth pursuit eye movements
and during WBR. Half of the Pk cells encountered were eye velocity Pk
cells whose firing rates were related to eye movements during smooth pursuit and WBR. Their sensitivity to eye velocity during WBR was
reduced when a visual target was not present, and their response to
unpredictable steps in WBR was delayed by 80-100 ms, which suggests
that eye movement sensitivity depended on visual feedback. They were
insensitive to WBR when the VOR was canceled. The other half of the
Purkinje cells encountered were sensitive to eye velocity during
pursuit and to head velocity during VOR cancellation. They resembled
the gaze velocity Pk cells previously described in rhesus monkeys. The
head velocity signal tended to be less than half as large as the eye
velocity-related signal and was observable at a short (40 ms)
latency when the head was unpredictably accelerated during ongoing VOR
cancellation. Gaze and eye velocity type Pk cells were found to be
intermixed throughout the ventral paraflocculus and flocculus. Most
gaze velocity Pk cells (76%) were sensitive to ipsilateral eye and
head velocity, but nearly half (48%) of the eye velocity Pk cells were
sensitive to contralateral eye velocity. Thus the output of flocculus
region is modified in two ways during cancellation of the VOR. Signals
related to both ipsilateral and contralateral eye velocity are removed,
and in approximately half of the cells a relatively weak head velocity
signal is added. Unilateral injections of muscimol into the flocculus
region had little effect on the gain of the VOR evoked either in the
presence or absence of visual targets. However, ocular pursuit velocity and the ability to suppress the VOR by fixating a head stationary target were reduced by approximately 50%. These observations suggest that the flocculus region is an essential part of the neural substrate for both visual feedback-dependent and nonvisual mechanisms for canceling the VOR during passive head movements.
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INTRODUCTION |
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The vestibulo-ocular reflex (VOR) is a central pattern generator that rotates the eyes so that visual images of interest can be stabilized on the retina when the head moves. The vestibular signals that are the origin of the VOR eye movement commands carried by central VOR pathways must be modified or supplemented as the behavioral context of the reflex changes. One circumstance in which the VOR must be modified is when a visual image remains stationary with respect to the head while the head moves in space. The correspondence between image and head motion can occur in natural circumstances when the head is passively perturbed in space during either movements of the body or movements of the substrate on which it stands. An example of this is when a squirrel monkey looks at an object on the moving tree branch on which it stands. A second circumstance in which the VOR must be canceled occurs when voluntary head movements contribute to gaze shifts made to pursue moving visual targets. In that circumstance the VOR must be canceled in order for the gaze shift to progress.
One way for the VOR to be suppressed during passive head movements is
through programming a predictive pursuit command that also functions to
cancel the VOR (Barnes 1988; Barnes and Eason 1988
; Lanman et al. 1978
). A second method would
be to produce a parametric reduction in the oculomotor signals of the
VOR (Cullen et al. 1991
; Robinson 1982
;
Tomlinson and Robinson 1981
). Squirrel monkeys use both
parametric and predictive mechanisms to cancel the VOR (Cullen
et al. 1991
), and different classes of secondary VOR neurons
are preferentially related to each mechanism (Cullen and McCrea
1993
; Cullen et al. 1993
). During VOR
cancellation the signals carried by position-vestibular-pause (PVP)
neurons and secondary vestibular neurons whose firing behavior is
related to smooth pursuit eye movements, the eye-head velocity (EHV)
neurons, are modified. However, the changes in PVP head movement
sensitivity do not depend on visual following or smooth pursuit
signals, while the changes in EHV activity apparently do depend on
pursuit inputs (Cullen et al. 1993
). The two mechanisms
for cancellation of the VOR possibly reflect two general mechanisms for
changing VOR gain. One involves the input of visual feedback or pursuit
signals to VOR pathways (Barnes 1993
; Collins and
Barnes 1999
; Lisberger 1990
; Lisberger et
al. 1981
). The second mechanism involves the removal or
addition of vestibular reafferent signals as determined by behavioral
context (Cullen and McCrea 1993
; McCrea et al.
1996
).
The cerebellar flocculus and contiguous regions of the ventral
paraflocculus are a critical part of the central neural substrate that
functions to modify VOR performance. The floccular region (FLR)
receives inputs conveying signals related to retinal image slip, head
movements, and eye movements (Lisberger and Fuchs 1978b; Miles et al. 1980
; Noda 1986
;
Simpson and Alley 1974
; Simpson et al.
1981
; Waespe and Henn 1981
; Zhang et al.
1993
). The Purkinje (Pk) cells that form the output of the FLR
inhibit neurons in the vestibular nuclei that project to the
extraocular motor nuclei (Fukuda et al. 1972
;
Highstein 1973
; Ito et al. 1977
;
Lisberger et al. 1994b
; Sato and Kawasaki
1990
). The firing behavior of most FLR Pk cells is correlated
with eye velocity during smooth pursuit and during optokinetic
nystagmus (Leung et al. 2000
; Miles et al.
1980
; Noda et al. 1981
; Waespe et al.
1985
). Moreover, many FLR Pk cells carry signals related to
head velocity when the VOR is canceled during passive whole body
rotation (Lisberger and Fuchs 1978a
; Miles et al.
1980
; Waespe and Henn 1981
). These signals
appear to be necessary for producing the changes in the responses of
many secondary vestibular neurons that are observed when the VOR is
canceled during passive head rotation (Lisberger et al.
1994a
,b
; Partsalis et al. 1995
; Zhang et
al. 1995a
) and to be essential for producing smooth ocular
following eye movements and for modifying the VOR during
visual-vestibular conflict (Takemori and Cohen 1974
;
Waespe et al. 1983
; Zee et al. 1981
).
The purpose of the studies described in this and the accompanying paper
was to assess the contribution of the cerebellar flocculus region to
the ability of squirrel monkeys to cancel their VOR during passive and
active head movements. The results of our recent studies suggest that
vestibular signal processing in the vestibular nuclei is contingent on
behavioral context (Chen-Huang and McCrea 1999;
McCrea et al. 1996
, 1999
). The
signals produced by most squirrel monkey secondary vestibular neurons
are profoundly modified during VOR cancellation both during passive and
active head movements (Chen-Huang and McCrea 1999
;
Cullen et al. 1993
; McCrea et al. 1999
).
Thus we were particularly interested in whether and to what extent
inputs from the floccular region might be responsible for those
changes. We describe the signals generated by the Pk cells in the FLR
during VOR cancellation and compare them to the signals observed when
the VOR is not suppressed and when gaze shifts are generated by smooth
pursuit eye movements alone. We also studied the effect of inactivating
the flocculus by injection of muscimol on the ability to cancel the VOR
during passive and active head movements.
In this paper we describe the firing behavior of squirrel monkey FLR Pk
cells when they cancel their VOR during passive whole body rotation. We
conclude that the FLR may be sufficient to mediate both the visual and
nonvisual mechanisms squirrel monkeys utilize for canceling the VOR
during passive whole body rotation. A preliminary report of some of the
findings has been published (Belton and McCrea 1999).
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METHODS |
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The methods used for recording and analyzing eye movements and
single-unit activity in squirrel monkeys were similar to those that
have been described previously (Chen-Huang and McCrea
1999; Gdowski and McCrea 1999
).
Surgical preparation
Three adult squirrel monkeys were prepared for recording both single-unit activity and eye movements. Surgeries were carried out under aseptic conditions on animals anesthetized with pentobarbital sodium (20 mg/kg ip, supplemented as necessary with 1-2 mg/kg iv). A woven coil of fine, Teflon-coated wire (Cooner) was sutured to the sclera of one eye for the recording of eye movements using the magnetic search coil technique. A small stainless steel stud was affixed to the occipital bone with dental acrylic for restraining the head in the plane of the horizontal semicircular canals. A Plexiglas well was fixed onto the parietal bone for the placement of microelectrodes, and a metal reference pin was permanently affixed to the skull adjacent to the probe insertion site.
Experimental recording conditions
During experiments animals were seated in a primate chair atop a vestibular turntable (Inland 832). A harness was placed over the animal's shoulders and in front of the trunk to inhibit trunk and arm-raising movements. The implanted stud was attached to a rod that allowed the head to move in the plane of the horizontal semicircular canals. The rotational axis of the rod was coincident with the rotational axis of the turntable and was positioned within 5 mm of the C1-C2 axis of head rotation at the level of the external auditory meatus. The rod rotated within a low-friction ball bearing assembly fixed to the table and had a universal joint that permitted small postural adjustments. The head could be fixed to the turntable by disabling the universal joint and attaching a block that prevented angular rotation of the rod. The experiments described in this paper concern recordings obtained when the head was restrained from moving.
The monkeys were trained to fixate and pursue a small visual target (0.5 W HeNe laser, <0.2° diam) projected onto a cylindrical projection screen 90 cm distant from the monkey. The background presented by the screen was not an effective optokinetic stimulus during constant velocity turntable rotations (30-60°/s). The target movement was produced with a pair of galvanometer-controlled mirrors mounted on the turntable. The animals were rewarded for fixation of the target using a sweetened milk mixture according to a variable reinforcement schedule. After training, the monkeys were able to produce on-demand performance for sustained periods of 5 h or more, three to four times per week.
Two of the monkeys were also used in the head-free pursuit experiments
described in the accompanying paper (Belton and McCrea 2000). The training paradigms and rewards were identical in the monkeys in the head-free and head-restrained conditions: the monkeys were rewarded when the angular position of the right eye was within 2° of the target. It is conceivable that monkeys attempted to follow
targets with head movements when their heads were restrained; however,
any such effort was unnecessary and unrewarded. One monkey was not used
in head-free experiments until after recordings in the flocculus had
been completed. The Purkinje cell responses recorded in that animal
were similar to the responses observed in the other two animals when
the head was restrained.
Eye and head movement recording
Eye movements were measured using a magnetic search-coil system (40 cm diam, Neurodata Instruments). The eye position signal was calibrated by assuming that the gain of the VOR recorded during fixation of an earth stationary target was unity. The position of the head was monitored with a second search coil. Behavioral monitoring, data acquisition, and stimulus generation were controlled with a personal computer. Turntable, target, gaze, and head signals were low-pass filtered (5-10 kHz) and sampled (2-500 Hz) at 16-bit resolution with a Cambridge Electronics 1401 data acquisition system.
Single-unit recording techniques
Single-unit recordings were made using varnish-coated tungsten
microelectrodes (4-7 M impedance) introduced into the FLR through a
guide tube. The guide tube was mounted onto the slave cylinder of a
hydraulic microdrive (Trent Wells). A manual micromanipulator was used
for moving the guide tube covering the electrode approximately 0.7 mm
into the cerebellum. The electrode was then advanced into the FLR using
the hydraulic microdrive.
Single-unit potentials were conventionally amplified (Dagan 2400) and filtered (band-pass 300 Hz to 8 kHz). Action potentials were discriminated with a window discriminator (BAK Electronics) that triggered an event channel of the Cambridge Electronics 1401 system at 0.1 ms resolution. These events were subsequently converted into values of instantaneous firing frequency corresponding to each A/D sample.
Histology and location of recording sites
Before recording from the FLR, an attempt was made to estimate the location of the cerebellar tentorium and the rostral and lateral extent of the ventral paraflocculus. Once these were ascertained, a region extending 4 mm caudal from the rostral end of the paraflocculus and 2-3 mm medial from the lateral edge of the ventral paraflocculus was systematically explored. On each track the location of the ventral aspect of the ventralmost folium, and, when encountered, of the vestibular nerve were noted. These landmarks were used as aids in reconstructing recording probes. In two monkeys the position of a microelectrode tract was confirmed histologically.
The most salient anatomical landmark during recording was the presence of VIIIth nerve axons 300-500 µm ventral to the cerebellar cortex. In squirrel monkeys the posterolateral fissure is typically a millimeter or less rostral to the center of the ventrally emerging eighth nerve (Fig. 1B). The region of the flocculus and ventral paraflocculus explored was bounded dorsally by an area approximately 700 µm ventral to the tentorium, and laterally by the petrosal bone. No Purkinje cells whose firing behavior was related to eye or head movement were encountered >2.25 mm medial to the estimated lateral edge of the ventral paraflocculus. Ventrally the FLR was bounded by bone and, most medially, the cochlear nuclei, where acoustically responsive, smaller neurons could be encountered. The results of our reconstructions suggest that only the caudal-medial most folium of the flocculus was not explored (see Anatomical location of horizontal Pk cells). No effort was made to explore the dorsal paraflocculus.
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Single-unit recordings
Isolated single units (signal-to-noise ratio was typically >3:1) were tested for responsiveness during horizontal smooth pursuit of a visual target moved sinusoidally at 0.5 Hz, 40°/s peak velocity, and during suppression of the VOR using the same stimulus. Units that were apparently unresponsive to horizontal pursuit and turntable rotation were often tested for their responsiveness during vertical pursuit. Units that were sensitive to vertical pursuit were usually not sensitive to horizontal pursuit and were not studied further.
Most Pk cells were easily isolated and discriminated from background activity. No recordings were obtained from poorly discriminated units or from recordings that included more than one unit.
EXPERIMENTAL PROTOCOLS.
The responses of each Pk cell were studied using the following four
paradigms.
1)
Sinusoidal smooth pursuit (0.5 Hz, 40°/s peak target velocity)
Inactivation of the FLR using muscimol
After extensive recordings had been made from single units in the FLR, injections of muscimol were made in the estimated center of the region that contained the highest concentration of horizontal eye movement-related Pk cells. In each case this site was dorsal and slightly anterior to the VIIIth nerve. In one of the monkeys, the cannula used for muscimol injection was fixed in place immediately on completion of the behavioral experiment, and the animal was killed by transcardial perfusion of a fixative. Histological reconstruction showed that the tip of the cannula was located in the ventral-most folium of the ventral paraflocculus approximately 1 mm rostral to the flocculus.
After confirming the location by recording single-unit activity, the
recording microelectrode was replaced with a Hamilton syringe
(model 7002) that contained 1.2-1.4 µL of a 20-mg/ml solution of
muscimol in normal saline. This solution was injected over 10 min. The
concentration and volume injected were similar to that used in
previously published studies in which muscimol was used to inactivate
the squirrel monkey FLR (Partsalis et al. 1995). VOR eye
movements were periodically recorded postinjection to ensure the normal
functioning of the vestibular nerve, and of vestibular nucleus neuronal pathways.
Data analysis
ANALYSIS OF PURKINJE CELL SENSITIVITY TO EYE POSITION. Static eye position sensitivity was assessed by measuring firing rate during intersaccadic periods (0.5-2 s) of spontaneous stationary eye position in the absence of a target. Multiple regression estimates of the sensitivity to horizontal and vertical eye position were computed from at least 20 stable eye positions (>150 ms before or after a saccade). For those units with nonlinear firing rate-eye position relationships, separate fits of firing rate to eye position were made across sub-ranges of the averaged response that were at least 180° in length and that appeared to be linear by visual inspection.
ANALYSIS OF DATA OBTAINED WITH SINUSOIDAL STIMULI.
Most of the experimental paradigms described in this paper utilized
sinusoidal target or turntable movements. Unit activity was recorded
during periods of 30 s duration, with multiple tests usually
obtained for each of the behavioral paradigms described above. Cycles
were selected for further analysis only if the monkey's gaze position
was within 2-3° of the visual target. In experiments in which the
visual target was not present, cycles in which sleepy eye movements
occurred (epochs of 10 s or more without saccades or where the
position of the eye drifted) were eliminated. Records from 20-100
selected cycles (mean, 26 at 0.5 Hz) were concatenated, desaccaded,
averaged, and fit with sinusoidal functions. An iterative fitting
technique was used to eliminate the significant deviations from
linearity associated with periods of low firing rate (Chen-Huang et al. 1997). A significant minority of the Purkinje cells
exhibited nonlinear responses during sinusoidal pursuit and VOR
cancellation that were not associated with low firing rate. In these
cases an estimate of unit response gain was obtained by fitting a
sinusoidal function to the units firing rate to a portion of the cycle
(always >180°) in which the response was linearly related to the
stimulus (see Fig. 5 for an example).
ANALYSIS OF DATA OBTAINED WITH VELOCITY TRAPEZOID STIMULI.
The methods used for analysis of unit responses during steps in head
acceleration generated during VOR cancellation or fixation have been
described in detail elsewhere (Cullen and McCrea 1993). Briefly, 5-22 records of behavioral and neural responses when the
monkey was either fixating the target or not moving the eyes prior to
and after brief unpredictable steps in head acceleration (
400°/s2) were averaged. Records were
included in the analysis only if saccades were absent 100 ms prior to
and 100 ms after the onset of the head acceleration step and if the
monkey reacquired the target within 200 ms after onset.
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RESULTS |
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The results are based on recordings from 187 Pk cells in the
ventral paraflocculus and flocculus of three squirrel monkeys whose
firing behavior was sensitive to horizontal smooth pursuit eye
movements and/or VOR cancellation in the plane of the horizontal semicircular canals. Horizontal Pk cells constituted a large minority (45%) of the Pk cells encountered in this region of the cerebellum. The remaining Pk cells were neither sensitive to horizontal smooth pursuit eye movements nor to cancellation of the VOR. They were usually
sensitive to vertical eye movements and were strongly modulated during
vertical smooth pursuit when tested. Approximately 10% of the units
encountered appeared to be unresponsive during both horizontal and
vertical pursuit eye movements.
Anatomical location of horizontal Pk cells
An attempt was made to systematically explore the entire flocculus and ventral paraflocculus. After reconstruction of electrode tracks we estimate that only the most caudal and medial folium of the flocculus was unexplored. Pk cells with firing behavior related to horizontal smooth pursuit eye movements could readily be grouped into two categories, eye velocity Pk cells (Ev Pk cells) and gaze velocity Pk cells (Gv Pk cells), based primarily on their responses during whole body rotation (see below). The two cell types were intermixed and were found in every region of the flocculus and ventral paraflocculus that was explored.
Figure 1 shows the estimated location of the Ev and Gv Pk cells in the cerebellar FLR in all three monkeys. Figure 1A is a photograph of a lateral view of the FLR of one of the monkeys. In Fig. 1B the estimated location of Ev and Gv Pk units in all three monkeys in the sagittal plane is superimposed on an outline drawing of the flocculus and ventral paraflocculus. The location of each cell in the plot was calculated on the basis of the relative position of the tip of the electrode to the estimated rostral edge of the paraflocculus and to the estimated location of the vestibular nerve. Dorsal and coronal views of the distribution of Pk cells recorded are illustrated in Fig. 1, C and D.
Neither Ev nor Gv Pk cells were confined to one region of the FLR, although Purkinje cells within a small local region of cortex tended to be of the same variety. In 22 of 39 tracts in which 3 or more Pk cells were encountered, both Ev and Gv Pk cell types were recorded. However, when three or more Pk cells were separated by <1 mm on the same probe, they were more likely (4 of 6 instances) to be of the same type. No significant physiological differences were found in the eye or head movement sensitivity of Pk cells recorded in the most rostral part of the FLR as compared with Pk cells located in the most caudal regions of the FLR. In sum, Pk cells within a small local region of cortex tended to be of the same variety, but neither of the two types of units were confined to any one rostro-caudal region of the FLR.
Eye velocity and gaze velocity Purkinje cells
The firing rate of Pk cells in the FLR was modulated during
smooth eye movements and during passive whole body rotation. In some
units (n = 17; 9%) this modulation was small (gain re
stimulus velocity was <0.2 spike/s/deg/s) and difficult to analyze
quantitatively. The remaining 170 units were classified on the basis of
firing behavior during smooth pursuit eye movements and passive WBR. Nearly half of the Pk cells tested (80/170) were sensitive to head
velocity during turntable rotation and were designated as Gv Pk cells,
since they were similar to the Gv Pk cells that have been described in
rhesus monkeys (Lisberger and Fuchs 1978a; Miles et al. 1980
). The firing rate of the remaining Pk cells
(90/170) was not significantly related to head velocity during WBR but was related to horizontal eye movements, particularly during smooth tracking of visual targets. Although the firing rate of some of these
eye movement only Pk cells was related to both eye velocity and eye
position (see below) in some circumstances, we refer to them as eye
velocity (Ev) Pk cells because the eye position signals were not
present in every paradigm (see below).
Sample records of the firing behavior of a typical Ev Pk cell and Gv Pk cell during sinusoidal smooth pursuit, VOR cancellation, and WBR are shown in Figs. 2 and 3. The firing rate of Ev Pk cells was modulated when the monkey pursued a moving target (Fig. 2A) and when it fixated an earth stationary target during passive whole body rotation (Fig. 2C). When the monkey attempted to cancel its VOR (Fig. 2B), any modulation apparent in the activity of these cells was in phase with the uncanceled eye velocity. No activity related to head velocity could be discerned. The averaged response of the unit in each condition is illustrated on the right in Fig. 2.
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The distinguishing characteristic of Gv Pk cells in the squirrel monkey FLR was their sensitivity to head velocity during passive whole body rotation. The Gv Pk cell shown in Fig. 3 was typical. Like the Ev unit illustrated in Fig. 2, it was sensitive to ipsilateral smooth pursuit eye movements (Fig. 3A). However, during VOR cancellation (Fig. 3B) the cell's firing rate was related to ipsilateral head velocity. This head velocity signal was smaller than the eye velocity-related modulation recorded during ocular pursuit. When the monkey fixated an earth stationary target during WBR (Fig. 3C), the Gv Pk cell's response was in phase with eye velocity, but reduced. The reduction could be accounted for by the presence of the concomitant head velocity signal, which in this condition was out of phase with the eye velocity signal.
Sensitivity of FLR Pk cells to eye movements
FIRING BEHAVIOR DURING SACCADES AND STEADY FIXATION. The majority (112/187, 59%) of the Ev and Gv Pk cells in the FLR exhibited some sensitivity to ocular saccades, but the signals they generated were typically weak and were not consistent in the absence of a visual target. Most of the units that were sensitive to saccades generated inconsistent bursts of spikes in the pursuit eye velocity ON-direction and/or were inconsistently inhibited during saccades to the unit's OFF-direction. Some of the saccade-sensitive units (22%) exhibited the opposite behavior; i.e., they were excited during saccades to their pursuit OFF-direction and inhibited during saccades to the ON-direction. A few cells (11%) generated bursts or pauses during saccades in all directions.
Most FLR Pk cells whose firing rate was modulated during horizontal smooth pursuit eye movements were not sensitive to eye position during steady fixation. Static eye position sensitivity was estimated in 119 Pk cells by multiple regression of tonic firing rate versus horizontal and vertical eye position recorded during periods of steady fixation in the absence of a target. The tonic firing rate of a minority of those units (29/119, 24%) was significantly related to horizontal eye position (mean, 4.5 spikes/s/deg). The horizontal eye position signal, when present, was related to eye movements in the same direction as the pursuit signal and was usually similar to an estimate of dynamic eye position sensitivity measured during ocular pursuit. A comparison of unit sensitivity to static eye position (Ks) and "dynamic" eye position sensitivity recorded during sinusoidal smooth pursuit (Kd) was comparable. Dynamic eye position sensitivity was calculated from 0.5-Hz responses of 23 units using the following formula
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FIRING BEHAVIOR DURING SMOOTH PURSUIT EYE MOVEMENTS. The firing rate of nearly half of the Purkinje cells in the flocculus and ventral paraflocculus was related to horizontal smooth pursuit eye movements, but their sensitivity varied over a large range (0.13-4.49 spikes/s/deg/s re eye velocity). Only a few horizontal eye movement-related Purkinje cells were sensitive to vertical eye position or to vertical smooth pursuit eye movements. Five units were encountered that were sensitive to both horizontal and vertical pursuit eye movements; four of these exhibited nonlinear responses during horizontal smooth pursuit (see below). Three were related to downward eye velocity and two to upward eye velocity during vertical pursuit. Vertical and horizontal directional preferences were not related in any consistent way.
The gain and phase of Pk cell responses during 0.5-Hz horizontal ocular pursuit are summarized in Fig. 4 and Table 1.
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NONLINEAR PURSUIT SIGNALS.
In macaque monkeys some Pk cells code the velocity of smooth pursuit
eye movements only when eye velocity achieves a threshold value
(Lisberger et al. 1994a; Miles et al.
1980
; Noda and Warabi 1982
). Similar nonlinear
responses were observed in the squirrel monkey. A significant fraction
of both Ev Pk cells (22/90, 24%) and Gv Pk cells (16/80, 20%) did not
generate signals related to pursuit eye velocity until it had achieved
a threshold value.
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Firing behavior of Purkinje cells during VOR cancellation
During single-unit recordings, VOR cancellation was rarely perfect, and the average gain of the VOR at 0.5 Hz recorded concomitantly with unit recordings was 0.21 ± 0.12. When VOR cancellation was near perfect, the firing rate of Ev Pk cells was not modulated (Fig. 6A1). Ev Pk unit responses recorded during cycles in which the VOR cancellation was relatively poor were always larger than responses recorded when VOR cancellation was effective, and they increased in tandem with uncanceled eye velocity at higher stimulus frequencies. The sensitivity of Ev Pk cell to eye velocity during VOR cancellation was comparable to that measured during ocular pursuit (see Table 1), although responses were more phase-advanced.
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In contrast to Ev Pk cells, the response amplitude of Gv Pk cells during VOR cancellation was inversely related to the gain of the VOR. The sensitivity of Gv Pk cells to head velocity during VOR cancellation varied over a wide range (Fig. 6B1), and the gain of their responses (Fig. 6B2) tended to be slightly more phase-advanced with respect to head velocity than with respect to eye velocity during ocular pursuit. In Fig. 6C1 unit sensitivity to eye velocity during smooth pursuit is plotted as a function of unit response gain re head velocity during VOR cancellation. The filled circles represent Gv Pk cells, and the open symbols represent Ev Pk cells. The dashed line indicates equal sensitivity to eye and head velocity. The mean eye velocity sensitivity of all Gv Pk cells during pursuit was 1.31 spikes/s/deg/s, while the mean gain of the head velocity signals generated by these cells during VOR cancellation was 0.56 spikes/s/deg/s.
The disparity between pursuit and VOR cancellation responses of Gv Pk cells could not be attributed to incomplete cancellation of the VOR. Figure 6C2 plots unit eye velocity sensitivity during pursuit versus an estimate of head velocity sensitivity calculated after subtraction of any residual eye velocity signal from the responses recorded during VOR cancellation. The change in unit responses as a function of canceled eye velocity was also estimated by comparing responses recorded during cycles when the VOR was less well canceled (but with eye position still kept within 2° of the target) to responses recorded when cancellation was more effective. The sensitivity of these cells to canceled eye velocity was similar to the corrected estimate of head velocity sensitivity obtained after subtraction of any residual eye velocity-related component of the response.
The VOR cancellation response of 13 Gv Pk cells was studied at higher stimulus frequencies (1.0 and 2.3 Hz). Gv Pk cells were equally sensitive to head velocity at stimulus frequencies of 0.5 and 1.0 Hz (1.27 and 1.25 spikes/s/deg/s; n = 7). At 2.3 Hz monkeys were not able to cancel their VOR, which increased to a mean gain of 0.80. The modulation in firing rate of most (4/6) of the Gv units tested at 2.3 Hz reversed in direction and was in phase with unsuppressed eye velocity rather than with head velocity.
The poor VOR cancellation performance during high-frequency head
rotation was particularly evident when the head was unpredictably accelerated during fixation of a head stationary target. Steps in head
acceleration evoke compensatory eye movements for brief periods, and
the VOR does not begin to be suppressed until 80-100 ms after the
onset of such a perturbation (Cullen et al. 1991). Responses to head acceleration steps
(300-400/s2) were studied in 14 Gv Pk cells and
4 Ev Pk cells. Figure
7A shows
the averaged firing behavior of a type I Gv and a type II Ev Pk cell
during contralateral steps in head acceleration (cH") that were
generated during fixation of a target that remained stationary with
respect to the head. The steps produced a transient VOR eye velocity
(
) that was in the ipsilateral, ON-direction of the Gv Pk
cell and in the Ev Pk cell's OFF-direction. The
compensatory eye velocity evoked by the step [E' (VORc)] did not
begin to be suppressed until approximately 90 ms after
acceleration onset. The responses of Pk cells were also delayed. Gv Pk
cells typically began to respond approximately 40 ms (mean latency = 37 ± 20 ms) after the onset of the acceleration step. The
response of Ev Pk cells was even more delayed with a mean latency of
77 ± 27 ms.
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When a step in head acceleration occurs in the context of ongoing VOR
cancellation, VOR eye movements evoked by the step are suppressed at a
shorter latency (Cullen et al. 1991). The responses of a
Gv Pk cell during steps in head acceleration that were generated while
the monkey was suppressing its VOR are illustrated in Fig. 7B. Unit and eye movement responses to steps in both the
contralateral (cH", red traces) and ipsilateral (iH", blue traces)
direction are superimposed on a response evoked in the dark in the
absence of a target (black traces). When the step in head acceleration was produced in the dark, the Gv Pk cell did not respond. However, a
head velocity-related modulation was present in the Gv Pk cell both prior to and during the step when the monkey was already canceling
VOR eye movements by fixating a head stationary target. The response of
the cell (red histogram) closely matched the response predicted by a
model of firing rate based on its sensitivity to head velocity measured
during 0.5-Hz VOR cancellation and to eye velocity during ocular
pursuit at 0.5 Hz (dashed line superimposed on firing rate histograms
in Fig. 7B).
Signals generated by Purkinje cells during whole body rotation in the presence and absence of targets
The firing rate of most Pk cells was modulated during whole body rotation when the monkey fixated an earth stationary target. However, these rotational responses were reduced or absent when the rotation was done either in darkness or in the lit room without the visual target present. Figure 8 shows the responses of both an Ev Pk and a Gv Pk cell during 0.5-Hz sinusoidal WBR in the presence of an earth stationary target (Fig. 8A) and during rotation in the light when no target was present (Fig. 8B). The gain and phase of the VOR in the presence and absence of a target were comparable (Table 1), but the gain and phase of the signals generated by Pk cells were substantially affected by target presence.
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The firing rate of Ev Pk cells was strongly modulated during WBR when an earth stationary target was present. The amplitude and phase of the rotational responses of Ev Pk cells were similar to those recorded during ocular pursuit. Eye velocity Pk units were slightly less sensitive to eye velocity during VOR with a target present (1.37 spikes/s/deg/s) than during smooth pursuit (1.53 spikes/s/deg/s), yet the phase lag re eye velocity observed during WBR was very similar to that observed during ocular pursuit. Units with nonlinear responses during pursuit also exhibited similar response nonlinearity during WBR.
In the absence of a target, the signals generated by Ev Pk cells during WBR were reduced by more than half and phase led rather than lagged eye velocity (Fig. 8B). The reduction in response amplitude was observed both during WBR in the dark and during WBR in ambient light when the monkey faced the projection screen. In Fig. 8C Ev Pk unit response gains re eye velocity during WBR are plotted as a function of the gain of their response during smooth pursuit. The open symbols were responses recorded during fixation of an earth stationary target; the closed symbols were responses recorded when the target was not present. The dashed line indicates identical eye velocity sensitivity during VOR and pursuit. The dotted line is the best linear fit to the responses recorded in the absence of a target. The slope of the regression of unit WBR responses in the absence of a target re responses during pursuit (dotted line in Fig. 8C) was 0.29. Thus the sensitivity of Ev Pk cells to eye movements during the VOR in the absence of a foveal target was less than one-third of that observed during pursuit.
Most Gv Pk cells were modulated during WBR when a target was present. That modulation was approximately equal to the vector sum of the eye velocity-related response measured during pursuit and the head velocity-related response recorded during VOR cancellation (e.g., dashed line superimposed on the averaged firing rate histogram in Fig. 8A). For most Gv Pk cells this response was in phase with eye velocity, rather than head velocity, since the eye velocity signal was usually the larger of the two. In Fig. 8D the Gv Pk unit responses evoked by WBR during fixation of an earth stationary target are plotted as a function of the response predicted from their sensitivity to eye velocity during smooth pursuit and to head velocity during VOR cancellation (open circles). The correlation between recorded and predicted responses was 0.93.
Gv Pk cell responses during VOR were reduced in gain, and in some cases were abolished in the absence of the target (Fig. 8B). In a few cells the response recorded without the target was reversed in direction from the response recorded when it was present. In Fig. 8D the filled symbols are the responses recorded in the absence of a target. The slope of a regression line fit to the responses recorded in the absence of a target (dotted line in Fig. 8D) was 0.5. This decreased slope, and the 180° phase reversal of some units, suggests that Gv Pk cells were nearly twice as sensitive to VOR eye velocity when a foveal target was present than when it was absent.
In sum, Ev and Gv Pk cells responded in opposite ways during VOR cancellation. Ev Pk cells generated signals that increased with VOR gain, while Gv Pk cells generated signals that increased as the gain of the VOR decreased. The eye velocity signals generated by both types of Pk cell were proportionally reduced if eye movements were suppressed and were significantly reduced in the absence of a visual target. These signals were apparently not used to suppress the VOR, since they were related primarily to unsuppressed eye velocity during VOR cancellation. The head velocity-related signals of Gv Pk cells were inversely proportional to eye velocity during VOR cancellation and led eye velocity suppression when the head was passively perturbed during fixation of a head stationary target and thus could be used to cancel the VOR.
Effects of unilateral muscimol injection into the FLR on VOR cancellation and smooth pursuit
In two monkeys, small injections of muscimol were made into a caudal region of the ventral paraflocculus where horizontal Gv Pk cells were concentrated. The muscimol injections were carried out only after single-unit recordings had been completed, and a map of the FLR had been constructed based on encountered eighth nerve axons and other prominent adjacent landmarks (see METHODS).
After recording behavioral responses during smooth pursuit, VOR and VOR cancellation in both head-restrained and head-free conditions, 1.25 µl of a 2% muscimol solution was injected. Behavioral responses during sinusoidal experiments were then recorded over a period of several hours. During this time the amplitude of the slow phase of spontaneous nystagmus in the dark and the gain of the VOR in the presence and absence of a target were carefully monitored to determine whether the muscimol had diffused to the vestibular nuclei. In both monkeys a small (3-8°/s) spontaneous nystagmus began to appear 10-15 min after completion of the injection. In one monkey this spontaneous nystagmus increased to 8°/s in the ipsilateral direction and 1°/s in the downward direction. In the other monkey the spontaneous nystagmus was 5°/s in the contralateral direction. The gain of the VOR in the dark was unaffected by muscimol injection in both monkeys.
The earliest detectable effect of muscimol injection on visual or
vestibular evoked eye movements was a decrease in the gain of the
ipsilateral optokinetic following response evoked by rotation of a
striped pattern-projection drum mounted above the monkeys head. No
attempt was made to study this behavior in detail. The effects of
muscimol injection on head-restrained smooth ocular pursuit, VOR
cancellation, and VOR will be presented here, and the effects of the
injections on responses recorded in the head-free condition will be
presented in the accompanying paper (Belton and McCrea
2000).
The changes in smooth pursuit eye movements, VOR cancellation, and WBR resulting from muscimol injection are shown in Fig. 9. The first column (A1-A3) illustrates records of eye velocity evoked in each condition just prior to muscimol injection. The second column (B1-B3) contains sample records recorded 40-60 min after the injection. The records in the last column (C1-C3) are the averaged, desaccaded eye velocity before (dark filled traces) and after (lightly shaded traces) injection of muscimol. The gain of smooth pursuit eye movements declined gradually from a preinjection value of 0.84 to <0.50 following muscimol injection (Fig. 9, A1-C1). These smooth pursuit eye movements were superimposed on the spontaneous nystagmus, so pursuit gain in each monkey was higher in one direction than in the other. However, the reduction in pursuit eye velocity was bilateral in both monkeys. The gain of the VOR evoked by WBR in the presence of an earth stationary target was reduced in amplitude by approximately 10% (Fig. 9, A3-C3). The gain of the VOR in the dark was unchanged.
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VOR cancellation was strongly affected by muscimol injection in both animals. Within 30 min after the injection, the gain of the eye movements evoked during VOR cancellation increased from 0.1 to more than 0.5 (Fig. 9, A2-C2). The monkey was able to keep its eye position within 2° of the head stationary target only by generating numerous saccades. Slow phase eye velocity increased during both ipsilateral and contralateral turntable rotations, but it was slightly larger in the direction of the spontaneous nystagmus. The effect of muscimol on VOR cancellation developed earlier than the deficit in smooth pursuit eye movements and recovered earlier.
In sum, a unilateral injection of muscimol in the FLR produced a bilateral deficit in the ability to produce smooth pursuit eye movements and to suppress the VOR. It also produced a small decrease in the gain of compensatory eye movements evoked by WBR in the presence of a visual target.
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DISCUSSION |
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Purkinje cells in the flocculus and ventral paraflocculus are an
important part of the neural substrate involved in producing visual
following responses and in modifying the gain of the VOR (Fukushima et al. 1996, 1999
;
Lisberger and Fuchs 1978a
; Miles et al.
1980
; Noda and Suzuki 1979
; Waespe and
Henn 1981
; Waespe et al. 1983
). However, a
moving visual target can be followed with different combinations of
eye, head, and trunk movements for matching the speed of the gaze in
space to that of the image. We had two questions when we began our
experiments. One was whether Pk cells in the FLR play a more general
role in gaze control when head and trunk movements contribute to gaze
velocity. The other asked what part the FLR has in canceling VOR eye
movements during passive or active, i.e., imposed or voluntary head
movements. In this study we compared the contribution of the FLR of the
squirrel monkey to control of gaze during pursuit eye movements and
during passive whole body rotation. We found that most Purkinje cells whose firing behavior was related to smooth pursuit eye movements were
also sensitive to eye velocity when passive rotation of the head
contributed to smooth tracking. Approximately half of these cells were
also sensitive to head velocity, but this signal was usually half as
large as the eye velocity signal.
Although the firing rate of most Pk cells was modulated during passive
whole body rotation, the output of the squirrel monkey FLR is
apparently balanced in such a way that it has little net effect on the
VOR in the absence of visual targets. This idea is supported by three
observations. Pk cells whose firing rate was related to contralateral
eye velocity were almost as frequently encountered as Pk cells that
were related to ipsilateral eye velocity. Second, the modulation in
firing rate of most Purkinje cells during WBR was absent or
significantly reduced when a target was absent, while the gain of the
VOR was essentially unaffected by removal of a target. Finally, as
noted by Highstein and colleagues (Partsalis et al.
1995; Zhang et al. 1995b
), inactivation of the
FLR had little effect on the VOR.
If the FLR has little effect on the VOR in the absence of a visual
target or during fixation of earth stationary targets that are at a
distance, it is clearly necessary for changing the gain of the VOR when
the eye velocity required to fixate a visual target is different from
head velocity (Waespe et al. 1983; Zee et al. 1981
). The firing rate of all FLR Pk cells is profoundly
modified during VOR cancellation. When squirrel monkeys suppressed
their VOR the eye velocity signals produced by Ev and Gv Pk cells were also suppressed. In addition, the modulation in Gv Pk cell output reversed in direction; presumably this was because vestibular inputs to
those cells were not opposed by a concomitant eye velocity signal.
These modifications in the output of the FLR were apparently necessary
for VOR cancellation, since the ability to suppress the VOR was
significantly compromised when muscimol was injected. Similar
observations have been made previously in squirrel monkeys and other
primates (Partsalis et al. 1995
; Takemori and
Cohen 1974
; Waespe et al. 1983
; Zee et
al. 1981
; Zhang et al. 1995b
).
Mixture of different Pk cell types in the FLR
The regions of the vestibular nuclei that give rise to the
horizontal canal-related VOR receive inputs from Purkinje cells distributed in a rostrocaudal strip of cortex that extends throughout the flocculus and ventral paraflocculus (Balaban et al.
1981; Belknap and McCrea 1985
; Langer et
al. 1985
; Voogd et al. 1996
). Both Ev and Gv Pk
cells were in every part of the FLR explored, which included all but
the most caudal-medial folium of the flocculus. On some probes Ev and
Gv Pk cells were found on the same tract within less than 1 mm of one
another. The results do not support the idea that the flocculus and
ventral paraflocculus contain fundamentally different types of Purkinje
cells (Nagao 1992
).
A mixture of Ev and Gv Pk cell types has been observed in other
species. In goldfish, Ev and Gv Pk cells as well as a third class of
cell, related only to head velocity, have been found (Pastor et
al. 1994). In the rabbit, most of the Pk cells in the flocculus
are of the Ev Pk type (Ghelarducci et al. 1975
;
Leonard and Simpson 1986
), although some may have head
velocity signals (Nagao 1990
). Two types, comparable to
the Ev and Gv types described in this study, have been found in the cat
(Cheron et al. 1997
; Fukushima et al.
1996
). Although most studies in rhesus monkeys have focused on
Gv Pk cells, the presence of Ev Pk cells in the FLR has often been
noted (Fukushima et al. 1999
; Kahlon and
Lisberger 1997
; Lisberger and Fuchs 1978a
;
Miles et al. 1980
; Raymond and Lisberger
1997
). In early studies as many as a quarter of the Purkinje
cells in the FLR of the rhesus monkey were Ev Pk cells (Lisberger and Fuchs 1978a
; Miles et al.
1980
).
While the primary difference between Ev Pk cells and Gv Pk cells was their sensitivity to head velocity, the two classes of cells differed in other respects. Ev Pk cells were equally likely to be related to ipsilateral or contralateral eye movements while only a minority of the Gv Pk cells was sensitive to contralateral eye and head movements (29%). Ev Pk cells generated signals during pursuit eye movements that lagged eye velocity substantially, while the signals of Gv Pk cells were in phase with eye velocity. Ev Pk cells tended to be more sensitive to ocular pursuit than Gv Pk cells. Finally, the eye movement signals generated by Ev Pk cells were delayed when the head was passively perturbed during fixation of a head-stationary target, while the responses of Gv Pk cells led eye velocity suppression.
The different responses of different classes of Pk cell might be
presumed to be due to different afferent inputs. However, we were not
able to detect a clear segregation of Ev and Gv cells, which suggests
that the anatomical organization of those inputs may not be grossly
detectable. A similar lack of segregation was described by
Fukushima et al. (1999) in the Japanese macaque. Consequently, it seems unlikely that different Purkinje cell types reside in different folia of the ventral paraflocculus or the flocculus, or are located exclusively in one rostro-caudal region. On
the other hand, if different classes of Pk cells were confined to
parasagittal microzones extending throughout the FLR, it is possible
that a single microelectrode tract might pass from one microzone to
another. Such a level of organization might not have been detected with
the methods we used.
Both Ev and Gv Pk cells appear to be involved in producing visual
following reflexes, smooth pursuit eye movements, and plastic changes
in the VOR (Raymond and Lisberger 1997,
1998
). However, the differences in the responses of Ev
and Gv Pk cells during cancellation of the VOR suggest that each cell
type has a different role in controlling eye movements. Gv Pk cells
provide a gated vestibular reafferent input to VOR pathways that can be
used to cancel the VOR, whereas during VOR suppression the eye movement signals normally produced by Ev Pk cells are removed. The relatively small size of the vestibular signal in squirrel monkey Gv Pk cells and
the relatively large fraction of Ev Pk cells encountered compared with
rhesus monkeys probably reflect important differences in the strategy
each species uses to modify signal processing in VOR pathways. The
pursuit eye velocity signals generated by Ev Pk cells are clearly not
used to suppress VOR oculomotor signals since their firing behavior is
related only to unsuppressed eye velocity during VOR cancellation.
Target-dependent responses of FLR Pk cells
The eye velocity-related signals produced by FLR Pk cells were
strongly influenced by the presence of a foveal target. Target-related activity could account for 50% or more of observed Purkinje cell modulation. An analogous target sensitivity has been observed from
neurons receiving input from the flocculus in the superior vestibular
nucleus of the squirrel monkey (Zhang et al. 1995a). When those monkeys were rotated within a lighted optokinetic drum, as
against simple rotation in darkness, unit response amplitudes increased. Similar phenomena have been previously described in cats and
rabbits (Fukushima et al. 1996
; Ghelarducci et
al. 1975
), although in the rabbit this may be attributed in
some cases to a retinal slip signal (Leonard 1986
).
Neurons in many regions of the brain, including several precerebellar
nuclei, exhibit target-dependent oculomotor responses. Target-dependent
eye movement signals have been observed in many regions of the cerebral
cortex that are involved in controlling smooth pursuit eye movements
(Bizzi and Schiller 1970; Bruce and Goldberg
1985
; Komatsu and Wurtz 1988
; Newsome et
al. 1988
; Sakata et al. 1980
). The target
dependence of eye movement signals in the FLR presumably reflects the
predominant role of this structure in modifying signal processing in
VOR pathways as a function of visual context (Goldreich et al.
1992
; Grasse and Lisberger 1992
; Robinson
1965
; Robinson et al. 1986
; Stahl and
Simpson 1995
).
It is doubtful that this effect is due to a retinal slip signal. There
was little evidence of an augmentation of Pk simple spike activity when
target slip on the retinal changed during periods of varying pursuit
efficacy (see also Suh et al. 1999). The visually driven
changes in Pk firing rate observed by Stone and Lisberger were in the
opposite direction from that reported here. During
ON-direction pursuit for ipsilaterally responsive Gv Pk,
the peak activity was reduced, not increased by the visual component of
firing rate (Stone and Lisberger 1990
). Neither is the
target sensitivity likely to be the influence of olivary inputs. When
Leonard inactivated the inferior olive using lidocaine in the rabbit,
only DC (background) shifts of simple spike activity were observed. No
changes in simple spike eye movement signal gain were evident
(Leonard 1986
). As for full field slip signals, the
results from the VOR no-target experiments (Fig. 8), one where the room
lights were on, the other where they were off, demonstrated essentially
unchanging firing rate modulation across the two conditions.
Role of the FLR in VOR cancellation
Squirrel monkeys have at least two means of canceling or
suppressing the VOR during passive whole body rotation (Cullen
et al. 1991, 1993
). One mechanism involves the
use of visual feedback to suppress the VOR. The visual feedback
mechanism depends on retinal image slip signals to produce VOR
suppression and is closely related to mechanisms that produce visual
following reflexes and smooth pursuit eye movements (McCrea and
Cullen 1992
). A second, nonvisual mechanism is also utilized
that produces a parametric reduction in the gain of passive head
movement signals in central VOR pathways (Cullen et al.
1991
; Lisberger 1990
; Robinson
1982
). It has a shorter latency than the visual mechanism, and
contributes 30-50% of the reduction in sensitivity of central VOR
pathways to head movements during VOR cancellation (Cullen et
al. 1993
). The FLR is clearly an essential part of the central
neural substrate that mediates the ability to cancel or suppress the
VOR during passive whole body rotation (Zhang et al.
1995b
). It seems likely that it is part of the neural substrate
that mediates both visual and nonvisual VOR suppression
(Tomlinson and Robinson 1981
).
The contribution of FLR Pk cells to VOR cancellation appears to be more complex than the simple addition of a pursuit signal to central VOR pathways. The output signals produced by Gv Pk cells during VOR cancellation are only half as large as those observed during pursuit, and the pursuit-related signals produced by Ev Pk cells are abolished when the VOR is canceled. Thus the output of the FLR during VOR cancellation is best characterized as a reduction in target-contingent eye velocity signals plus the addition of a head velocity signal. The former may be approximately three times as important as the latter (Fig. 10). The head velocity signal produced by Gv Pk cells is demonstrable at a short latency, which suggests that these cells are involved in nonvisual and well as visual mechanisms for canceling the VOR.
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The nonvisual mechanism for VOR cancellation may be part of a
general mechanism for context-dependent modification of the gain of the
VOR (McCrea et al. 1996). The head movement signals produced by secondary vestibular neurons involved in producing the VOR
are not only modified when the reflex is suppressed, but also when gain
or phase of the reflex is modified as a function of viewing distance
(Chen-Huang and McCrea 1998
, 1999
). We
have previously suggested the possibility that these modifications involve gated feedback of inhibitory or excitatory vestibular signals
to VOR pathways as a function of behavioral context. These transformed
vestibular signals correspond to central eye velocity commands when
imposed on secondary VOR pathways and are thus strongly correlated with
slow phase eye velocity. It seems likely that the FLR is not only an
important component of the central pathways for mediating visual
feedback-induced modification of signal processing in VOR pathways, but
also part of a central mechanism that adds or subtracts vestibular and
eye velocity signals to VOR pathways as a function of behavioral context.
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ACKNOWLEDGMENTS |
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This work was supported by National Institutes of Health Grants RO1-EY-08041 and P60-DC-02072.
Present address of T. Belton: Dept. of Physiology and Neuroscience, New York University Medical Center, 550 First Ave., New York, NY 10016.
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FOOTNOTES |
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Address for reprint requests: R. A. McCrea, Dept. Neurobiology, Pharmacology and Physiology, University of Chicago, 5830 So. Ellis Ave., MC 0926, Chicago, IL 60637 (E-mail: ramccrea{at}midway.uchicago.edu).
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 3 January 2000; accepted in final form 23 May 2000.
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REFERENCES |
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