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The Journal of Neuroscience, November 1, 1998, 18(21):9112-9129
Neural Learning Rules for the Vestibulo-Ocular Reflex
Jennifer L. Raymond and Stephen G. Lisberger Howard Hughes Medical Institute, Department of Physiology and W. M. Keck Foundation Center for Integrative Neuroscience, University of California, San Francisco, California 94143
ABSTRACT
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Abstract
Introduction
Mechanisms for the induction of motor learning in the vestibulo-ocular reflex (VOR) were evaluated by recording the patterns of neural activity elicited in the cerebellum by a range of stimuli that induce learning. Patterns of climbing-fiber, vestibular, and Purkinje cell simple-spike signals were examined during sinusoidal head movement paired with visual image movement at stimulus frequencies from 0.5 to 10 Hz. A comparison of simple-spike and vestibular signals contained the information required to guide learning only at low stimulus frequencies, and a comparison of climbing-fiber and simple-spike signals contained the information required to guide learning only at high stimulus frequencies. Learning could be guided by comparison of climbing-fiber and vestibular signals at all stimulus frequencies tested, but only if climbing fiber responses were compared with the vestibular signals present 100 msec earlier. Computational analysis demonstrated that this conclusion is valid even if there is a broad range of vestibular signals at the site of plasticity. Simulations also indicated that the comparison of vestibular and climbing-fiber signals across the 100 msec delay must be implemented by a subcellular "eligibility" trace rather than by neural circuits that delay the vestibular inputs to the site of plasticity. The results suggest two alternative accounts of learning in the VOR. Either there are multiple mechanisms of learning that use different combinations of neural signals to drive plasticity, or there is a single mechanism tuned to climbing-fiber activity that follows activity in vestibular pathways by ~100 msec.
Key words: vestibulo-ocular reflex; plasticity; horizontal gaze velocity Purkinje cells; climbing fibers; parallel fibers; cerebellar LTD
INTRODUCTION
A major goal in neuroscience is to link systems-level analyses of learning with cellular analyses of plasticity. At the interface of these two levels of inquiry is the question of what patterns of neural activity are necessary and sufficient to induce synaptic plasticity in the awake behaving animal. Such neural signals must transduce the sensory stimuli that guide learning into the cellular changes that encode memory. In the present study, we ask what patterns of neural activity drive plasticity in vivo by examining the neural signals present during stimuli that induce motor learning in the vestibulo-ocular reflex (VOR).
The VOR stabilizes images on the retina by causing eye rotation in the opposite direction to head turns. Motor learning calibrates the VOR by modifying the amplitude of the reflex whenever retinal image motion is associated persistently with head turns (Gonshor and Melvill Jones, 1973
; Ito et al., 1974
Learning in the VOR is associative: it depends on the pairing of head turns and image motion. Therefore, one would expect the information that guides learning in the VOR to be carried in the correlation between two or more neural signals. Three likely candidates for the neural signals that guide learning in the VOR are the activity in vestibular pathways, activity in climbing fibers carrying visual signals, and the simple-spike activity in Purkinje cells carrying visual, vestibular, and eye movement signals (see Figs. 2, 4, left). All three of these neural signals are present at the putative sites of plasticity in the circuit for the VOR, which are in the floccular complex of the cerebellar cortex and in the vestibular nuclei (for review and citations to the relevant literature, see duLac et al., 1995
In the present study, we constrain hypotheses regarding the neural signals that guide cerebellum-dependent learning by examining the patterns of climbing-fiber, simple-spike, and vestibular signals present during a range of stimuli that induce learned decreases or increases in the gain of the VOR. We focus on a well studied subclass of Purkinje cells called the horizontal gaze velocity Purkinje cells (HGVPs) (Lisberger and Fuchs, 1978a
MATERIALS AND METHODS
Experiments were conducted on two male rhesus monkeys that had been trained to perform a visual fixation task (Wurtz, 1969
During experiments, each monkey sat in a specially designed primate chair, to which his implanted head holder was secured. Platinum-iridium electrodes were used to make recordings from Purkinje cells in the floccular complex of the cerebellum (flocculus and ventral paraflocculus) (Gerrits and Voogd, 1989
After a Purkinje cell was isolated, it was first characterized by its responses (1) during the smooth pursuit eye movements evoked by sinusoidal motion of a small visual target along a horizontal or vertical axis at 0.5 Hz, ±31.4°/sec (position amplitude ±10°) and (2) as the monkey canceled his VOR by tracking a spot that moved exactly with sinusoidal head rotation about a vertical axis at 0.5 Hz, ±31.4°/sec. For these initial behavioral conditions, the visual stimulus was a small spot subtending 0.5° of visual angle. The present work focuses on HGVPs, a well studied class of Purkinje cells in the floccular complex (Lisberger and Fuchs, 1978a
Recordings were made from HGVPs under conditions that had been shown in a previous study to cause learning in the VOR (Raymond and Lisberger, 1996
For each frequency of sinusoidal vestibular stimulation, ×0 and ×2 stimuli were alternated, and each stimulus was presented for 60 to 120 sec. Recordings were made when the gain of the VOR was close to 1.0, and the ×0 and ×2 stimuli were not presented for long enough to cause measurable changes in the gain of the VOR in the dark. Thus, Purkinje cell responses were recorded under conditions that cause learning but were not followed as the gain of the VOR was modified. To maintain a constant level of alertness and to keep the visual stimulus approximately centered in the visual field during vestibular stimulation, monkeys were rewarded at intervals of 1.5-4 sec for keeping their gaze within ±10° of the spot in the center of the visual stimulus. This reward contingency was the same as that used previously to study behavioral changes in the VOR (Raymond and Lisberger, 1996
Electrodes were introduced daily and driven by a hydraulic microdrive through the cerebral cortex toward the cerebellum. Entry into the cerebellum was recognized by a large increase in background activity and the presence of the complex spikes of Purkinje cells. Entry into the floccular complex was signaled by the presence of background activity related to eye movements and confirmed by the location relative to landmarks such as the vestibular nerve and bone. We did not perform histology to verify the location of the electrodes, because HGVPs are known to localize to the floccular complex (Lisberger and Fuchs, 1978a
The responses of individual Purkinje cells were isolated by careful movements of the electrode and then followed for up to 1 hour. Voltages related to eye position, eye velocity, head velocity, and visual stimulus position were recorded during the experiment at 500 Hz/channel. An eye velocity signal was obtained by using an analog circuit to differentiate the eye position output from the eye coil electronics, and the head velocity signal was obtained from a tachometer attached to the shaft of the turntable. The simple-spike activity of Purkinje cells was triggered with a hardware window discriminator, and the times of the resulting pulses were recorded to the nearest 10 µsec. In addition, unit activity was sampled at 50 kHz, and off-line spike sorting with time and amplitude windows was used to discriminate complex spikes and record their time of occurrence to the nearest 1 msec. Of our total sample of 54 HGVPs, complex spikes were analyzed for the 26 in which the complex-spike wave form could be clearly and reliably differentiated from the simple-spike wave form. In 15 HGVPs, the complex spike could be seen or heard, but not discriminated with confidence from the simple spikes in all records. In the remaining 13 Purkinje cells, complex spikes were not observed, but the cells were deemed likely to be Purkinje cells because of their simple-spike wave form, their irregular simple-spike firing rate, the ability to record the cells through several hundred micrometers of cerebellum, and, in some cases, their characteristic injury discharge at the end of the recording.
The data were analyzed after the experiment by aligning the records on the negative-to-positive zero crossings of sinusoidal head velocity or visual stimulus position. For ×0 and ×2 stimuli, tracking was not a criterion, so that all stimulus cycles were included in the analysis. For pursuit and cancellation of the VOR at 0.5 Hz, only cycles with good tracking were included in the analysis. Each cycle was divided into 64 equal-length bins, and head velocity, simple-spike firing rate, and complex-spike firing rate were averaged. The amplitude of modulation and phase of the responses were estimated as the amplitude and phase of the fundamental components provided by Fourier analysis of the averages.
RESULTS
To evaluate which neural signals guide the induction of learning in the VOR, we compared the patterns of neural activity present at the putative sites of plasticity during stimuli that induce learned decreases and increases in the gain of the VOR (Fig. 1). Conditions that induce a learned decrease in gain were created by pairing a vestibular stimulus with a visual stimulus that moved exactly with the head (×0 stimulus). Conditions that induce a learned increase in gain were created by pairing a vestibular stimulus with a visual stimulus that moved exactly opposite to the head (×2 stimulus). We performed a pairwise analysis of the simple-spike, climbing-fiber, and vestibular signals present during ×0 and ×2 stimuli to determine whether each pair of signals contained the information required to guide learning.
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Figure 1. Stimuli that induce learned decreases (×0, A) and increases (×2, B) in the gain of the VOR. From top to bottom, the traces are eye velocity with respect to the orbit, angular head velocity in space, visual stimulus velocity in space, and gaze velocity in space. Gaze velocity was computed as the sum of head velocity in space plus eye velocity in the orbit. In all traces, upward deflections represent leftward position or velocity (L); downward deflections represent rightward position or velocity (R). The brief deflections in the eye and gaze velocity traces are caused by saccadic eye movements; their amplitudes have been cropped. The frequency of the stimuli is 0.5 Hz.
We used two criteria for evaluating whether a particular combination of neural signals could provide suitable guidance for the cellular mechanisms of learning in the VOR. First, signals that guide learning must discriminate ×0 stimuli, which decrease the gain of the VOR, from ×2 stimuli, which increase the gain of the VOR. Patterns of neural activity that are the same during both stimulus configurations would contain no information about whether the gain should decrease or increase and therefore could not be responsible for the opposite learned changes in the VOR induced by the ×0 and ×2 stimuli. This criterion is illustrated by previous analyses of the correlation between the vestibular stimulus and simple-spike activity in HGVPs (Lisberger and Fuchs, 1978a
In the present paper, we applied an additional criterion: if there is a single mechanism that mediates learning in the VOR, then a single pair of neural signals should evince similar patterns of activity during all stimuli that induce similar learned changes in the VOR. For example, ×0 stimuli are effective at inducing learned decreases in the gain of the VOR, and ×2 stimuli are effective at inducing learned increases in the gain of the VOR for sinusoidal stimulus frequencies up to at least 5 Hz (Raymond and Lisberger, 1996
We examined three pairs of neural signals: simple-spike activity in Purkinje cells versus vestibular signals; climbing-fiber activity versus vestibular signals; and simple-spike versus climbing-fiber activity. We were able to evaluate all three pairs simultaneously by recording from Purkinje cells under conditions in which we controlled the vestibular inputs. Simple-spike activity was recorded directly from the Purkinje cells. Climbing-fiber activity was recorded by isolating complex spikes from recordings of Purkinje cells, because complex spikes are driven in a one-to-one manner by spikes in the climbing-fiber input to the Purkinje cell. We did not record the vestibular inputs to either the brainstem or cerebellar site of plasticity directly. Because we controlled the vestibular stimulus, however, we could be confident that these inputs were identical for ×0 and ×2 stimuli at a particular frequency. As a result, comparison of Purkinje cell complex-spike or simple-spike discharge with the head velocity stimulus at a particular frequency reveals whether learning could be guided by correlating climbing-fiber responses or simple-spike activity in Purkinje cells with the activity of any set of vestibular neurons. Here, we present the results from the HGVP subclass of Purkinje cells (Lisberger and Fuchs, 1978a
Correlation of Purkinje cell simple-spike activity with the vestibular stimulus during learning
The histograms in Figure 2 show the simple-spike activity in a typical HGVP during stimuli that, if prolonged, would have induced learned changes in the gain of the VOR. All four stimuli caused modulation of the simple-spike activity around a fairly high-average firing rate of ~70-80 spikes/sec. Because of the high spontaneous firing rate of the HGVPs, we analyze the modulation of simple-spike activity rather than absolute levels of activity. At 0.5 Hz, the timing of elevated simple-spike activity relative to the vestibular stimulus discriminated the ×0 stimulus configuration from the ×2 stimulus configuration. When a 0.5 Hz vestibular stimulus was paired with ×0 visual stimulus motion, peak simple-spike activity in the HGVP coincided with ipsiversive head motion (Fig. 2A, vertical dashed line, Ipsi). When the same vestibular stimulus was paired with ×2 visual stimulus motion, peak simple-spike activity coincided with contraversive head motion (Fig 2C, vertical dashed line, Contra). Simple-spike activity also was modulated during the 5 Hz stimuli. However, at this frequency, the relative timing of the vestibular stimulus and simple-spike activity in the HGVP failed to discriminate the ×0 stimulus from the ×2 stimulus. Simple-spike activity peaked during contraversive head velocity, regardless of whether the stimulus induced a decrease (Fig. 2B, ×0) or increase (Fig. 2D, ×2) in the gain of the VOR.
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Figure 2. Histograms showing the simple-spike activity recorded in a representative Purkinje cell during stimuli that induce learned decreases (×0, A, B) and increases (×2, C, D) in the gain of the VOR. Head velocity, Angular head velocity in the horizontal plane. Vertical dashed lines mark peak contraversive and ipsiversive head velocity. Note the different time scales in the left (A, C) and right (B, D) panels, which show data for sinusoidal stimuli at 0.5 and 5 Hz, respectively. Twenty to 500 stimulus cycles were averaged to obtain each histogram. The simplified circuit diagram on the left highlights the loci of vestibular and Purkinje cell (PC) simple-spike signals in the circuit for the VOR.
Figure 3 summarizes the correlation of the vestibular stimulus with simple-spike activity recorded in the entire sample of 54 HGVPs. Responses are plotted in polar coordinates, at a distance from the origin corresponding to the amplitude of response modulation and an angle corresponding to the phase of peak simple-spike activity relative to the vestibular stimulus. Simple-spike responses in phase with peak ipsiversive head velocity are plotted in Figure 3 to the right of the origin, responses in phase with peak contraversive head velocity are plotted to the left of the origin, and clockwise rotation around the graph represents increased phase lead. Thus, in these polar plots, the phase reflects the relative timing of the simple-spike and vestibular signals. The key question is whether the responses to ×0 and ×2 stimuli plot in separate parts of each graph or whether the responses during ×0 and ×2 stimuli are similar and plot together.
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Figure 3. Summary of Purkinje cell simple-spike responses, plotted relative to the vestibular stimulus. Each plot compares responses during ×0 stimuli and ×2 stimuli at the single frequency indicated in the bottom right quadrant. Each point represents the simple-spike activity recorded in a single Purkinje cell, plotted in polar coordinates with distance from the origin corresponding to the amplitude of response modulation and an angle corresponding to the phase shift between peak simple-spike activity and head velocity. Responses in phase with peak ipsiversive head velocity are plotted to the right of the origin, responses in phase with peak contraversive head velocity are plotted to the left of the origin, and clockwise rotation around the graph represents increased phase lead. An individual Purkinje cell contributed two symbols for each stimulus frequency: a + (monkey D) or X (monkey E) symbol for the ×0 stimulus, and a filled square (monkey D) or filled triangle (monkey E) for the ×2 stimulus. The plots in A-D are on the same scale, with inner and outer circles representing 10 simple spikes/sec (SS/s) and 50 simple spikes/sec, respectively.
At 0.5 Hz (Fig. 3A) and 2 Hz (Fig. 3B), the patterns of simple-spike and vestibular signals present during the ×0 stimuli (Fig. 3, + and X symbols) were clearly different from the patterns of signals present during the ×2 stimuli (Fig. 3, filled symbols). Responses to the ×0 and ×2 stimuli form distinguishable, almost nonoverlapping populations that plot on opposite sides of each graph. Thus, the timing of the simple spikes relative to the vestibular stimulus can discriminate ×0 from ×2 stimuli at these low frequencies. In contrast, at 5 Hz (Fig. 3C) and 10 Hz (Fig. 3D), the patterns of simple-spike and vestibular signals present during the ×0 stimulus configuration were quite similar to those present during the ×2 stimulus configuration. The polar plots in Figure 3 show extensive overlap in the response populations, even for the 5 Hz stimuli, which produced simple-spike responses of amplitudes similar to those produced by lower-stimulus frequencies. This indicates that the relative timing of simple-spike and vestibular signals cannot distinguish the ×0 stimuli from the ×2 stimuli at frequencies of 5 Hz or above.
Correlation of complex-spike activity with the vestibular stimulus during learning
The histograms in Figure 4 illustrate the relationship between the vestibular stimulus and the complex-spike activity of one HGVP during ×0 and ×2 stimuli at 0.5 and 5 Hz. Complex-spike activity precisely reflects the activity of the climbing-fiber input to the HGVP, because spikes in the climbing fiber produce complex spikes in the Purkinje cell target in a one-to-one manner. Complex-spike activity was modulated during all four stimuli and, at each frequency, satisfied the criterion that comparison with the vestibular stimulus discriminated the stimuli that decreased (×0) versus increased (×2) the gain of the VOR. For example, during the 5 Hz vestibular stimulus, complex-spike activity was in phase with ipsiversive head velocity when the gain of the VOR needed to decrease (Fig. 4B, ×0) but was in phase with contraversive head velocity when the gain needed to increase (Fig. 4D, ×2). However, the phase of the peak complex-spike response relative to the vestibular stimulus depended not just on whether the stimulus would induce a decrease or increase in the gain of the VOR but also on the stimulus frequency. During the ×0 stimuli, for example, complex-spike activity was in phase with ipsiversive head velocity at 5 Hz (Fig. 4B) but was in phase with contraversive head velocity at 0.5 Hz (Fig. 4A).
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Figure 4. Histograms showing climbing-fiber activity during stimuli that induce learned decreases (×0, A, B) and increases (×2, C, D) in the gain of the VOR. Climbing-fiber activity was recorded as complex spikes in the representative Purkinje cell whose simple-spike responses are shown in Figure 2. Climbing-fiber responses from 20-500 stimulus cycles were averaged to obtain each histogram. Note the different time scales in the left (A, C) and right (B, D) panels, which show data for sinusoidal stimuli at 0.5 and 5 Hz, respectively. Vertical dashed lines mark peak contraversive and ipsiversive head velocity. The simplified circuit diagram on the left highlights the loci of vestibular signals and climbing-fiber (CF) signals in the circuit for the VOR. IO, Inferior olive.
Figure 5 uses polar plots to summarize the correlation of the vestibular stimulus with the complex-spike responses in all 26 HGVPs in which the complex spike was isolated. For each stimulus frequency, the complex-spike responses to the ×0 and ×2 stimuli plot on opposite sides of the graph, forming distinguishable, almost nonoverlapping populations. However, in the different graphs, the phase of the complex-spike responses relative to the vestibular stimulus rotated as a function of stimulus frequency, indicating that the relative phase of climbing-fiber and vestibular signals was not similar for all stimuli that produced similar learned changes in the gain of the VOR. During the ×2 stimuli (Fig. 5, filled symbols), for example, peak complex-spike activity led ipsiversive head velocity slightly at 0.5 Hz (Fig. 5A), it lagged ipsiversive head velocity at 2 and 10 Hz (Fig. 5B,D), and it was almost exactly out of phase with ipsiversive head velocity at 5 Hz (Fig. 5C). Similarly, complex-spike responses to ×0 stimuli at different frequencies peaked during different phases of the vestibular stimulus (Fig. 5, + and X symbols).
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Figure 5. Summary of climbing-fiber responses, plotted relative to the vestibular stimulus. A-D, Climbing-fiber responses to stimulus frequencies of 0.5, 2, 5, and 10 Hz. Responses are plotted in polar coordinates, with distance from the origin corresponding to the amplitude of response modulation and an angle corresponding to the phase shift between peak climbing-fiber activity and head velocity. Responses in phase with peak ipsiversive head velocity are plotted to the right of the origin, responses in phase with peak contraversive head velocity are plotted to the left of the origin, and clockwise rotation around the graph represents increased phase lead. An individual climbing fiber contributed two symbols for each stimulus frequency: a + (monkey D) or X (monkey E) symbol for the ×0 stimulus, and a filled square (monkey D) or a filled triangle (monkey E) for the ×2 stimulus. R×0 marks the point in the vestibular stimulus leading peak contraversive head velocity by 46°, and R×2 marks the point in the vestibular stimulus leading peak ipsiversive head velocity by 46°. Open arrows show the predicted phase at each frequency for a fixed delay in the climbing-fiber response of 122 msec from R×0. Filled arrows show the predicted phase at each frequency for a fixed delay in the climbing-fiber response of 122 msec from R×2. In all panels, inner and outer circles represent 1 climbing-fiber spike per second (CFR/s) and 2 climbing-fiber spikes/sec, respectively. Note the difference in scale from Figure 3.
The change in phase of the complex-spike responses with frequency can be described by a fixed time delay between a fixed reference point in the vestibular stimulus and peak complex-spike activity. We fit the phases of the complex-spike responses to ×0 and ×2 stimuli at 0.5, 2, 5, and 10 Hz with the following equations:
(1) where
(2) ×0,
and
, T is a fixed time delay, R×0 is the reference point for ×0 stimuli, R×2 is the reference point for ×2 stimuli, and R×2 is constrained to be exactly 180° opposite R×0: R×2 = R×0 +
. We found that a fixed delay (T) of 122 msec and reference points on the vestibular stimulus leading peak contraversive (for R×0) and ipsiversive (for R×2) head velocity by 46° yielded the best fit. Thus, the frequency dependency of the complex spike responses is approximately consistent with the 100 msec latency between visual stimuli and complex-spike responses reported previously (Stone and Lisberger, 1990
The open and filled arrows in Figure 5 show the fixed time delay of 122 msec from R×0 and from R×2, respectively. The fixed delay translates into a progressively larger phase lag at higher frequencies (22°, 88°, 220°, and 439° at 0.5, 2, 5, and 10 Hz). Overall, the average peak complex-spike responses to ×0 stimuli at all four frequencies were well fit as occurring 122 msec after R×0 (Fig. 5, open arrows), and the average peak complex-spike responses to ×2 stimuli were well fit as occurring 122 msec after R×2 (Fig. 5, filled arrows). We constrained the reference points R×0 and R×2 to be 180° apart so that a single time delay would have the same meaning for both ×0 and ×2 stimuli. Although R×0 and R×2 were obtained by fitting the complex-spike responses, they correspond to points on the vestibular stimulus that coincide, within 30°, with peak activity of the primary afferents in the contralateral and ipsilateral vestibular nerves, respectively. On average, peak firing in the primary afferents leads peak ipsiversive head velocity by ~15° at 0.5 Hz and by ~55° at 8 Hz (Fernandez and Goldberg, 1971
Correlation of complex-spike and simple-spike activity during learning
Comparison of Figures 3 and 5 reveals that the correlation of simple-spike and complex-spike activity discriminates ×0 from ×2 stimuli during a subset, but not all of the stimulus frequencies tested. At 5 Hz, simple-spike and complex-spike activity were approximately in phase during the ×2 stimulus (Figs. 3C, 5C, filled symbols) and 180° out of phase during the ×0 stimulus (+ and X symbols). At 10 Hz (Figs. 3D, 5D), simple-spike and complex-spike activity were in phase during the ×0 stimulus and 180° out of phase during the ×2 stimulus. At 0.5 Hz (Figs. 3A, 5A) and 2 Hz (Figs. 3B, 5B), simple-spike and complex-spike activity were 180° out of phase during both ×0 and ×2 stimuli. Thus, the correlation of simple-spike and climbing-fiber signals discriminated stimuli that increase the gain of the VOR from stimuli that decrease the gain of the VOR at high stimulus frequencies, such as 5 or 10 Hz, but not at lower frequencies, such as 0.5 or 2 Hz. Even at the higher stimulus frequencies, the simple-spike and climbing-fiber signals failed the second criterion for signals that guide learning, of evincing similar patterns of activity during all stimuli that induce similar learned changes in the VOR.
Computational analysis of plasticity mechanisms driven by the correlation of climbing-fiber activity and vestibular signals
The only pair of signals examined that discriminated ×0 from ×2 stimuli at each stimulus frequency was the correlation of climbing-fiber (complex-spike) and vestibular signals. Therefore, this is the only pair of signals that potentially could guide learning across the full range of sinusoidal stimulus frequencies that induce learning. Moreover, the fits to Equations 1 and 2 suggest that a single plasticity mechanism must be tuned to climbing-fiber activity that follows activity in vestibular pathways by ~100 msec if it is to account for all motor learning in the VOR. To assess a number of factors that could affect this conclusion, we present a computational analysis of the features a plasticity mechanism must have to permit the correlation of climbing-fiber and vestibular signals to guide learning.
First, we must consider how the vestibular stimuli might be represented at the sites of plasticity. This issue is of particular importance in the cerebellar cortex, because the responses of vestibular parallel fibers have not been described, and the question of how to identify granule cell recordings in behaving animals has not been resolved. In vestibular primary afferents, sinusoidal vestibular stimuli are represented by sinusoidal modulation of firing rate. At frequencies of 0.5, 2, 5, and 10 Hz, firing rate leads ipsiversive head velocity by phases that average ~15°, 25°, 40°, and 60° (Fernandez and Goldberg, 1971
We demonstrate that a plasticity mechanism tuned to a 100 msec delay between its vestibular and climbing-fiber inputs is required to account for motor learning in the VOR, even if the vestibular inputs do exhibit a broad range of response phases. We further show that this tuning must be implemented in the plasticity mechanism itself and not by using neural circuits to delay the incoming vestibular signals.
Neural circuit model
In our simulations, we consider a single Purkinje cell with 36 vestibular parallel-fiber inputs, five of which are illustrated in Figure 6. We assume that each parallel fiber exhibits sinusoidal modulation of its firing rate during a sinusoidal head velocity stimulus. Each parallel fiber has a unique phase of peak activity, distributed evenly from
90° to +260° with respect to head velocity:
(3) where t is time, and
) correspond to parallel fibers with progressively more phase lag. Our simulations thus consider the full range of possible response phases in the vestibular parallel fibers.
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Figure 6. Schematic showing several simulated vestibular parallel-fiber (PF) inputs to a single Purkinje cell (PC). The trace above each parallel fiber shows its activity during sinusoidal head rotation about a vertical axis. The dashed vertical line marks the time of peak ipsiversive head velocity. Activity in PF lags peak ipsiversive head velocity by
Equations 4-7 below are a formal description of widely accepted principles about functional connectivity in the circuit for the VOR. We used these equations to calculate the predicted changes in the VOR resulting from changes in the weights of the vestibular inputs to the Purkinje cell from parallel fibers with different phases. We assume that the VOR-driven eye movement response before learning is equal in amplitude and opposite in direction to head velocity (H). Thus, during a sinusoidal vestibular stimulus of amplitude A, the prelearning VOR-driven eye movement is described by:
Positive values for H(t) and VORpre(t) represent ipsiversive head or eye velocities. The VOR-driven eye movement response after learning (VORpost) is equal to the sum of the prelearning VOR (VORpre) and the change in the VOR attributable to learning (
(4) VOR):
Activation of Purkinje cells in the floccular complex produces ipsiversive eye movement by inhibiting neurons in the direct VOR pathways through the brainstem (Baker et al., 1972
(5) where K is a constant >0 (K = 1.0 in all simulations).
(6) We can describe the learned change in activity of the Purkinje cell attributable to learned changes in the parallel-fiber weights as:
where w
(7) A critical feature of the circuit for the VOR captured in Equations 3-7 is that the timing of activity in a Purkinje cell will determine the effect of that activity on the gain of the VOR. Purkinje cell activity drives ipsiversive eye movement (or, equivalently, it reduces contraversive eye movement). Enhanced ipsiversive eye movement during contraversive head movement constitutes an increase in the gain of the VOR. Enhanced ipsiversive eye movement (reduced contraversive eye movement) during ipsiversive head movement constitutes a decrease in the gain of the VOR, and thus:
Increasing Purkinje cell activity during contraversive head movement increases the gain of the VOR.
Increasing Purkinje cell activity during ipsiversive head movement decreases the gain of the VOR.
The timing of Purkinje cell activity relative to head movement is determined by the balance of synaptic input from parallel fibers that fire at different phases of the head movement. Thus, if multiple parallel-fiber weights are changed, the effect on the VOR will depend on the change in the balance of synaptic strength in vestibular parallel fibers with different phases. A relative increase in the synaptic strength of parallel fibers that fire most during contraversive head velocity will increase the gain of the VOR. A relative increase in the synaptic strength of parallel fibers that fire most during ipsiversive head velocity will decrease the gain of the VOR. We will consider primarily the effects of synaptic depression rather than potentiation and the corresponding principles:
If depression is greater in the parallel fibers that fire most during contraversive head velocity, then the gain of the VOR decreases.
If depression is greater in the parallel fibers that fire most during ipsiversive head velocity, then the gain of the VOR increases.
Figures 7 and 8 illustrate the above principles by showing the predicted effects on the VOR for changes in the weights of individual parallel fibers with different phases. Figure 7 illustrates the values of the variables in Equations 3-7 during two cycles of a sinusoidal vestibular stimulus (H). In each panel, the synaptic weight of one of the 36 parallel fibers was decreased: PF0 in A, PF90 in B, and PF180 in C. In Figure 7, the bottom three traces show the predicted effects of changing the weight of that single parallel fiber on Purkinje cell activity during the vestibular stimulus (
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Figure 7. Predicted learned changes in the VOR for a reduction in the weight of parallel fibers that fire at different phases of the vestibular stimulus. Traces representing the variables in Equations 3-7 are shown for a reduction in the weight of a parallel fiber whose activity peaks during ipsiversive head velocity (A,
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Figure 8. Predicted learned changes in the gain (A) and phase (B) of the VOR, plotted as a function of the phase of the vestibular parallel fiber (PF) undergoing synaptic depression (LTD) (Eq. 7,
Figure 8 summarizes the changes in the gain (A) and the phase (B) of the VOR that are predicted for reductions in the weights of individual parallel fibers whose activity peaks at different phases of the vestibular stimulus. Changes in the gain and phase of the VOR were obtained by first computing VORpost(t) and measuring its amplitude and phase. The gain of the VOR after learning was then computed as the amplitude of VORpost(t) divided by the amplitude of H(t). This postlearning gain value was also equal to the change in VOR gain (post/pre), because the gain of the VOR before learning was assumed to be 1.0 (Eq. 4). Note that computation of VORpost(t) involves summation of multiple sine waves (Eqs. 3-7) and that the amplitude of VORpost(t) depends on both the amplitude and phase of those sine waves. In Equation 5, for example, the amplitude of VORpost(t) is not equal to the sum of the amplitude of VORpre(t) and the amplitude of
For each parallel fiber phase
Simultaneous plasticity mechanism
Figures 7 and 8 illustrate that to understand how plasticity mechanisms with different features will affect the gain of the VOR, we need to calculate how those plasticity mechanisms will change the relative weights of vestibular parallel fibers that exhibit peak activity during different phases of the vestibular stimulus. The first plasticity mechanism evaluated was one that decreased the weight of a parallel fiber in proportion to the level of activity in that parallel fiber at the time of a climbing-fiber spike:
where T1, T2, ... , Tj, ... , Tk are the times of spikes in the climbing fiber, and B is a constant >0. To avoid possible artifacts that might result from using any type of fit to approximate the climbing-fiber responses, the values of Tj were obtained from the actual complex-spike times, recorded to a resolution of 1 msec, during a 60-120 sec epoch of a ×0 or ×2 stimulus. Each Tj was used once in a simulation, and division by k normalized for the number of climbing-fiber spikes used in each simulation. Multiplication by
![&Dgr;w<SUB>ϕ</SUB>=<LIM><OP>∑</OP></LIM><SUB>(j<UP>=1:</UP>k)</SUB>[<UP>−</UP>B PF<SUB>ϕ</SUB>(T<SUB>j</SUB>)]/k,](/content/vol18/issue21/fulltext/9112/img009.gif)
(8) Figure 9 summarizes the results of simulations that used Tj values obtained from the complex spike responses shown in Figure 4 to drive the simultaneous plasticity mechanism. The two graphs on the left side of Figure 9, A1 and A2, show the predicted changes in the weights of the different vestibular parallel fibers for 0.5 and 5 Hz stimuli. These two graphs are summarized in Figure 9B, which plots the phase of the parallel fiber with the greatest synaptic depression as a function of the frequency of the ×0 and ×2 stimuli. Finally, the predicted changes in all parallel-fiber weights were converted to predicted changes in the VOR using Equations 3-7, and the predicted changes in the gain of the VOR are plotted as a function of stimulus frequency in Figure 9C.
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Figure 9. Predicted synaptic and behavioral changes produced by a plasticity mechanism driven by simultaneous activity in climbing fibers and vestibular parallel fibers. Spike trains from the typical climbing fiber, whose responses are shown in Figure 4, were used as the input to the simultaneous plasticity mechanism (Eq. 8). Open symbols, Predicted changes for the climbing fiber spike trains present during ×0 stimuli; filled symbols, predicted changes for the climbing fiber spike trains present during ×2 stimuli. A, Predicted changes in the synaptic weights of parallel fibers that fire at different phases of the vestibular stimulus. A1, Changes predicted for 0.5 Hz stimuli. A2, Changes predicted for 5 Hz stimuli. B, Phase of the parallel fiber undergoing largest weight reduction (LTD) as a function of the stimulus frequency. The thin vertical lines to the right of the graph mark the range of phases for ×0 stimuli at frequencies of 0.5, 2, 5, and 10 Hz, and the thick vertical lines represent the range of phases for ×2 stimuli. C, Predicted change in the gain of the VOR as a function of stimulus frequency. Arrows of the same style mark results corresponding to the same simulation.
During a 0.5 Hz, ×0 stimulus, most Tj values (complex spike times) coincided with contraversive head motion (Fig. 4A), so the greatest weight changes occurred in parallel fibers that fired most vigorously during contraversive head motion (Fig. 9A1,B, open single arrows). As a result, the predicted change in the VOR was an appropriate decrease in gain (Fig. 9C, open single arrow). During the 0.5 Hz, ×2 stimulus, most Tj values coincided with ipsiversive head motion (Fig. 4C), the biggest weight changes occurred in parallel fibers that fired most vigorously during ipsiversive head motion (Fig. 9A1,B, filled single arrows), and the predicted change in the VOR was an appropriate increase in gain (Fig. 9C, filled single arrow). Thus, as suggested previously (Ito, 1972
In contrast, the simultaneous plasticity mechanism fails to predict the induction of appropriate changes in the VOR by the activity of this climbing fiber during the 5 Hz stimuli. During the 5 Hz, ×2 stimulus, most Tj values coincided with contraversive head motion (Fig. 4D), so the parallel fibers that fired during contraversive head motion underwent the most weight reduction (Fig. 9A2,B, filled double arrows). These changes in synaptic weight predicted a decrease in the gain of the VOR (Fig. 9C, filled double arrow), which is opposite to the gain change observed experimentally. Similarly, the simultaneous plasticity mechanism incorrectly predicted an increase in the gain of the VOR when the complex spikes recorded during the 5 Hz, ×0 stimulus (Fig. 4B) provided Tj values (Fig. 9C, double open arrow). Similar computations were performed using Tj values obtained from the complex-spike times recorded in the same cell during 2 and 10 Hz stimuli, and the results are plotted in Figure 9, B and C. For these stimulus frequencies, predicted changes in gain were in the correct direction.
Figure 9B illustrates that the parallel fiber undergoing the biggest weight change varied with the frequency of the stimulus, as well as the stimulus configuration (×0 vs ×2). For the climbing fiber in this example, the parallel fibers undergoing the most depression during ×2 stimuli at frequencies from 0.5 to 10 Hz spanned a range of phases from
We have focused on the parallel-fiber weights that underwent the greatest decrease under each stimulus condition. Inspection of Figure 9, A1 and A2, reveals that there were decreases in the weights of all parallel fibers. This results from our use of a plasticity mechanism that yields exclusively synaptic depression. We obtained the same effects on the gain of the VOR with a mixture of increases and decreases in parallel-fiber weights if we used a plasticity mechanism like that suggested by Bienenstock et al. (1982)
We performed similar computations to those illustrated in Figure 9 using Tj values derived from the eight other individual HGVPs in which complex-spike times were recorded during all four stimulus frequencies. The results shown in Figure 9 are typical. For none of the nine cells did computations using the simultaneous plasticity mechanism predict appropriate gain changes for all stimulus frequencies. Thus, a plasticity mechanism guided by coincident activity in climbing fibers and vestibular inputs cannot account for the induction of appropriate learned changes in the gain of the VOR across the range of effective stimulus frequencies.
Nonsimultaneous plasticity mechanism
We next evaluated whether a plasticity mechanism tuned to nonsimultaneous activity in climbing fibers and vestibular parallel fibers might provide consistent guidance for learning across the range of effective stimulus frequencies:
where TPF-CF is a constant time delay we will refer to as the parallel fiber to climbing fiber (PF-CF) interval. When TPF-CF = 0, the nonsimultaneous plasticity mechanism described by Equation 9 is equivalent to the simultaneous plasticity mechanism of Equation 8. When TPF-CF
![&Dgr;w<SUB>ϕ</SUB>=<LIM><OP>∑</OP></LIM><SUB>(j=1:k)</SUB>[<UP>−</UP>B PF<SUB>ϕ</SUB>(T<SUB>j</SUB>−T<SUB>PF–CF</SUB>)]/k,](/content/vol18/issue21/fulltext/9112/img010.gif)
(9) 0, climbing-fiber spikes induce a change in the weight of each parallel fiber proportional to the level of activity in that parallel fiber TPF-CF milliseconds before (for positive TPF-CF) or after (for negative TPF-CF) the climbing-fiber spike.
Figure 10 compares the results for several different values of TPF-CF when complex spike times from the example in Figure 4 provided the Tj values used by the nonsimultaneous plasticity mechanism. Changes in the weights of each of the 36 parallel fibers were computed for the ×0 and ×2 stimuli from Equation 9, with TPF-CF = 50 msec (Fig. 10A,D), TPF-CF = 100 msec (Fig. 10B,E), or TPF-CF = 200 msec (Fig. 10C,F). As in Figure 9B, the top panels of Figure 10 plot the phase of the vestibular parallel fiber that underwent the largest reduction in weight as a function of the stimulus frequency. The predicted changes in all the parallel-fiber weights were used to compute predicted changes in the gain of the VOR from Equations 3-7 and were plotted as a function of the stimulus frequency in the bottom panels of Figure 10. When TPF-CF was 100 msec, parallel fibers with a phase close to 180° (those that fire most during contraversive head velocity) underwent the greatest weight reduction for ×0 stimuli at all frequencies tested, and parallel fibers with a phase of ~0° (those that fire most during ipsiversive head velocity) underwent the greatest weight reduction for all ×2 stimuli (Fig. 10B). There was no overlap in the sets of parallel fibers undergoing the greatest weight reduction in response to the ×0 versus ×2 stimuli (thin and thick vertical lines at right edge of graph). These changes in parallel-fiber weights for TPF-CF = 100 msec predicted consistent decreases in the gain of the VOR in response to the ×0 stimuli and consistent increases in the gain of the VOR in response to the ×2 stimuli for the full range of stimulus frequencies included in the experiments (Fig. 10E). In contrast, when TPF-CF = 50 or 200 msec, there was considerable variation in the phase of the parallel fibers undergoing the greatest weight changes for ×0 or ×2 stimuli at different frequencies, and there was overlap in the range of parallel fibers undergoing the largest weight reductions in response to ×0 versus ×2 stimuli (Fig. 10A,C). These changes in parallel-fiber weights predicted appropriate gain changes at some frequencies and inappropriate gain changes at other frequencies (Fig. 10D,F).
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Figure 10. Predicted synaptic and behavioral changes for a plasticity mechanism driven by nonsimultaneous activity in
