Cerebellar Role in Predictive Control of Eye Velocity Initiation and Termination

General characteristics during training

Figure 1A illustrates horizontal eye position (top) and velocity (bottom) traces of a typical experiment (Control) and 3 h after (Trained) the beginning of repetitive presentation of bidirectional velocity step visual stimulation. Traces from left (orange) and right eyes (green) are superimposed, showing that both eyes move almost identically during OKR. The eye position traces show slow and fast phases (gray arrows), and the eye velocity traces are shown by thin gray lines. Clearly, the slow phase eye velocity of ±13 deg/s in the Control did not catch the stimulus velocity of ±20 deg/s (solid gray lines), whereas it was close to the stimulus velocity after training. Namely, OKR gain adaptation occurred as previously well described (Ito et al., 1979; Nagao, 1983; Marsh and Baker, 1997); however, in addition, there was a noticeable change in the eye velocity profile. In Figure 1A (Control), eye velocity continued to build up until stimulus direction changed, whereas in Figure 1A (Trained) it began to decrease before stimulus direction changes (black arrows), confirming the observations of a previous study (Marsh and Baker, 1997). In respect to stimulus direction, this change in timing produced predictive eye movements.

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Figure 1.

Predictive OKR trained by bidirectional velocity steps. A, Performance of eye movement before (left, Control) and after (right, Trained) 180 min bidirectional velocity step training of a representative goldfish in response to the training stimulation whose half-period is 8 s. Top, Orange represents left eye position. Green represents right eye position. Gray arrows indicate slow and fast phases. Bottom, Slow phase eye velocity and visual stimulus velocity (gray). Gray thin lines indicate fast phases in eye velocity. +, Rightward (CW) directed eye positions; −, leftward (CCW) directed eye positions. B, Averaged eye velocity over 8 experiments before (blue, Control) and after (red, Trained) bidirectional velocity step training in response to the visual stimulation used for training (left, gray) and during extended period stimulation whose half-period was 16 s (right, gray). Black arrows indicate OKR components consisting of the following: ➀, Direct; ➁, Indirect; ➂, Termination. C, Performance of eye velocity in the dark before (blue) and just after (red) bidirectional velocity step training of the same fish as in A. Visual stimulation (gray) was turned off at the black down arrowhead. D, A system model of the OKR (Cohen et al., 1977; Waespe and Henn, 1987) consisting of direct and indirect pathways whose outputs are Direct and Indirect components in B, respectively.

To evaluate general characteristics of the eye velocity profiles, we calculated average eye velocity from 8 experiments (Fig. 1B) as opposed to single traces evaluated without averaging in the previous study. Figure 1B (left) illustrates averaged Control (blue) and Trained (red) eye velocity superimposed with stimulus velocity trace (gray). After the visual stimulus changed direction, both Control and Trained eye velocity showed a rapid initial jump (➀) followed by a gradual buildup (➁). Classically, the rapid initial jump has been considered to be generated by the OKR direct pathway, whereas the gradual buildup occurs through the OKR indirect pathway (Waespe and Henn, 1985; Fuchs and Mustari, 1993) as schematically illustrated in Figure 1D (Cohen et al., 1977).

The OKR indirect pathway is considered to include the velocity storage mechanism (VSM) that charges and discharges eye velocity signals like a capacitor in an electrical circuit charging and discharging electrical current (Cohen et al., 1977). The VSM is characterized by its capacity (how much eye velocity can be stored) and the charging and discharging time constants (how fast eye velocity can be charged and discharged). When velocity step visual stimulation is applied, the eye velocity signal gradually builds up; and when the visual stimulation is suddenly turned off, the stored eye velocity signal gradually decreases until the VSM is completely discharged. The alternating slow and fast phase eye velocity profile produced in the dark is called optokinetic after-nystagmus (OKAN). Unlike a passive capacitor in an electrical circuit, the VSM's time constants for charging and discharging are different. Noduluar cerebellectomy in monkeys altered the discharging (OKAN) time constant, although it did not affect charging behavior (Cohen et al., 1977; Waespe et al., 1985). Figure 1B shows that, after training, the Direct component increased, whereas the Indirect building-up time constant shortened. Also noticeable is that eye velocity began to slow down at ∼3 s before the direction of the stimulus changed in Trained compared with Control (Fig. 1B, red trace, ➂). This predictive slowing was called the Termination component (➂), even though in this paradigm the bidirectional stimulus profile could not distinguish the beginning (➀) from the end (➂).

Predictive eye velocity after training manifested by visual stimulus with longer duration

Figure 1B (right) illustrates averaged Control and Trained eye velocity over 8 experiments superimposed on stimulus velocity (gray) whose duration (16 s) is twice as long as the training stimulus duration (8 s). Control (blue) and Trained (red) data were recorded just before the beginning, and then after the end of the 3 h training, respectively. The Termination component (➂) appeared in the Trained eye velocity around 8 s after the directional switch of the visual stimulus, even though the visual stimulation continued at the constant velocity. This predictive eye velocity behavior seen after the 3 h training continued, on average, 15–30 min before gradually returning toward control behavior.

Predictive eye velocity after training manifested in the dark

In addition to the predictive decrease in eye velocity before the stimulus directional switch, and as seen previously, an oscillatory eye velocity was observed in the dark when the visual stimulation was suddenly turned off after 3 h bidirectional training (Fig. 1C, red). For comparison, control eye velocity data (blue) in the dark are shown after presenting 10 cycles of the bidirectional visual stimulation before training. Durations of the eye velocity oscillation in the dark after the 3 h training varied from 15 to 60 s in the 8 experiments sampled.

Single velocity steps

The bidirectional velocity step visual stimulation shown in Figure 1 did not allow the onset and offset timings of the stimulus to be distinguished because offset in one direction was always onset to the other direction. Although we called ➂ Termination in Figure 1, it could have been an anticipatory component generated for onset of the visual stimulus to the opposite stimulus direction. To discriminate visual stimulus onset from offset, we used unidirectional velocity step visual stimulation in which periodic visual stimulation rotated only in one direction (Fig. 2). Control (Fig. 2A, blue) and Trained (Fig. 2A, red) eye velocity from a typical animal during unidirectional velocity step stimulation is shown in Figure 2. Traces on the left show the first (top) and the last (bottom) 2 cycles of stimulus and eye velocity during the training, whereas the traces on the right show averaged eye velocity over the first (top) and the last (bottom) 10 cycles of the training to better characterize the differences in eye velocity waveforms in this experiment. As observed in Figure 1A for bidirectional stimulation, Trained eye velocity showed a gradual decrease before the offset of each cycle of the visual stimulation (solid curved arrows). Thus, the Termination component (➂) is actually a predictive component of the visual stimulus offset. The Termination component is clearly seen in the averaged Trained eye velocity traces from 8 different experiments (Fig. 2B, red arrow, ➂). This behavior was not seen in the superimposed averaged Control eye velocity (blue arrow).

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Figure 2.

Predictive OKR trained by unidirectional velocity steps. A, Performance of eye velocity before (top, Control) and after (bottom, Trained) 180 min unidirectional velocity step training in response to the training stimulation (gray). Left traces, Two stimulus cycles of raw eye velocity whose fast phases were eliminated. Right traces, Eye velocity averaged over 10 first (top) and last (bottom) cycles of the training. Bottom, Black curved arrows indicate decreases in eye velocity before the offset timing of visual stimulation (gray). B, Averaged eye velocity over 8 experiments before (blue, Control) and after (red, Trained) unidirectional velocity step training in response to the visual stimulation used for training (gray). Inset, Magnified eye velocity traces just before the onset of the visual stimulation. , ➀, ➁, and ➂ indicate Initiation, Direct, Indirect, and Termination components, respectively, of OKR. C, Performance of eye velocity in the dark just after unidirectional velocity step training in the same experiment as in A. Visual stimulation (gray) was turned off at the black down arrowhead.

In addition to the Termination component, the averaged traces (Fig. 2B) revealed that Trained eye velocity started to increase before onset of the visual stimulation, as shown in Figure 2B (inset, ). Control and Trained eye velocity at the onset of the stimulus was 0.2 and 1.1 deg/s, respectively. These values were significantly different (p < 6.47e-8, t test). For referral purposes, we have labeled the Initiation component ().

The maximum eye velocity reached during stimulus ON periods was significantly larger in Trained than in Control. Thus, OKR gain increased in response to unidirectional velocity step training as it did to bidirectional velocity step training shown in Figure 1. The mean averaged OKR gains of Control and Trained were 0.54 and 0.89, respectively, and significantly different (p < 3.04e-13, t test). Similarly, the Direct component eye velocity (➀) was larger in Trained (13.6 deg/s) than in Control (4.4 deg/s) (p < 2.05e-6, t test). The time constant 1/τ of the Indirect component (➁) was shorter in Trained (1.0 s) than in Control (2.3 s) conditions (p < 0.00228, t test). These changes in eye velocity parameters during training are further quantitatively evaluated later in Figure 8.

Figure 2C illustrates eye velocity in the dark in the same experiment just after 3 h unidirectional velocity step training. Unlike eye velocity traces after bidirectional velocity step training, more robust eye velocity oscillations were observed in the dark after unidirectional velocity step training. Notably oscillations occurred in only the trained direction, with durations varying between 0.5 and 3 min.

These results from unidirectional single velocity step experiments revealed Initiation and Termination prediction components that, respectively, are eye velocity increases and decreases before stimulus onset and offset. Further, it showed that eye velocity oscillation in the dark after this training occurred only toward the trained direction.

Double velocity steps

To further confirm individuality of the Initiation component shown in Figure 2B (), we used unidirectional double velocity step visual stimulation, as shown in Figure 3 with a format the same as in Figure 2. In this training paradigm, optokinetic visual stimulation (Fig. 3A, gray line) stepped up from 10 to 20 deg/s at 4 s after the onset of each visual stimulation cycle. Figure 3B shows not only a Termination component (➂), but also an Initiation component (), to be present in the averaged Trained eye velocity trace before the stimulus velocity stepped up. Namely, Trained eye velocity started to increase gradually and actually exceeded the stimulus velocity (10 deg/s) before the visual stimulus stepped up (inset, ). The average eye velocity over 8 experiments at the onset of the second velocity step was 10.6 deg/s, which was significantly greater than the stimulus speed (p < 2.32e-4, t test). By contrast, the Initiation component for the first velocity step was not as large as that shown in Figure 2B likely due to the 0 to 10 deg/s versus 20 deg/s in the two paradigms. However, the two 10 deg/s steps combined in Figure 3 exceeded the single 20 deg/s step shown in Figure 2.

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Figure 3.

A–C, Predictive OKR trained by unidirectional double velocity steps. Formats are the same as in Figure 2.

Unidirectional eye velocity modulation in the dark was observed after the 3 h double step visual stimulation training (Fig. 3C). Noticeably, in this paradigm, the eye velocity profile did not show a clear double step-up in the dark (Fig. 3C), resembling more the unidirectional single step-up (Fig. 2C).

These results from unidirectional double velocity step experiment revealed that the Initiation component can also be acquired when the eyes are following the visual stimulus and become even more accentuated than when the visual stimulus is stationary. Notably, eye velocity at the Initiation of stimulus step-up timing exceeds stimulus velocity, which hardly occurs in ordinary OKR.

Single velocity steps with fixed/variable duration at variable/fixed interval

To test whether Initiation and Termination components could be acquired independently, we used unidirectional velocity step visual stimulation in which either duration (ON period) or interval (OFF period) was randomized so that the offset or the onset of the stimulation was not predictable. Fixed duration at variable interval experiments is shown in Figure 4A from one representative experiment and in Figure 4B for 8 experiments averaged. The stimulus ON duration was constant at 8 s while stimulus OFF duration was randomized between 1 and 15 s such that onset timing could not be predicted. After presentation of this stimulus for 3 h, a Termination component was acquired (Fig. 4B, ➂) comparable with that after the fixed duration/interval training (Fig. 2B). However, clearly no Initiation component was observed (Fig. 4B, ).

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Figure 4.

Predictive OKR trained by unidirectional velocity steps with randomized interval or duration. A, B, Results of fixed duration at randomized interval experiments. C, D, Those of randomized duration at fixed interval experiments. A, Performance of eye velocity before (top, Control) and after (bottom, Trained) 180 min training in response to the training stimulation (gray). B, Averaged eye velocity over 8 experiments before (blue, Control) and after (red, Trained) the training in response to the visual stimulation used for training (gray). Averaged eye velocity traces during the stimulus interval are shown only for 1 s after the offset and before the onset of the stimulus. , ➀, ➁, and ➂ indicate Initiation, Direct, Indirect, and Termination components, respectively, of OKR. C, D, Formats are the same as A and B, respectively.

By contrast, after presentation of variable duration at fixed interval stimulation for 3 h in which duration of the stimulus ON period was randomized, an Initiation component was clearly acquired (Fig. 4C from one representative experiment; and Fig. 4D for 8 experiments averaged). However, because the stimulus offset could not be predicted, a Termination component was not seen (Fig. 4C,D). Therefore, the Initiation and Termination predictions can be independently acquired. Notably, Direct (➀) and Indirect (➁) components changed after both the fixed duration at variable interval (Fig. 4B) and the variable duration at fixed interval training (Fig. 4D) as after unidirectional fixed duration/interval training (Fig. 2B). Gain and prediction behaviors are further evaluated quantitatively in Figure 8.

These results confirmed that the Initiation and Termination components can be acquired independently.

Cerebellectomy after unidirectional velocity step training

Figure 5 illustrates results of acute cerebellectomy experiments in the same format as in Figures 2 and 3. Acute cerebellectomy after 3 h of unidirectional fixed duration/interval training resulted in significant changes in eye velocity profile. Both Control and Trained eye velocity in Figure 5A is similar to those shown in Figure 2A for the same training paradigm in which both Termination and Initiation components were present in the Trained condition. After acute cerebellectomy (Fig. 5A, Cerebellectomized), overall eye velocity became slower than that in the Trained condition, closely resembling the Control eye velocity profile. Comparison of averaged eye velocity profiles of Control (Fig. 5B, blue), Trained (red), and Cerebellectomized (green) revealed that acquired Initiation, Direct, and Termination components (, ➀, ➂) were removed by cerebellar removal. Notably, maximum eye velocity (OKR gain) that is closely related to the Indirect component (➁) decreased to a lower value than Control eye velocity.

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Figure 5.

Effects of acute cerebellectomy on predictive OKR trained by unidirectional velocity steps. Formats are the same as in Figure 2, except that eye velocity traces after acute cerebellectomy that were conducted just after 180 min training are shown in green in A–C as “Cerebellectomized.”

Eye velocity oscillation in the dark acquired during the 3 h unidirectional velocity step with fixed duration/interval training (Fig. 5C, red) also was immediately removed after acute cerebellectomy (green). The record shown was acquired in the dark 80 min after additional unidirectional velocity step fixed duration/interval training.

These results demonstrated that maintenance of acquired Initiation and Termination predictions as well as that of Direct component are fully cerebellar-dependent. However, the changes in the Indirect component after training may involve a neuronal substrate other than the cerebellum.

Cerebellectomy before unidirectional velocity step training

Figure 6 shows results of chronic cerebellectomy experiments illustrated in the same format as in Figures 2, 3, and 5. Figure 6A shows an eye velocity trace sampled before (Control, blue) and after 3 h unidirectional fixed duration/interval training (Trained, red) in an experiment in which the cerebellectomy was performed 1 week earlier. Without the cerebellum, no clear changes occurred in eye velocity after 3 h training, even in the cycle averaged traces (Fig. 6A, right). However, averaged over 8 experiments, Control (Fig. 6B, blue) and Trained (red) eye velocity traces showed quite similar differences as seen in those following acute cerebellectomy (Fig. 5B, blue vs green). Namely, while the Initiation (), Direct (➀), and Termination (➂) components were hardly altered, maximum buildup eye velocity reached during the stimulus ON period (OKR gain) appeared significantly smaller in cerebellectomized experiments. To the best of our knowledge, this is the first demonstration showing OKR gain modification in cerebellectomized animals.

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Figure 6.

A–C, Effects of chronic cerebellectomy on predictive OKR trained by unidirectional velocity steps. Formats are the same as in Figure 2.

None of the cerebellectomized experiments (N = 8) showed eye velocity oscillation in the dark after 3 h training as exemplified in Figure 6C from a representative experiment, as observed in cerebellar intact experiments (Fig. 2C).

These results demonstrated that the acquisition of Initiation and Termination prediction as well as the increase in the Direct component are fully cerebellar-dependent, whereas changes in the Indirect component may involve a neuronal substrate other than the cerebellum.

Eye velocity components during different training paradigms

To quantitatively further evaluate how each OKR component changed during the various training paradigms, we calculated a representative value, as described in Materials and Methods, from each component during the 3 h training paradigm consisting of 675 stimulus periods. The evaluated parameters are illustrated in Figure 8A: eye velocity at stimulus onset, Initiation in deg/s (), maximum value of the Direct component in deg/s (➀), building-up time constant for the Indirect component (➁τ) in seconds and magnitude (➁ gain) in deg/s, and eye velocity reduction extent at stimulus end timing from the maximum eye velocity for Termination in deg/s (➂).

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Figure 8.

Changes in eye velocity components during each kind of predictive OKR training. A, Definition of OKR eye velocity components. , Initiation eye velocity at the stimulus onset timing; ➀, peak velocity of Direct component; ➁τ, time constant of building-up Indirect component; ➁ gain, peak velocity of Indirect component; and ➂, amount of decrease in Termination eye velocity. B, Unidirectional velocity step with fixed duration at randomized interval training. Values that changed from pretraining to post-training: Initiation () from −0.5 to −2.1 deg/s (p < 0.167, t test); Direct (➀) from 3.7 to 10.5 deg/s (p < 1.08e-6, t test); Indirect (➁τ) from 1.7 to 0.9 s (p < 0.000560, t test), gain from 11.9 to 18.9 deg/s (p < 6.46e-8, t test); and Termination (➂) from 0.0 to 3.2 deg/s (p < 5.01e-9, t test). C, Unidirectional velocity step with randomized duration at fixed interval. Values changed from pretraining to post-training: Initiation () from −0.1 to −0.4 deg/s (p < 0.00516, t test); Direct (➀) from 3.5 to 10.9 deg/s (p < 2.69e-7, t test); Indirect (➁τ) from 1.9 to 0.6 s (p < 9.81e-5, t test), gain from 11.8 to 17.4 deg/s (p < 0.000291, t test); and Termination (➂) from 0.1 to 1.2 deg/s (p < 0.00159, t test). D, Unidirectional velocity step. Values changed from pretraining to post-training: Initiation () from 0.2 to 1.1 deg/s (p < 6.47e-8, t test); Direct (➀) from 4.4 to 13.6 deg/s (p < 2.05e-6, t test); Indirect (➁τ) from 2.3 to 1.0 s (p < 0.00228, t test), gain from 14.0 to 19.3 deg/s (p < 6.83e-5, t test); and Termination (➂) from 0.1 to 4.1 deg/s (p < 1.76e-10, t test). E, Acute cerebellectomy after unidirectional velocity step. Values changed from pretraining to post-training: Initiation () from 0.1 to 0.7 deg/s (p < 0.000384, t test); Direct (➀) from 4.8 to 12.4 deg/s (p < 2.70e-7, t test); Indirect (➁τ) from 1.6 to 0.8 s (p < 0.0121, t test), gain from 12.7 to 19.3 deg/s (p < 7.86e-6, t test); and Termination (➂) from 0.2 to 4.1 deg/s (p < 9.23e-7 t test). The values changed from pretraining to postcerebellectomy: Initiation () from 0.1 to −0.1 deg/s (p < 0.249, t test); Direct (➀) from 4.8 to 3.9 deg/s (p < 0.0914, t test); Indirect (➁τ) from 1.6 to 1.0 s (p < 0.0869, t test), gain from 12.7 to 8.67 deg/s (p < 0.000541, t test); and Termination (➂) from 0.2 to 0.1 deg/s (p < 0.147 t test). F, Chronic cerebellectomy before unidirectional velocity step. Values changed from pretraining to post-training: Initiation () from 0.2 to 0.1 deg/s (p < 0.463, t test); Direct (➀) from 4.8 to 3.3 deg/s (p < 0.00263, t test); Indirect (➁τ) from 1.8 to 0.8 s (p < 0.00527, t test), gain from 12.5to 8.25 deg/s (p < 0.000176, t test); and Termination (➂) from 0.1 to 0.0 deg/s (p < 0.141 t test). B–F, Top, Averaged eye velocity over 10 last cycles of each training of 8 experiments (black) and visual stimulation used for each training (gray).

Figure 8D shows the time course changes in each of the 5 parameters throughout the 3 h for unidirectional velocity step with fixed duration/interval training. In each panel, gray dots represent an estimated value from a single stimulus period, and the colored traces represent the moving averages spanning 15 periods. During this training, all of the values changed significantly. Namely, Initiation () changed from 0.2 to 1.1 deg/s, Direct (➀) from 4.4 to 13.6 deg/s, Indirect (➁τ) from 2.3 to 1.0 s, gain from 14.0 to 19.3 deg/s, and Termination (➂) from 0.1 to 4.1 deg/s. These changes were all statistically significant (p values, Fig. 8).

During the variable interval training in which the onset of the visual stimulus was unpredictable (Fig. 8B, same format as Fig. 8D), Initiation () remained unchanged from the initial value. By contrast, Indirect (➁τ) and gain, and Termination (➂) showed almost identical changes to those in unidirectional velocity step with fixed duration/interval training (corresponding values and statistical significance, Fig. 8D). In contrast, the change in Direct (➀) was significantly less than that during unidirectional velocity step with fixed duration/interval training (D), suggesting that the Direct component contains a predictive factor that could not be acquired when onset timing of visual stimulation was unpredictable.

During unidirectional velocity steps with variable duration at fixed interval training (Fig. 8C, same format as B,D), the stimulus for OFF timing could not be predicted. As a result, Termination (➂) changed very little, whereas Direct (➀), Indirect (➁τ), and gain showed comparable changes with those seen during unidirectional step with fixed duration/interval training (for values and statistics, see Fig. 8D). A possible reason for small change in Termination during this training paradigm was likely the limited random range of the variable stimulus from 1 to 15 s. As a result, the predictive mechanisms adapted with uncertainty. Initiation () also changed less than that during unidirectional velocity step with fixed duration/interval training (Fig. 8D), suggesting that this predictive component depended not only on the interval time, but also on the preceding duration of the stimulus ON period.

Effects of cerebellectomy on eye velocity components

The acute cerebellectomy experiments, first, confirmed that changes in the four OKR features during the 3 h unidirectional velocity step with fixed duration/interval training (Fig. 8E) were statistically identical to those during the same training paradigm in cerebellar intact experiments (Fig. 8D). After acute cerebellectomy, Initiation (), Direct (➀), and Termination (➂) acquired by 3 h training returned to pretraining values (corresponding values and statistics in Fig. 8 legend). By contrast, the acquired change in Indirect (➁τ) (0.8 s) was only slightly affected by acute cerebellectomy and did not return to pretraining values (1.6 s). Indirect (➁) gain decreased after acute cerebellectomy to a significantly lower value than its original value (p < 0.000541, t test), suggesting that presentation for part of the modified memory regarding the Indirect component does not require the cerebellum. The absence of training during the acute cerebellectomy, averaging at most 4 min (Method), should have minimal effects on these parameters as a similar paradigm in a previous study showed the learned predictive eye velocity persisted for up to 50 min (Marsh and Baker, 1997).

The results from the chronic cerebellectomy experiments showed that all the pretraining values were comparable with those of the cerebellar intact. Initiation (), Direct (➀), and Termination (➂) did not change during 3 h training in the chronic cerebellectomy experiments. These were the same three parameters that returned to pretraining values after acute cerebellectomy. In contrast, Indirect (➁τ), which did not return to pretraining values after acute cerebellectomy, decreased significantly in the chronic cerebellectomy experiments. The final value (0.8 s) was equivalent to that of cerebellar intact after 3 h training (1.0 s), but the rate of change during the 3 h training was slower in the chronic cerebellectomy experiment (compare Fig. 8D,E; ➁τ). The Indirect (➁) gain also gradually decreased to values comparable with that after acute cerebellectomy. The amount of decrease during 3 h training from 12.5 to 8.3 deg/s was significant (p < 0.000179, t test).

Together, the cerebellum was demonstrated to be necessary for acquisition and maintenance of Initiation and Termination components as well as changes in Direct component; although it was not necessary for maintaining the acquired Indirect component, the acquisition process was slower without the cerebellum.