Motor Dynamics Encoding in Cat Cerebellar Flocculus Middle Zone During Optokinetic Eye Movements

Toshihiro Kitama,1 Tomohiro Omata,2 Akihito Mizukoshi,3 Takehiko Ueno,2 and Yu Sato1

Departments of  1Physiology,  2Neurosurgery, and  3Otolaryngology, Yamanashi Medical University, Tamaho, Yamanashi 409-3898, Japan


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Kitama, Toshihiro, Tomohiro Omata, Akihito Mizukoshi, Takehiko Ueno, and Yu Sato. Motor Dynamics Encoding in Cat Cerebellar Flocculus Middle Zone During Optokinetic Eye Movements. J. Neurophysiol. 82: 2235-2248, 1999. We investigated the relationship between eye movement and simple-spike (SS) frequency of Purkinje cells in the cerebellar flocculus middle zone during the optokinetic response (OKR) in alert cats. The OKR was elicited by a sequence of a constant-speed visual pattern movement in one direction for 1 s and then in the opposite direction for 1 s. Quick-phase-free trials were selected. Sixty-six cells had direction-selective complex spike (CS) activity that was modulated during horizontal (preferring contraversive) but not vertical stimuli. The SS activity was modulated during horizontal OKR, preferring ipsiversive stimuli. Forty-one cells had well-modulated activity and were suitable for the regression model. In these cells, an inverse dynamics approach was applied, and the time course of the SS rate was reconstructed, with mean coefficient of determination 0.76, by a linear weighted superposition of the eye acceleration (mean coefficient, 0.056 spikes/s per deg/s2), velocity (5.10 spikes/s per deg/s), position (-2.40 spikes/s per deg), and constant (mean 34.3 spikes/s) terms, using a time delay (mean 11 ms) from the unit response to the eye response. The velocity and acceleration terms contributed to the increase in the reconstructed SS rates during ipsilateral movements, whereas the position term contributed during contralateral movements. The standard regression coefficient analyses revealed that the contribution of the velocity term (mean coefficient 0.81) was predominant over the acceleration (0.03) and position (-0.17) terms. Forward selection analysis revealed three cell types: Velocity-Position-Acceleration type (n = 27): velocity, position, and acceleration terms are significant (P < 0.05); Velocity-Position type (n = 12): velocity and position terms are significant; and Velocity-Acceleration type (n = 2): velocity and acceleration terms are significant. Using the set of coefficients obtained by regression of the response to a 5 deg/s stimulus velocity, the SS rates during higher (10, 20, and 40 deg/s) stimulus velocities were successfully reconstructed, suggesting generality of the model. The eye-position information encoded in the SS firing during the OKR was relative but not absolute in the sense that the magnitude of the position shift from the initial eye position (0 deg/s velocity) contributed to firing rate changes, but the initial eye position did not. It is concluded that 1) the SS firing frequency in the cat middle zone encodes the velocity and acceleration information for counteracting the viscosity and inertia forces respectively, during short-duration horizontal OKR and 2) the apparent position information encoded in the SS firing is not appropriate for counteracting the elastic force during the OKR.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The cerebellar cortex is anatomically parceled into longitudinal zones that have different Purkinje cell outputs and climbing fiber inputs (cf. Andersson and Oscarsson 1978a,b; Groenewegen and Voogd 1977; Groenewegen et al. 1979; Voogd 1964). Each anatomic zone is a functional module for regulation of specific motor mechanisms as originally proposed by Oscarsson (1979). The flocculus, including the adjacent ventral paraflocculus, has two kinds of functional modules: one for eye movement control in the horizontal plane and the other for eye movement control in vertical planes in the cat (Sato et al. 1982a,b, 1983, 1988; Sato and Kawasaki 1987, 1990a,b) and the rabbit (De Zeeuw et al. 1994; Van der Steen et al. 1994). On the basis of studies that clarified neural pathways from the middle-zone Purkinje cell to the extraocular motoneurons, the middle zone of the cat flocculus was suggested to be a functional module for eye movement control in the horizontal plane (Sato et al. 1988; Sato and Kawasaki 1991). At present, it is not clear how the middle zone controls motor dynamics of the horizontal eye movement in the alert cat.

The aim of the present study is to clarify the relationship between the firing pattern of the middle-zone Purkinje cells and eye movements in the alert cat. The present study focuses on the optokinetic response (OKR), which is known to elicit simple spike (SS) activity of flocculus Purkinje cells in the alert rabbit (Nagao 1990, 1991), the cat (Fukushima et al. 1996), and the monkey (Buttner and Waespe 1984; Markert et al. 1988; Waespe and Henn 1981; Waespe et al. 1985). Other eye movements that elicit SS activity in the monkey flocculus and the ventral paraflocculus (mostly, if not all, the ventral paraflocculus) include smooth pursuit eye movements, the ocular following response (OFR), and the suppression of the vestibuloocular reflex by fixation of a small target moving with the head (Lisberger and Fuchs 1978; Miles et al. 1980; Noda and Suzuki 1979a-c; Noda and Warabi 1987; Shidara and Kawano 1993; Stone and Lisberger 1990). These movements are not certain to exist in the cat (Evinger and Fuchs 1978).

To study the correlation between the firing rate and the motor parameters, we adopted the inverse dynamics approach (Gomi et al. 1998; Kawato et al. 1987; Shidara et al. 1993), which was recently proposed as a general technique for examining the relation of neural firing in a given part of the brain with the final motor command. The reason we adopted the inverse dynamics approach as the appropriate method is the following. First, the inverse dynamics approach has the advantage of reconstructing the single cell firing from the movement if its output contributes to the final motor command. For example, the SS firing patterns of individual Purkinje cells were well reconstructed by a linear weighted superposition of the eye position, velocity, and acceleration during the OFR in the monkey ventral paraflocculus (Gomi et al. 1998; Shidara et al. 1993). In marked contrast, the forward dynamics approach adopted in some previous studies (e.g., Krauzlis and Lisberger 1994) predicts the movement pattern from the firing pattern and cannot be used for the reconstruction of the firing of individual cells from the movement. For prediction of the movement pattern from the firing pattern, the forward dynamics approach requires all the transfer functions of the system for the movement in question and all the inputs converging to the oculomotor plant through the final common path. Although the forward dynamics simulation of Krauzlis and Lisberger (1994) has shown that the floccular output drives the oculomotor plant and generates an accurate smooth eye-velocity profile in the monkey, there may be a number of unknown subsystems for the OKR in the cat, and it is actually difficult to know all the transfer functions of the OKR-related subsystems and all the inputs converging to the oculomotor plant.

Second, the inverse dynamics approach has the advantage of simultaneously estimating the multiple (acceleration, velocity, and position) motor sensitivities on the basis of the moment-by-moment data: the SS firing rate with time resolution of 1 ms was reconstructed from the time course of the eye acceleration, velocity, and position (Gomi et al. 1998; Shidara et al. 1993). This utilization of complete records of firing rate is in contrast to the methods of other studies. For example, Miles et al. (1980), Lisberger and Fuchs (1978), and Stone and Lisberger (1990) measured eye velocity and position sensitivities of floccular Purkinje cells of the monkey in smooth pursuit and fixation paradigms. Buttner and Waespe (1984) and Waespe et al. (1985) measured the eye velocity sensitivity during the OKR in monkeys. Fukushima et al. (1996) measured the eye velocity sensitivity during the vertical OKR in cats. These studies evaluated the sensitivity based on the mean or peak values of the data. For instance, the eye-velocity sensitivity of the Purkinje cell was evaluated by the parameter of half of the peak-to-peak firing frequency divided by peak eye velocity during sinusoidal smooth pursuit (Lisberger and Fuchs 1978) or by the correlation between the mean firing rate and the mean eye velocity during a given period of the optokinetic stimulus (Waespe et al. 1985). The eye-position sensitivity was evaluated based on the correlation between the mean firing rate of a given period of ocular fixation and the eye position (Miles et al. 1980). Thus the exact temporal relationship between SS rate and eye movement was not demonstrated in most of these studies. Moreover, we do not know whether or not the same value of the eye-position sensitivity that was evaluated during a static eye position can be regarded as the eye-position sensitivity for another modality of eye movement, for example, the OKR eye movement.

The inverse dynamics approach has been applied only to the OFR in the monkey and not yet to other eye movements, nor to other species. In the present study, applying the inverse dynamics approach to the cat OKR, we will present two new findings. First, Purkinje cells recorded from the middle zone of the cat flocculus had a SS rate that responded to ipsiversive eye movements during the OKR. Second, the inverse dynamics representation of the SS firing pattern revealed a close relation between the firing and eye movement patterns during the OKR. The relation was obtained for eye movements lasting 1 s (in one direction), i.e., for a substantially longer period than the 0.2 s of the OFR for which a relation was found using the inverse dynamics approach in previous studies (Gomi et al. 1998; Shidara et al. 1993). We discuss the likelihood that the middle zone Purkinje cells encode motor dynamics information for counteracting the viscosity and inertia forces during OKR eye movements.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Three adult cats were chronically prepared for single-unit recordings. The experimental procedures described below were performed in accordance with Guidelines for Animal Experiments, Yamanashi Medical University.

Animal preparation

Under pentobarbital sodium anesthesia (initial dose 40 mg/kg) and aseptic conditions, the cat had a recording chamber implanted. It was formed with dental acrylic on the occipitoparietal bone. A round opening was made in the bone overlying the cerebellum, and the dura was removed for microelectrode access. Between recording sessions, the cerebellar surface was covered with a piece of silicone rubber, and the chamber was closed with bone wax. Four fine needles were fixed stereotaxically to the chamber as reference points for putting the head in the accurate stereotaxic position during recording session. Two metal blocks were embedded in the dental acrylic cap for immobilization of the head. A scleral search coil made of Teflon-coated stainless steel wire was implanted beneath the insertions of the four extraocular recti muscles on the right eye for measuring eye movements (Fuchs and Robinson 1966). The tympanic bulla was opened, and a pair of silver ball electrodes was implanted on the round window and the adjacent bone on each side for the electrical stimulation of the eighth nerve.

Recording procedures

After 1-wk postoperative recovery, the recording sessions began. The cat's body was gently wrapped with a cloth bag. The cat was placed on a stereotaxic apparatus. The head was restrained by holding bars attached to the stereotaxic frame, which was mounted on a turntable. The head was pitched down 26.5° from the stereotaxic horizontal plane. The interauricular midpoint was positioned at the intersection of the two axes of the table rotation.

Eye movements were measured using a magnetic search-coil system described by Remmel (1984). The horizontal eye movement was measured in a 50-kHz magnetic field, and the vertical in a 75-kHz field. The position signals from the search coil system in addition to the stimulation data were sampled at 2-ms intervals by a computer and stored on hard disk.

Calibration of the eye movement was done in two ways. First, the horizontal 0° position in the eye-position recording was determined by evaluating the eye position when the cat watched a target (bell, diameter of 0.5°) ringing and moving along the vertical meridian on the screen. Horizontal right 10, vertical 0, and up 10° positions were also evaluated in similar ways, thus calibrating the amplitude of the horizontal and vertical 10°, respectively. Second, according to Iwamoto et al. (1990), the eye movement evoked by sinusoidal head rotation at 0.5 Hz and ±3° amplitude was recorded in stationary large-field visual surroundings. There were no differences in the results between the two methods of calibration.

A glass electrode (tip diameter, 5 µm; resistance, 1-2 MOmega ) filled with 2 M NaCl was stereotaxically inserted into the middle zone of the flocculus. One of the needles fixed in the recording chamber was used as a stereotaxic reference point. For initial identification of the flocculus the characteristic field potentials evoked by eighth nerve stimulation with single pulses of 0.1 ms duration were utilized (Shinoda and Yoshida 1975). Only single cells, in which both the complex spike (CS) and SS were clearly discriminated, were recorded as Purkinje cells in the flocculus. An initial spike of the multiple spikes of the CS was electrically discriminated using the time and amplitude window technique described by Sato et al. (1992). The SS was discriminated with the use of another window discriminator. The spike-occurrence outputs from the window discriminators were directly captured by a computer with a time resolution of 2 µs as the digital input for construction of the CS and SS density histograms.

Stimulation procedures

For optokinetic stimulation a pattern of random dots (diameters 0.2-1.0°) was projected through a fish-eye lens onto a half-cylinder screen in front of the animal, which was placed in the center of the screen. The screen was 100 cm in radius and 90 cm in height and subtended 80° horizontally and 50° vertically of the visual field of the animal. The distance from the cat's eyes to the screen was 100 cm. For optokinetic stimuli moving horizontally, the random dot pattern was rotated horizontally around the vertical axis at the screen's center of curvature under the control of a computer. For vertical optokinetic stimulation, the screen together with the projector was rotated manually by 90° around a horizontal axis approximating the cat's interauricular line. The stimulus velocity was monitored by an optical encoder. Optokinetic stimuli were applied as a sequence of constant-speed (5-40 deg/s) visual pattern movements in one direction for 1 s and then in the opposite direction for 1 s (Fig. 2A, 3rd trace). The relatively short stimulus duration of 1 s was chosen to reduce the occurrence of nystagmus. The horizontal OKR gain (maximal eye velocity/stimulus velocity) decreased with the stimulus velocity in our preliminary study: 0.59 ± 0.14 (SD; n = 8), 0.34 ± 0.13 (n = 8), 0.16 ± 0.05 (n = 7), and 0.06 ± 0.03 (n = 4) at stimulus velocities of 5, 10, 20, and 40 deg/s, respectively. In the present study, the stimulus velocity of 5 deg/s was used in most trials. Alertness of the cat was maintained by making a noise. In addition, caffeine and sodium benzoate (0.2-0.3 mg/kg) mixed with food were given when necessary.

Data preparation

The OKR eye movement is composed of quick and slow phases (nystagmus). We noted that the recorded Purkinje cells sometimes had SS firing modulation in association with the quick phases. Therefore to avoid SS activity related to the quick phase, we selected only the trials (sequences of ipsiversive and contraversive visual motion) during which quick phases did not occur. To obtain a total of 2,765 quick-phase-free trials, 7,645 trials were recorded during 5 deg/s horizontal stimuli. Similarly, a total of 2,246 quick-phase-free trials were obtained from 7,042 trials during 5 deg/s vertical stimuli. Data analysis was performed on a unit if >20 quick-phase-free trials were obtained.

Using the quick-phase-free trials, CS and SS density histograms were constructed aligned with the onset of pattern movement toward the right or upward. The "horizontal modulation" was defined as the difference in the average firing rate between ipsiversive and contraversive stimuli. The "vertical modulation" was defined as that between upward and downward stimuli. Because there was a latency of the spike response from the abrupt change of the stimulus direction (Fig. 2), the intervals over which firing rates were averaged were actually shifted 100 ms relative to the stimulus direction changes. The spike response latency was estimated to be 100 ms because 1) the latency of the OKR eye movement, calculated as the time interval from the abrupt change of the stimulus direction to the time the eye acceleration reached a value equal to 1 SD of the acceleration traces recorded over a full stimulus cycle was 108.0 ± 13.4 ms (range, 80.0-140.0 ms, n = 47), and 2) the spike response latency, which is technically difficult to determine precisely, was approximately equal to the OKR latency. A modulation >0.37 spikes/s in CS activity was defined to be a significant CS response to a horizontal or vertical stimulus. This is because, in spontaneous CS density histograms from 2-s recordings, the absolute value of the difference in the CS rates between the 1st second and the 2nd second of the recording was 0.15 ± 0.11 (SD) spikes/s (n = 40). The mean + 2 X SD = 0.37 spikes/s.

For the multiple regression analysis the eye position signal was low-pass filtered by a 2-pole digital Butterworth filter with a cutoff frequency of 20 Hz and then differentiated using 5 points for obtaining the eye velocity signals. The eye acceleration signal was obtained by digital differentiation of the eye velocity signal. The SS density histogram was also low-pass filtered by a 2-pole digital Butterworth filter with a cutoff frequency of 20 Hz. The computer program was user-written using MATLAB (Mathworks).

Regression with the inverse dynamics model

The inverse dynamics model (Gomi et al. 1998; Kawato et al. 1987; Shidara et al. 1993) was applied by performing a linear multiple-regression analysis to reconstruct the time course of the SS firing frequency (criterion variable) with a linear function of eye position and its first and second time derivatives (explanatory variable). The regression equation is given by
<IT>f</IT>(<IT>t</IT><IT>−&Dgr;</IT>)<IT>=</IT><IT>ae</IT><IT>″</IT>(<IT>t</IT>)<IT>+</IT><IT>be</IT><IT>′</IT>(<IT>t</IT>)<IT>+</IT><IT>ce</IT>(<IT>t</IT>)<IT>+</IT><IT>d</IT>
where f(t), e"(t), e'(t), e(t), and Delta  are the SS rate at time t, the eye acceleration, velocity, and position at time t, and the time delay between firing rate and movement, respectively. The coefficients (a, b, and c), the constant term (d), and the time delay were estimated by the ordinary least squares method (OLS). The search range for Delta  was from -40 to 40 ms. The number of sample points was maintained to be 500 during sliding of the time delay in the search range.

Modeling check

To obtain reliable fits of the data, a modeling check was performed. First, we investigated the correlation between explanatory variables. Generally, the confidence interval (CI), which is used as a measure of a coefficient's reliability, increases with the correlation. If we used a sinusoidal stimulus pattern, the acceleration and position variables would be expected to have a high negative correlation. To reduce the correlation between explanatory variables, we adopted a velocity-step stimulus protocol. Correlation can also produce multiple equally good solutions that are not necessarily exposed by high CIs. The variance inflation factor (VIF) was used to check this multicollinearity. The VIF of a given explanatory variable is
VIF=1/(1−<IT>R</IT><SUP><IT>2</IT></SUP>)
where R is a multiple correlation coefficient of a given explanatory variable fitted by the remaining explanatory variables. That is, a given explanatory variable was regarded as the criterion variable, which was fitted by the remaining explanatory variables, and the correlation coefficient between the criterion variable and the estimated data were calculated. The data are unreliable if the VIF is >= 10 according to Chatterjee and Price (1977).

Second, the distribution pattern of the residual error (difference between the actual and reconstructed SS rates at time t) was analyzed by plotting it against the reconstructed SS rate (Fig. 9A). It is a basic assumption underlying the application of OLS that the mean is close to 0, and the variance takes a constant value. To fulfill this OLS assumption, the plot of the residual error should make a distribution pattern of roughly uniform thickness along the horizontal axis (Fig. 9A). If the range of the residual error becomes wider with increase in the estimated SS rate, the assumption of constant variance would be violated. The model is inapplicable to data that do not fulfill the OLS assumption.

Third, the autocorrelation function of the residual error was calculated, and the periodicity was checked (Fig. 9, B and C). If the residual error can be regarded as white noise, the autocorrelation function should be 0 at all tau  except for tau  = 0. The threshold level of ±0.25 over tau  > 100 ms was adopted in the present study according to Gomi et al. (1998). The function had to stay beneath the threshold for a period lasting >100 ms. Periodicity would be observed if the model is inapplicable (e.g., important explanatory variables missing from the model).

Fourth, the coefficient of determination (CD), which is the square of the coefficient of correlation between the raw and reconstructed firing rates, was used as the parameter of the goodness-of-fit of the regression. The CD increases with the goodness-of-fit. The CD is also a function of the signal/noise (S/N): the CD increases with the S/N ratio of the SS firing data. As mentioned above, because of the contamination by quick phases of the eye movement data, it was difficult to obtain a large number of quick-phase-free trials. To increase the S/N ratio of the spike data, the data were averaged at a binwidth of 4 ms. Therefore in the present study, the time resolution of the analysis is 4 ms.

Fifth, the coefficient reliability was checked by the 95% CI. In the present study the 95% CI was calculated as the amplitude of the 95% certainty of the coefficient. The coefficient ranges, with 95% certainty, from A - B to A + B, where A is the coefficient and B is the 95% CI.

Sixth, the standard regression coefficient (SRC) was calculated. The SRC is the coefficient of each explanatory variable calculated by the regression of the standardized criterion variable (mean = 0, SD = 1) with the standardized explanatory variables. By comparing the SRCs of the different explanatory variables, we can compare the relative contributions of each explanatory variable to the regression of the criterion variable.

Finally, the statistical significance of the contribution of each explanatory variable to the regression of the criterion variable was tested by the forward selection method. The model started as a no-explanatory-variable model, and a simple regression analysis was performed (step 0). The explanatory variable whose F-value for the regression was the largest was then chosen. If the F-value was >2.62 (P < 0.05), this explanatory variable was selected, and the regression analysis was performed (step 1). Additional variables were selected in steps 2 and 3 if the F-value was >2.62. If the F-value was <2.62 (P > 0.05), the test was finished without selecting the variable. In some cases, we forced the forward selection analysis to reach step 3 regardless of the F-value, and the CD in each step was calculated.

Regression by the equation including the slide term

A general problem is that missing explanatory variables undetected by the residual autocorrelation test could cause the remaining coefficients to be erroneously computed. The regression analysis was also performed by adding the slide term in the inverse-dynamics equation as an additional variable. Inclusion of the slide term adds a zero to the transfer function of our original inverse dynamics model (2 poles and no zero model). The regression equation by the two poles and one zero model is given by
<IT>f</IT>(<IT>t</IT><IT>−&Dgr;</IT>)<IT>=</IT><IT>ae</IT><IT>″</IT>(<IT>t</IT>)<IT>+</IT><IT>be</IT><IT>′</IT>(<IT>t</IT>)<IT>+</IT><IT>ce</IT>(<IT>t</IT>)<IT>+</IT><IT>d</IT><IT>−</IT><IT>T<SUB>z</SUB>f</IT><IT>′</IT>(<IT>t</IT><IT>−&Dgr;</IT>)
where Tz is the time constant and f '(t - Delta ) is the time derivative of f(t - Delta ), which is given by
<IT>f</IT><IT>′</IT>(<IT>t</IT>)<IT>=</IT>[<IT>f</IT>(<IT>t</IT><IT>+</IT><IT>t</IT><SUB><IT>bin</IT></SUB>)<IT>−</IT><IT>f</IT>(<IT>t</IT><IT>−</IT><IT>t</IT><SUB><IT>bin</IT></SUB>)]<IT>/2</IT><IT>t</IT><SUB><IT>bin</IT></SUB>
where tbin = 0.004 s in the present study. The contribution of each explanatory variable to the regression of the criterion variable was tested by the forward selection method. If the F-value was >2.39 (P < 0.05), the explanatory variable was selected.

A similar analysis was performed by considering the slide term as a substitute for the position term. The regression equation is then given by
<IT>f</IT>(<IT>t</IT><IT>−&Dgr;</IT>)<IT>=</IT><IT>ae</IT><IT>″</IT>(<IT>t</IT>)<IT>+</IT><IT>be</IT><IT>′</IT>(<IT>t</IT>)<IT>−</IT><IT>T<SUB>z</SUB>f</IT><IT>′</IT>(<IT>t</IT><IT>−&Dgr;</IT>)<IT>+</IT><IT>d</IT>

Identification of recording sites

At the termination of the experiment, some of the recording sites were marked by electrophoretic injection of pontamine sky blue (3 µA, 15 min). The animal was deeply anesthetized with pentobarbital sodium and perfused with 10% Formalin. The cerebellum was cut in sagittal sections and was stained with neutral red. Enlarged drawings of the cerebellar sections were made with the aid of a drawing tube attached to a microscope. Based on the dye-spot locations and electrode tracks, the recording sites were reconstructed on the drawings (Fig. 1).



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Fig. 1. Sagittal sections (a 1 in 10 series of 0.1-mm sections) through the flocculus (FL) and the adjacent ventral paraflocculus (VPF) at 3 different mediolateral levels. The cells were recorded in the diagonally striped area that corresponds to the middle zone of the FL. The gray areas represent the granular layer.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Identification of middle-zone Purkinje cells

Identification of the middle-zone Purkinje cells in the cat flocculus was made both anatomically and physiologically. Anatomically, the recording site was determined with reference to the dye spot and the electrode track and was confirmed to be located in the flocculus in an area corresponding to the middle zone (Fig. 1). Physiologically, the direction selectivity of the CS response to large-field movement stimuli was investigated according to Fushiki et al. (1994). In response to constant speed (5 deg/s) visual stimuli to the right side for 1 s and then to the left side for 1 s (Fig. 2A, 3rd trace), the OKR eye movement was elicited (Fig. 2A, 4th trace). The retinal slip velocity was calculated by subtracting the eye velocity from the stimulus velocity, and it was in the appropriate low speed range (<9 deg/s in Fig. 2A, bottom trace) to elicit vigorous CS responses in the cat flocculus (Fushiki et al. 1994). The responses of a typical Purkinje cell on the left side are shown in Fig. 2. The CS activity was strongly modulated during horizontal stimuli: the CS rate increased during contraversive (rightward) stimuli and decreased during ipsiversive (leftward) stimuli (Fig. 2A, 1st trace). The horizontal modulation (difference in the CS rate between ipsiversive and contraversive stimuli) was -2.22 spikes/s in this cell. On the other hand, during vertical stimuli (Fig. 2B), the vertical modulation (difference in the CS rates between upward and downward stimuli) was -0.31 spikes/s. The direction selectivity of the SS response during the OKR was in the opposite direction to that of the CS response: the SS firing increased during ipsiversive stimuli and decreased during contraversive stimuli (Fig. 2A, 2nd trace). The horizontal and vertical modulation of the SS was 26.16 and -5.13 spikes/s in the cell represented in Fig. 2.



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Fig. 2. Direction selectivity of a Purkinje cell in the middle zone of the left flocculus during horizontal (A) and vertical (B) optokinetic response (OKR) at a stimulus velocity of 5 deg/s. The mean of 49 quick-phase-free trials selected from 259 trials is shown in A, and the mean of 39 from 200 trials is shown in B. Top to bottom: complex spike (CS) and simple spike (SS) histograms, surround velocity (S), eye velocity (Edot), and retinal slip velocity (S-Edot). Binwidth is 4 ms. Note that the CS firing frequency increases during contraversive (r, rightward) stimuli and decreases during ipsiversive (l, leftward) stimuli, and that the SS response is reciprocal to the CS response. Upward (u) and downward (d) stimuli are not effective for evoking CS or SS responses.

We selected, in the middle zone of the flocculus, the 66 horizontal-type Purkinje cells whose CS horizontal modulation was >0.37 spikes/s and larger than the vertical modulation. Figure 3 summarizes the direction selectivity of the 66 horizontal-type cells during the OKR by plotting the vertical modulation as a function of the horizontal modulation. The CS rate increased during contraversive stimuli (open circle ), whereas the SS rate increased during ipsiversive stimuli () in all 66 cells. The mean horizontal and vertical modulation of the CS was 1.53 ± 0.64 and 0.01 ± 0.27 (SD) spikes/s, respectively, and the mean vector points in the contralateral direction with a small upward inclination of 0.37°. The mean horizontal and vertical modulation of the SS was 14.69 ± 7.95 and 1.90 ± 5.44 spikes/s, respectively, and the mean vector points in the ipsilateral direction with a small upward inclination of 7.37°. Thus the mean directional preferences of the CS and SS responses are nearly in the horizontal meridian and in opposite directions to each other (Fig. 3, thick lines).



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Fig. 3. Direction selectivity of middle-zone Purkinje cells (n = 66) during the OKR at a stimulus velocity of 5 deg/s. The vertical modulation (difference in the spike rate between upward and downward visual stimuli) vs. horizontal modulation (difference between ipsilateral and contralateral stimuli) is plotted for each cell. Note that the mean vectors (thick lines) of the CS responses (open circle ) and the SS responses () are nearly in the horizontal meridian and in opposite directions.

Inverse-dynamics approach

Figure 4A shows the time course of the SS firing frequency (1st trace) of an horizontal-type Purkinje cell on the left side middle zone together with the OKR eye acceleration (2nd trace), velocity (3rd trace), and position (bottom trace). The latency of the OKR eye movement in this trial is 92 ms, measured as the time interval from the abrupt change of the stimulus direction (time 0) to the time the eye acceleration reached a value equal to 1 SD of the acceleration trace. Two acceleration phases were distinguished in the velocity profile (Fig. 4A, 3rd trace) during rightward (contraversive) stimuli: a rapid acceleration phase followed by a slower acceleration phase. The rapid acceleration phase is very short in duration (56 ms), and the eye velocity changes rapidly by 3.72 deg/s (from 4.25 to 0.52 deg/s). The slower acceleration phase occupies the remaining longer period until the eye starts to reverse direction again, and the eye velocity changes slowly by 3.96 deg/s (from 0.52 to the mean steady-state velocity of -3.44 ± 0.17 deg/s). The SS firing rate also tends to change rapidly during the rapid acceleration phase, and slowly during the slower acceleration phase (Fig. 4A, 1st trace). A similar tendency was observed during leftward (ipsiversive) stimuli: the presence of rapid and slower acceleration phases in the eye velocity profile are a common feature in the present study.



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Fig. 4. Multiple regression analysis. A: time course of the SS firing frequency and the OKR eye movement at a stimulus velocity of 5 deg/s in the unit shown in Fig. 2. From top to bottom: SS firing rate, eye acceleration, velocity, and position. Binwidth is 4 ms. Time 0 indicates the onset of a trigger pulse, which drives a sequence of optokinetic stimuli. Upward direction in the figure means eye movements in the direction ipsilateral to the recording site. B: estimation of the SS firing frequency as a linear weighted superposition of the eye acceleration, velocity, and position data shown in A. The raw (dotted line) and reconstructed (thick solid line) SS frequency together with the eye position (broken line), velocity (medium solid line), and acceleration (thin solid line) components are illustrated. For the superposition, the SS profiles were shifted by the delay time (from SS response to eye movement response) of 12 ms.

A multiple regression analysis was performed to reconstruct the instantaneous SS firing frequency (criterion variable) from the eye position, velocity, and acceleration (explanatory variables). Figure 4B shows the superimposed traces of the raw (dotted line) and reconstructed (thick solid line) firing rates of the cell together with the contributions of the position (broken line), velocity (medium solid line), and acceleration (thin solid line) terms to the reconstructed SS rates. The reconstruction error had its minimum at a time delay of 12 ms and a constant term (d) of 20.4 spikes/s. The velocity coefficient (b) was 3.59 spikes/s per deg/s, and the contribution of the velocity term [be'(t), medium solid line] was dominant over most of the stimulus cycle. The position coefficient was -4.72 spikes/s per deg, and the position term [ce(t), dashed line] was of reversed sign compared with the direction of the movements, playing a key role in changing the reconstructed firing rate gradually during the slower acceleration phase. The acceleration coefficient (a) was 0.084 spikes/s per deg/s2, and the contribution of the acceleration term [ae"(t), thin solid line] was large during the rapid acceleration phase. The CD was 0.89, indicating that the regression model satisfactorily explains the time course of the SS firing frequency. The 95% CI of each coefficient was 0.027 spikes/s per deg/s2, 0.13 spikes/s per deg/s, and 0.83 spikes/s per deg for the acceleration, velocity, and position coefficients, respectively, indicating that the coefficient ranges are, with 95% certainty, from 0.057 to 0.111 spikes/s per deg/s2 for the acceleration, from 3.46 to 3.72 spikes/s per deg/s for the velocity, and from -5.55 to -3.89 spikes/s per deg for the position coefficient. The SRC was 0.11 for the acceleration, 0.78 for the velocity, and -0.48 for the position variable, indicating that the velocity variable is the largest of the three regarding the magnitude of contribution to the regression. The autocorrelation function of the residual error was within ± 0.14.

Data selection

Out of the 66 horizontal-type cells, the regression analysis just described was performed in 47 cells in which the SS firing was well modulated (horizontal modulation >10 spikes/s). In these 47 cells the modeling check was performed. First, the correlation between explanatory variables was examined with the use of the VIF, which was 1.7 ± 0.2 (maximum, 2.3) for the position, 1.1 ± 0.1 (1.2) for the velocity, and 1.6 ± 0.2 (2.3) for the acceleration variable. Because the VIF was at most 2.3 and <10, we concluded that the stimulus pattern of the velocity step adopted in the present study was adequate for avoiding the multicollinearity in the multiple regression analysis. Second, the scatter diagram of the residual error relative to the reconstructed SS rate was drawn (Fig. 9A). The plot of the errors formed a horizontal pattern (Fig. 9A); that is, it was symmetrical about the x-axis (error = 0), and the range did not change as a function of the estimated SS rate in any of the 47 cells, fulfilling the basic assumption of OLS (see METHODS). Third, the periodicity was studied in the autocorrelation function of the residual error. It was observed in six cells: the function stayed beyond the threshold level of ±0.25 for a period lasting >100 ms of tau  (Fig. 9B), suggesting that there were some significant features of the cell's response that were not fit by the inverse dynamics model in these six cells. Periodicity was not found at that threshold level in the remaining 41 cells, suggesting that the inverse-dynamics model was applicable to these 41 cells (Fig. 9C). The mean CD was 0.76 ± 0.12 in these applicable 41 cells.

Figure 5 shows the distribution of the time delay and each coefficient in those 41 cells. The mean time delay is 11 ± 10 ms (Fig. 5A). Gomi et al. (1998) found, in the monkey ventral paraflocculus, that the mean time delay estimated by the inverse-dynamics analysis was 7.47 ms, which was close to the latency of electrically induced eye movements (8.6-10.9 ms) (Shidara and Kawano 1993). Unfortunately there is no data available as to the latency of eye movements electrically induced in the alert cat's flocculus. The mean values of the coefficients were 0.056 ± 0.179 spikes/s per deg/s2 for the acceleration (Fig. 5B), 5.10 ± 2.41 spikes/s per deg/s for the velocity (Fig. 5C), and -2.40 ± 4.11 spikes/s per deg for the position (Fig. 5D) coefficient. The mean of the 95% CI of each coefficient was 0.060 ± 0.043 spikes/s per deg/s2, 0.266 ± 0.139 spikes/s per deg/s, and 0.817 ± 0.511 spikes/s per deg for the acceleration, velocity, and position coefficients. These CIs were three to nine times smaller than the SDs of each coefficient, indicating sufficient reconstruction reliability. Based on the CI, all of the 41 velocity coefficients are significantly positive, 22 of the acceleration coefficients are significantly positive, whereas 11 are negative; and 10 of the position coefficients are positive, whereas 28 are negative. With the use of the SRC, we analyzed the relative contributions of the explanatory variables to the regression. The mean SRC was 0.03 ± 0.11 for the acceleration, 0.81 ± 0.11 for the velocity, and -0.17 ± 0.22 for the position variables. It may be worth mentioning that mean values of the position and acceleration coefficients and SRCs become smaller than what is expected from an individual cell's coefficients and SRCs (i.e., the cell presented in Fig. 4), because the position and acceleration coefficients of individual cells take both positive and negative values. Thus the mean velocity SRC was the largest of the three: the position SRC was 20.7% and the acceleration SRC was only 4% of the velocity SRC, suggesting that the SS firing pattern can be explained predominantly by the velocity term.



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Fig. 5. Distribution of the time delay (A) and the eye acceleration (B), velocity (C), and position (D) coefficients (n = 41). A positive time delay implies the unit response preceded the eye movement. A positive coefficient means the unit's SS rate tended to increase with increasing eye acceleration, velocity, or position toward the ipsilateral side.

Selection of explanatory variables

The statistical significance of the contribution of the three explanatory variables (acceleration, velocity, and position) to the regression of the criterion variable was investigated, in the 41 cells for which the model was applicable, with the forward selection method. Three cell types were found: the velocity-position-acceleration (VPA) type, in which all three explanatory variables were selected (n = 27); the velocity-position (VP) type, in which the velocity and position variables were selected (n = 12); and the velocity-acceleration (VA) type, in which the velocity and acceleration variables were selected (n = 2). The representative VPA-type cell has already been shown and explained in Fig. 4. Figure 6A illustrates a representative VP-type cell, in which the SS firing pattern was well reconstructed (CD, 0.79) by the linear addition of the velocity (coefficient, 5.98 spikes/s per deg/s), position (coefficient, -4.54 spikes/s per deg), and constant (29.1 spikes/s) components with a small acceleration (coefficient, 0.022 spikes/s per deg/s2) component. Figure 6B shows a representative VA-type cell, in which the SS firing was well reconstructed (CD, 0.88) by the velocity (coefficient, 4.32 spikes/s per deg/s), acceleration (coefficient, -0.035 spikes/s per deg/s2) and constant (24.5 spikes/s) components with a small position (coefficient, -0.164 spikes/s per deg) component.



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Fig. 6. Selection of the explanatory variable. A: VP-type cell. The raw (dotted line) and reconstructed (thick solid line) SS frequency together with the eye position (broken line), velocity (medium solid line), and acceleration (thin solid line) components are illustrated. For superposition, the SS profiles were shifted by the delay time of 12 ms. Estimated coefficients are given in the text. Note that the contribution of the acceleration component is small. B: velocity-acceleration (VA)-type cell. Shift of the SS profile is 20 ms. Note that the contribution of the position component is small, making the reconstructed SS firing rates constant during the steady eye-velocity phase.

Figure 7A shows the CD in steps 1, 2, and 3 of the forward selection analysis for the VPA-type cells. In step 1 the velocity variable (open circle ) was selected in most cells (26 of the 27 cells), and the mean CD was 0.67 ± 0.15. In step 2 the position variable (triangle ) was selected in most cells (15 of the 27 cells), and the mean CD increased to 0.76 ± 0.13. In step 3 the acceleration variable () was selected in most cells (16 of the 27 cells), and the mean CD increased to 0.77 ± 0.13. The results indicate that the contribution of the velocity variable is the largest and that of the acceleration variable is minimal in most VPA-type cells.



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Fig. 7. Coefficient of determination (CD) at each step (1, 2, and 3) in the forward selection analysis. A: velocity-position-acceleration (VPA)-type cells (n = 27) in which the velocity (open circle ), position (triangle ), and acceleration () variables were selected (solid line). B: VP-type cells (n = 12) in which the velocity and position variables were selected at steps 1 and 2, but the contribution of the acceleration variable was not significant (P > 0.05, broken line) at step 3. C: VA-type cells (n = 2) in which the velocity and acceleration variables were selected at steps 1 and 2, but the contribution of the position variable was not significant (P > 0.05, dashed line) at step 3.

The forward selection analysis was performed until the final step 3 in the 12 VP-type cells regardless of the F-value. In most cells (11 of the 12 cells) the velocity and position variables were selected in steps 1 and 2, respectively (Fig. 7B). The mean CD increased from 0.67 ± 0.11in step 1 to 0.76 ± 0.10 in step 2. In step 3, where the acceleration variable was added to the model, the CD does not change (Fig. 7B).

The same forward selection analysis was performed until step 3 in the 2 VA-type cells. In both the cells the velocity and acceleration components were selected in steps 1 and 2, respectively (Fig. 7C). The CD was 0.82 and 0.88 in step 1, and changed to 0.83 and 0.88 in step 2 (Fig. 7C). In step 3 the CD did not change (Fig. 7C).

Scalability of the model

Scalability of the model to different stimulus velocities was investigated. Figure 8A shows the regression analysis during a 5 deg/s stimulus velocity in a VPA-type cell. The raw SS firing rate (dotted line) is well fitted (CD, 0.89) by the reconstructed SS rate (thick solid line), which is the linear addition of the acceleration (thin solid line), velocity (medium solid line), position (broken line), and constant (31.7 spikes/s) components. In the reconstruction, the coefficients of eye acceleration, velocity, and position were 0.729 spikes/s per deg/s2, 12.5 spikes/s per deg/s, and -7.74 spikes/s per deg, respectively. Using this set of coefficients obtained with a 5 deg/s stimulus velocity, the SS rate during a 10 deg/s stimulus velocity was reconstructed. As shown in Fig. 8B, the reconstructed SS rate has a DC shift toward lower values relative to the actual SS rate. Comparison of the eye position data between Fig. 8, A and B (bottom trace) reveals a similar DC shift: -6.0° at 0 deg/s eye velocity in Fig. 8A and -2.1° in Fig. 8B. This DC shift of 3.9° in eye position was corrected in Fig. 8C (bottom trace). Using the corrected eye-position data, the SS rate during 10 deg/s stimulus velocity was well reconstructed (CD, 0.81) without a prominent DC shift (Fig. 8C), suggesting that the absolute eye position information is not encoded in the flocculus SS activities during the OKR. Thus the position information encoded in the middle zone is relative but not absolute, in the sense that a shift in eye position during the OKR affects the firing rate, but the initial eye position does not. It should be mentioned that this finding can be applied to the smooth OKR eye movements (slow phases of optokinetic nystagmus), but we are not sure whether or not it can be applied also to other kinds of eye movements, such as the rapid eye-position change of saccadic eye movements.



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Fig. 8. Generality of model for different stimulus velocities. A: regression of the SS rate at a stimulus velocity of 5 deg/s. B: global fitting of the SS rate at a stimulus velocity of 10 deg/s, using the set of coefficients obtained with the 5 deg/s stimulus velocity. Note a DC shift of the reconstructed SS rates relative to the actual SS rates. Note also the DC shift of the eye position at 0 deg/s eye velocity: -6.0° in A and -2.1° in B. C: after correction of the DC shift of the eye position, the DC shift of the reconstructed SS rates largely disappeared. See Fig. 4 for key.



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Fig. 9. Regression reliability. A: relationship between the residual error [difference between the raw and reconstructed simple-spike (SS) rates at time t] and the reconstructed SS firing rate. Note that the residual error is distributed in a horizontal zone, suggesting that the mean is close to 0 and the variance is constant regardless of the reconstructed SS rate. This cell satisfies the assumption of the ordinary least-squares method. B and C: autocorrelation function of the residual error in 2 different cells. If the residual error can be regarded as random white noise, the autocorrelation function will be close to 0 at all tau  except for tau  = 0. Periodicity is found in B at the threshold level of ±0.25 at some tau  > 100 ms, suggesting that the regression model is inapplicable to this cell. Periodicity is not found in C, satisfying one of the requirements that the model is applicable to this cell.

The SS firing pattern at different stimulus speeds was reconstructed with the use of the DC-compensated eye movement data multiplied by the single set of coefficients obtained with the 5 deg/s stimulus velocity in seven cells. In all seven of the cells with a 10 deg/s stimulus, in six of the seven with a 20 deg/s stimulus, and in two of the seven with a 40 deg/s stimulus, the SS firing modulation was >10 spikes/s and the number of quick-phase-free trials was >20. For these data sets the reconstruction fit well the actual SS firing pattern. The CD was > 0.7 in most cases (6 of the 7 cells, 4 of the 6 cells, and 2 of the 2 cells at stimulus velocities of 10, 20, and 40 deg/s, respectively), indicating that the single set of coefficients calculated during the 5 deg/s stimulus velocity (local fitting) could satisfactorily predict the time course of the SS firing during other stimulus velocities (global fitting). In these cases the OKR gain (maximal eye velocity/stimulus velocity) decreased with stimulus velocity: 0.63 ± 0.11 (n = 7), 0.35 ± 0.13 (n = 7), 0.18 ± 0.04 (n = 6), and 0.08 ± 0.02 (n = 2) at stimulus velocities of 5, 10, 20, and 40 deg/s, respectively. This decrease might be due to the short stimulus period of 1 s making the contribution of the velocity storage system to the OKR (Cohen et al. 1977) relatively small.

The CD with the use of the single set of coefficients applied to other velocities (global fitting) was compared with that with the original reconstruction of the SS response to the 5 deg/s stimulus (local fitting). The decrease in the CD of the global fitting compared with that of the local fitting was very small (mean decrease in the CD; 0.06, 0.05, and 0.04 at stimulus velocities of 10, 20, and 40 deg/s, respectively) but significant (P < 0.05), suggesting a very small nonlinearity in the relationship between the SS firing and the OKR eye movement under multiple stimulus velocities.

Regression analysis by the regression equation including the slide term

In the present study, the mean position coefficient was a negative value. One might suspect that the position coefficient would become a positive value if we analyzed the data by the regression equation including the slide term, because some investigators (Fuchs et al. 1988; Stahl and Simpson 1995) used the slide term in describing the decay of the firing rate during static eye position after a saccadic eye movement. This possibility was tested in the 41 cells to which the inverse dynamics model was applicable, and in which the mean acceleration, velocity, and position coefficients were, as mentioned before, 0.056 spikes/s per deg, 5.10 spikes/s per deg/s, and -2.40 spikes/s per deg, respectively, without the slide term.

Judging from Fig. 4B, in which the regression was made without the slide term, the negative position coefficient explains the gradual increase and decrease of the SS firing of ~20 spikes/s per s. These changes of 20 spikes/s per s might instead be explained by a slide term having a coefficient of ~1 s. In the regression analysis including the slide term as an additional variable in the inverse dynamics model, however, the mean Tz was only 5.5 × 10-5 ± 8.5 × 10-5 (SD) s (n = 41), contributing only 0.0011 spikes/s, on average, to the firing change of 20 spikes/s per s. Thus the contribution of the slide term is negligible compared with the amplitude of the gradual SS firing change during the OKR. Statistically, the slide term was rejected in the forward selection analysis in all of the 41 cells tested. Moreover, in the regression analysis including the slide term the mean acceleration, velocity, and position coefficients were the same as they were without the slide term.

Similar results were obtained in the regression analysis by adding the slide term as a substitute for the position term: mean Tz was only 1.1 × 10-4 ± 1.2 × 10-4 (SD) s (n = 41). The CD calculated with the slide term and lacking the position term (mean, 0.71 ± 0.13) was significantly (P < 0.01) better than that with the velocity-term-alone model (mean, 0.67 ± 0.15), but was significantly (P < 0.01) lower than that (0.76 ± 0.12) calculated by the basic inverse dynamics model (position, velocity, and acceleration terms, and no slide term).

Thus the position coefficient remained a negative value even after the inclusion of the slide term in the regression equation, and the contribution of the slide term to the regression is negligible during the OKR eye movement. It is concluded that we do not have to adopt the two poles and one zero model for analyzing the firing rate during the OKR in the present study.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

It has been reported that the CS activity of the Purkinje cell in the cat flocculus middle zone (Fig. 1) is modulated in a direction-selective manner during movement of a large-field visual pattern: the CS firing rate increases during contralateral movement and decreases during ipsilateral movement, and is not modulated by vertical stimuli (Fushiki et al. 1994). In the present study, following Fushiki et al. (1994), a middle-zone Purkinje cell was identified by the direction-selective CS activity during movement of a large-field visual pattern that elicits the OKR in the alert cat (Figs. 2 and 3). The present study has shown that the SS firing of an identified Purkinje cell is also modulated in a direction-selective manner during the stimuli. The SS modulation was reciprocal to the CS modulation: the SS-firing frequency increased during ipsiversive stimuli and decreased during contraversive stimuli (Figs. 2 and 3). Thus the SS activity of the middle-zone Purkinje cell is modulated during the OKR in the horizontal plane, and the preferred direction is ipsilateral to the recording side.

Two acceleration phases in OKR

There are two acceleration phases in the horizontal OKR evoked by constant-velocity (velocity-step) visual stimuli: a rapid rise to half of the stimulus velocity, followed by a slower rise to a steady state in the monkey (Cohen et al. 1977). The rapid rise is attributed to the direct-pathway system, whereas the slower rise is considered to be generated through the velocity-storage system in the vestibular system including the vestibular nuclei (Cohen et al. 1977). There are species differences in the relative contributions of the two systems. The rabbit shows a slower rise without an initial rapid rise, suggesting a dominant contribution of the velocity-storage system to the OKR (Collewijn 1976; Collewijn et al. 1980). The cat is situated between the monkey and the rabbit, showing a small (sometimes absent) rapid rise followed by a slow buildup (Maioli and Precht 1984). In the present study, the short-duration (1 s) velocity step was adopted as a stimulus paradigm, making the contribution of the velocity-storage system to the OKR smaller. The prominent SS modulation during the rapid rise phase in the present study may suggest that the cat flocculus is involved in the direct-pathway system. This view may be supported by the experimental results that the rapid rise, as well as steady-state velocities >60 deg/s, was impaired after flocculus lesion in the monkey (Waespe et al. 1983; Zee et al. 1981).

The SS responses of flocculus Purkinje cells during the horizontal OKR have been investigated previously in other species. In the albino rabbit, the SS activity was not modulated during sinusoidal OKR stimuli (Ghelarducci et al. 1975). In the pigmented rabbit, the SS activity was modulated during the sinusoidal OKR at a stimulus amplitude of 2.5° and a frequency of 0.33 Hz (Nagao 1990, 1991). In most (82 of 139 cells) cells the SS rate increased during ipsiversive stimuli and decreased during contraversive stimuli (Nagao 1991) in concordance with the direction selectivity found in the present study in the cat.

In the monkey the SS activity of the flocculus Purkinje cell was investigated during the OKR at trapezoid stimulus velocities lasting >20 s, which is long enough for full recruitment of the velocity-storage system (Waespe and Henn 1981). The SS activity was modulated at higher stimulus velocities (>30 deg/s) and was not modulated at lower velocities (<30 deg/s) (Waespe and Henn 1981). Taking account of the fact that the firing rate of the vestibular nuclear neuron increases linearly with the eye velocity at <40-60 deg/s and saturates at >40-60 deg/s (Waespe and Henn 1977, 1979), Waespe and Henn (1981) have proposed that the flocculus Purkinje cells are modulated if the vestibular neurons provide insufficient signals during the OKR. Supporting this proposal, Markert et al. (1988) have reported that the flocculus Purkinje cells are modulated at higher frequencies (>0.05 Hz) of the sinusoidal OKR, and Boyle et al. (1985) have shown that the vestibular nucleus neurons are modulated at lower frequencies (<0.2 Hz) in the monkey. In the present study, unfortunately, we did not perform experiments in the long-duration OKR paradigm that would fully activate the velocity storage system, because it was difficult to obtain quick-phase-free trials in the long-duration OKR.

Motor dynamics encoding in the middle zone

In the present study, most interestingly, the time course of the SS firing frequency in the flocculus middle zone was successfully reconstructed by a linear weighted superposition of the eye position, velocity, and acceleration during short-duration OKR in the alert cat (Figs. 4 and 5). The regression model used in the present study is based on the inverse dynamics model proposed by Kawato et al. (1987). The residual error analysis reveals that the inverse dynamics model is applicable to most cells (41 of the 47 cells investigated). The mean CD was 0.76 ± 0.12 (n = 41), indicating the good fit of the regression. Using a single set of coefficients obtained with a 5 deg/s stimulus velocity, the SS firing rates during other stimulus velocities were also successfully reconstructed (Fig. 8), suggesting the generality of the model for multiple stimulus velocities.

Reservations should be mentioned here. The mean of the CD in the 41 cells to which the model was applicable was 0.76 in the present study, indicating that the model did not account on average for 24% of the variance in the responses. These unaccountable components may be composed partly of real responses as well as noise because, although the model explains most parts of the SS responses, the overshoot and undershoot of the SS responses are underfitted (Fig. 4B). This lack of fit escaped detection by the autocorrelation function test. The aim of the present study is to clarify how the middle zone might play a role in the OKR eye movement, and we investigated the correlation between the SS activities and the motor parameters by using the inverse dynamics approach. The present study was not a systematic search for the complete model that fully reconstructs the SS firing pattern. In the monkey flocculus, gaze velocity Purkinje (GVP) cells during pursuit of a small target moving with triangle-wave motion, the overshoot and undershoot, which were not explained by the eye-velocity sensitivity, were discussed in terms of the eye acceleration and the retinal slip (Lisberger and Fuchs 1978; Stone and Lisberger 1990). In the future, potential explanatory variables should be systematically explored, searching for the full fitting of the SS activity.

Our results provide evidence that the eye acceleration, velocity, and position information is encoded in the SS firing pattern and that the SS firing precedes the eye movement by 11 ms on average, satisfying one of the requirements for activity that provides motor dynamics information to extraocular motoneurons used in driving the OKR eye movement. In the present study, the mean coefficient was 5.10 spikes/s per deg/s for the velocity, and 0.056 spikes/s per deg/s2 for the acceleration variable. To compare these coefficients in the Purkinje cells with those in other neurons, we use the coefficient ratio that normalizes the firing rate levels of neurons in different nuclei. The ratio of the mean acceleration to the velocity coefficients in the cat flocculus Purkinje cells is 0.011, which is very close to that of 0.015 calculated in the monkey extraocular motoneurons (Keller 1973), supporting the possibility that the flocculus Purkinje cell might be one of the neurons providing motor dynamics information for eye velocity and acceleration to the extraocular motoneurons. This dynamic information would be transmitted to the abducens motoneurons and the abducens internuclear neurons disynaptically through the floccular target neurons located in the rostral part of the medial vestibular nucleus (Sato et al. 1988) for counteracting the viscosity and inertia forces during the short-duration OKR eye movement.

Judging from the SRC (means are 0.81, -0.17, and 0.03 for the velocity, position, and acceleration variables, n = 41), the contribution of the velocity variable to the regression is larger than that of the position and acceleration variables (>4 times for the position and 27 times for acceleration variables), suggesting that the SS firing can be explained predominantly by the velocity variable. Statistically, the acceleration or position information is lacking in some cells (VP- and VA-type cells, Figs. 6 and 7), whereas the velocity information is encoded in all the cells tested (VPA-, VP-, and VA-type cells). These findings may suggest that the major role of the flocculus middle zone during the horizontal OKR is to counteract the viscosity dynamics by providing velocity information. This view may be supported by the finding that the dominant information encoded in the monkey flocculus GVP cell is the eye velocity during smooth pursuit eye movements (Lisberger and Fuchs 1978; Miles et al. 1980). The eye-velocity coefficient calculated in the present study in the cat OKR (mean 5.1 spikes/s per deg/s) is less than five times larger than those reported previously in the monkey smooth pursuit (e.g., Miles et al. 1980; Stone and Lisberger 1990).

In previous studies the eye-position sensitivity of the SS firing was investigated during maintained eye fixation but not during eye motion: according to Miles et al. (1980), during 20° eye fixation, mean position sensitivity was 0.26 spikes/s per deg for 56 horizontal GVP cells and -0.17 spikes/s per deg for 23 horizontal GVP cells, but the position sensitivity during the smooth pursuit was not estimated. In contrast, in the present study the position sensitivity (mean, -2.40 spikes/s per deg) was calculated during eye motion but not during maintained eye position. It is difficult to compare directly the present eye-position sensitivity, which was measured during eye motion, with that of the previous study, measured during static eye position.

In the present study, the mean position coefficient was negative, meaning that the SS rates tended to decrease with change in position toward the ipsilateral side. Considering that 1) the mean velocity and acceleration coefficients were positive and the SS firing frequency estimated from the eye velocity and the acceleration increased with ipsilateral eye movement in the present study, and 2) electric stimulation of the middle zone elicits ipsilateral eye movements (Sato and Kawasaki 1990b), the negative position information is inappropriate for counteracting the elastic forces on the eye. One may suggest that an inappropriate position coefficient is calculated here due to an inappropriate model in which the slide term is lacking, and that the slide term may explain the SS firing decay during the OKR as it explained the motoneuron firing decay during the static eye position after a saccade (Fuchs et al. 1988; Stahl and Simpson 1995). However, this possibility is unlikely because 1) as mentioned before, we demonstrated, using a residual error analysis, that the model is applicable to most cells, 2) the regression model that included the additional slide term did not significantly change the negative value of the position coefficients, and 3) the contribution of the slide term as a substitute for the eye position term to the regression was negligible. Rather, the negative position coefficient may suggest that some portion of the brain other than the flocculus would provide position information for counteracting the elastic force during short-duration OKR eye movement.

Comparison with other inverse dynamics model studies

This study compliments other inverse dynamics model studies of Shidara et al. (1993) and Gomi et al. (1998). That is, first, this study confirms the main conclusion of their studies that the SS firing patterns are well reconstructed by a linear weighted superposition of the eye acceleration, velocity, and position data in a different species (cat rather than monkey) and during a different behavior (OKR rather than OFR). Differences between their OFR and our OKR will be discussed here. Their studies for the OFR employed a large moving pattern back-projected onto a translucent tangent screen facing the subject. In response to this translational visual stimulus lasting a very short period (10-250 ms), the eye velocity changed rapidly at ultra-short latencies <50 ms (Gomi et al. 1998). The present study, on the other hand, avoided the translational problem completely by putting the subject inside a half-cylinder screen. In response to a rotational visual stimulus lasting a longer period of 1 s for one direction, the eye velocity changed rapidly (rapid acceleration phase) and then slowly (slower acceleration phase) to the steady state. The latency of the OKR was relatively long (mean, 108 ms; range, 80.0-140.0 ms in the present study). It has been proposed that the OFR may be part of the "rapid" component (Cohen et al. 1977) of the monkey OKR (Miles 1998; Miles et al. 1986). The present study has shown that the inverse dynamics approach is applicable to the OKR eye movement, including the slower acceleration phase as well as the rapid acceleration phase.

Second, the present study provided a new finding concerning the position information encoding. Gomi et al. (1998) did not distinguish between relative and absolute position encoding because in their experimental paradigm, the initial eye position was always at the horizontal and vertical 0° position. The present study has revealed that the middle zone encodes eye position relative to the initial eye position, but does not encode the absolute position in the orbit. Thus the position sensitivity estimated by the relationship between the firing rate and static eye position (absolute eye position) should not be regarded as the position sensitivity during the OKR.

In conclusion, the present experiments have demonstrated that the cat flocculus encodes velocity and acceleration information in Purkinje cell SS firing frequency, leading the OKR eye movement by ~11 ms, suggesting that the flocculus may provide information necessary for counteracting viscosity and inertia forces during short-duration OKR eye movements. The position information encoded in the flocculus is inappropriate for counteracting elastic forces, suggesting the necessity of additional neuronal structures that encode position information for controlling the short-duration OKR.


    ACKNOWLEDGMENTS

We thank Dr. David W. Sirkin for comments on the manuscript and Profs. Hideaki Nukui and Yoshitaka Okamoto for providing research facilities.

This study was supported by Grant 08680885 from the Japan Ministry of Education.


    FOOTNOTES

Address reprint requests to Y. Sato.

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 4 January 1999; accepted in final form 1 June 1999.


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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
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0022-3077/99 $5.00 Copyright © 1999 The American Physiological Society