Abstract

Lesion studies suggest that the oculomotor vermis (OMV) is critical for the initiation of smooth-pursuit eye movements (SPEMs); yet, its specific role has remained elusive. In this study, we tested the hypothesis that vermal Purkinje cells (PCs) may be needed to fine-tune the kinematic description of SPEM initiation. Recording from identified PCs from the monkey OMV, we observed that SPEM-related PCs were characterized by a formidable diversity of response profiles with typically only modest reflection of eye movement kinematics. In contrast, the PC population discharge could be perfectly predicted based on a linear combination of eye acceleration, velocity, and position. This finding is in full accord with a role of the OMV in shaping eye movement kinematics. It, moreover, supports the notion that this shaping action is based on a population code, whose anatomic basis is the convergence of PCs on target neurons in the cerebellar nuclei.

Introduction

Whenever an object of interest moves slowly across the visual field, human and nonhuman primates make use of smooth-pursuit eye movements (SPEMs) to keep the object image on the fovea to be able to scrutinize it with high acuity despite its movement. SPEM response depends on information on target movement. A feedback system uses information on motion of the target on the retina to stabilize the target image on the fovea (Robinson et al. 1986). However, when initiating the SPEM, due to the delay of the visual system, feedback is not available for some 100–150 ms, during which the eye movement response depends fully on a direct visuomotor transformation of the target movement. To generate an appropriate initial eye movement response requires optimizing the parameters of this visuomotor transformation. Observations based on experimental lesions have suggested that the oculomotor vermis (OMV) of the cerebellum, comprising vermal lobuli VI and VII, may be the key structure underlying the necessary parametric adjustment. Next to the floccular complex, the OMV is the major end point of an elaborate corticopontocerebellar pathway underlying the translation of target motion into a premotor pursuit command, controlling the motor neurons responsible for the eye movement response (for review, see Krauzlis 2004; Thier and Ilg 2005; Thier and Mock 2006; Thier 2011). The notion that the OMV may be the structure responsible for the parametric adjustment of the initial SPEM is prompted by the severe impairment of pursuit initiation following surgical lesions of this area vis-à-vis only at best a modest influence on the later closed-looped SPEM response (Takagi et al. 2000). Furthermore, the reversible inactivation of the caudal part of the fastigial nucleus (cFN), the immediate target of the OMV, also disrupts SPEM initiation by yielding inappropriate initial eye acceleration (Robinson et al. 1997). Finally, a specific role of this system in SPEM initiation is also suggested by the bursting responses of cFN pursuit-related neurons in register with pursuit onset (Fuchs et al. 1994). However, despite the compelling arguments for a role in SPEM initiation, previous studies trying to unravel the role of the OMV in SPEMs used sinusoidally moving targets, profitable for the analysis of maintained pursuit but arguably of little use in studies of SPEM initiation (Suzuki and Keller 1988a, 1988b; Shinmei et al. 2002).

Hence, in our experiments we resorted to step–ramp movements of the target, a pursuit stimulus optimally suited to study the transition from a stationary state of the eyes to smooth pursuit. We show that SPEM-related Purkinje cells (PCs) are characterized by a large diversity of response profiles to pursuit initiation with typically only modest reflection of eye movement kinematics. In contrast, collectively—when considered as a population—these PCs exhibit an almost perfect reflection of eye movement kinematics.

Materials and Methods

Animal and Surgical Procedures

Two male rhesus (Macaca mulatta) monkeys (A and N) were used in this study. Using surgical procedures that followed previous descriptions (Judge et al. 1980; Thier and Erickson 1992), they were implanted with a scleral search coil for eye position recording, a titanium head post for the painless immobilization of the head, and a titanium recording chamber for the introduction of microelectrodes. Based on information provided by presurgical anatomical magnetic resonance imaging (MRI), the position and orientation of the recording chamber on the skull was chosen such as to provide the most direct access to the OMV. Surgery was carried out under intubation anesthesia with isoflurane and nitrous oxide, supplemented by continuous infusion of remifentanyl (1–2.5 μg/kg. h) and tight monitoring of all relevant vital parameters (body temperature, heart rate, blood pressure, pCO2, and pO2) that allowed prompt and adequate reaction in case of deviations from normal. Buprenorphine was given to eliminate postoperative pain until any sign of pain had disappeared. All procedures complied with the NIH Guide for Care and Use of Laboratory Animals and were approved by the local animal care committee.

Behavioral Procedures

The monkeys were trained to generate the behavior of interest by rewarding them with units of fluid (juice or water, the latter if preferred by the monkey), needed to satisfy their daily fluid requirements, following recommendations as set up by the German Primate Center (Göttingen, Germany). Careful monitoring of fluid intake and body weight and supplementation of fluid outside the experiment if needed ensured that the animals were sufficiently hydrated at all the time.

The monkeys were trained to keep their line of sight within an eye position window of 2°–3° diameter centered on the fixation target (diameter 3 min of arc) presented on a computer monitor (Mitsubishi, 50-cm screen diagonal, frame rate 72 Hz, 1280 × 1024 pixels) placed 43 cm in front of the monkeys in an otherwise completely dark room. To elicit pursuit eye movements, we used a step–ramp sequence, consisting of an initial target step away from the central position in a direction opposite to the direction of the subsequent target ramp. The step amplitude depended on the ramp velocity and the pursuit latency of the individual monkey and was chosen such as to have the target back at straight ahead at pursuit onset, thereby minimizing the need for catch-up saccades (Rashbass 1961). Using this method we could elicit pursuit eye movements without any catch-up saccades for at least 200–250 ms. Two different behavioral paradigms were performed to elucidate the preferred direction and speed of a neuron. In the “direction preference” paradigm, the monkeys executed SPEMs from an initial central position at 10°/s in 8 different directions in the frontoparallel plane. The directions are labeled in angular coordinates and included 2 horizontal (rightward: 0° and leftward: 180°), 2 vertical (upward: 90° and downward: 270°), and 4 diagonal (right-up: 45°, left-up: 135°, left-down: 225°, and right-down: 315°) directions. The target motion directions were randomly chosen from trial to trial. The monkeys initially fixated the central position for a variable time period (500–800 ms), after which the point stepped back in 1 of the 8 directions and moved back at constant velocity. The selection of the preferred direction for which velocity tuning was obtained was based on the visual examination of online peristimulus time histograms for 8 different directions. The preferred direction was later verified statistically. In the “velocity tuning” paradigm, the animals executed SPEMs from a central position at 4–8 different target velocities (typically from 2.5°/s to 20°/s in steps of 2.5°/s) in the preferred direction. The target velocity in the velocity tuning paradigm was randomly chosen for each trial.

Electrophysiological Procedures

A postsurgical anatomical MRI was used to guide the approach of the electrode to vermal lobuli VI and VIIa. Additional clues were provided by the characteristic features of the signals picked up by the microelectrode entering the OMV, namely the dramatic increase in background activity and the presence of saccade-related bursts originating from granular cells as well as the abundance of saccade-related PC simple spikes (SSs).

Action potentials were recorded extracellularly using a 4-probe multielectrode system fitted out with commercially available glass-coated tungsten microelectrodes (Alpha-Omega Engineering, Nazareth, Israel; electrode impedance 0.8–1.2 Mohm). The 4 electrodes were linearly aligned with a spacing of 1 mm and independently positioned. After appropriate amplification and filtering, individual SSs were separated online based on template matching as provided by the Alpha-Omega Engineering Multi-Spike Detector. Neurons were identified as PCs if they were accompanied by complex spikes (CSs), and identified by their complex waveform and, correspondingly, the peculiar sound they evoke on the audio monitor. We first clarified if the SS discharge was pursuit-related, that is, if its activity during the first 200 ms of the pursuit eye movement differed significantly from the preceding baseline (300 ms during fixation period; Wilcoxon rank test, P < 0.05), for at least 1 of the 8 directions (0°–315°). If this was the case, then the preferred direction and the velocity tuning of the SSs were estimated.

Data Analysis

Trial history, eye position records sampled at 1 kHz, and the times of identified spikes were stored for later offline analysis. The analysis was carried out using customized MATLAB programs (The MathWorks Inc., Natick, MA). Instantaneous eye velocity and acceleration were derived from the eye position records, which were sampled at a rate of 1 kHz. The horizontal and vertical eye position records were smoothed using a Savitzky–Golay filter (window = 20 points, polynomial degree = 4), which replaces the data points in the specified window by a polynomial regression fit of chosen degree and subsequently differentiated. Pursuit onset was determined by identifying the time when eye velocity exceeded 2 times the standard deviation of eye velocity during fixation (=baseline eye velocity). Trials with saccades during the initial 200 ms of eye movement were discarded. Saccades were detected using a velocity threshold of 50°/s. Trials with peak velocity exceeding 50°/s were discarded. Trials with pursuit latency of more than 250 ms were deemed to reflect an unattentive state of the monkey, which is why such trials were as well discarded. We estimated the instantaneous firing rate of the recorded neurons with a continuous spike density function, generated by convoluting the spike train with a Gaussian function of σ = 10 ms width. We converted the discharge into spike density functions in order to obtain the continuous description of neuronal activity needed for the investigation of the relationship between likewise time-continuous kinematic variables and neuronal activity.

Response Characterization

PCs identified as pursuit-related based on the aforementioned responses to smooth pursuit in different directions were subjected to a more fine-grained analysis of their responses in the early phase of the pursuit eye movement in order to distinguish distinct response patterns. Using trials taken from a test of velocity preference in the preferred direction described later, pooling across all velocities used, we determined if their average discharge rates in the first 100 ms of the pursuit eye movement and/ or the period from 200 to 300 ms relative to eye movement onset deviated significantly from the period of 300 ms of fixation preceding target movement onset. Only trials without saccades within the first 300 ms of the SPEM were considered. The specific patterns of changes in these 2 periods of target movement allowed the differentiation of several subgroups of pursuit-related neurons: “phasic-only” neurons exhibiting increased or decreased activity only during the first 100 ms after SPEM onset, and “tonic neurons” (tonic increase or tonic decrease) showing concordant discharge changes in the first 100 ms as well as during the period between 200 and 300 ms after SPEM onset (without any significant difference in firing rates in these periods). Finally, “burst-tonic neurons” were the ones that showed increased activity in both time windows but significantly higher activity in the first 100 ms of SPEMs. All the comparisons were based on Wilcoxon rank tests (P < 0.05, corrected for multiple comparisons whenever required).

Direction Preference Paradigm

In order to capture the directional preferences of neurons we computed the average number of spikes in the first 200 ms after pursuit onset (test) and the 300 ms preceding target onset (baseline) for all the directions (i = 0°, 45°, … 270° and 315°). PCs tested with a minimum of 8 trials per direction were considered for an evaluation of their directional tuning. For the neurons showing increased spiking during the test period (burst, burst-tonic, or tonic responses), the difference between the test and the baseline discharge rates was computed for each of the directions i: 

(1)
graphic

For the neurons showing decreased spiking in the test period, the difference between baseline and test period spiking activity was computed for each direction i: 

(2)
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Based on the X, we computed the preferred direction of the neuron using circular statistics. We computed the mean direction for the circular data (X) and also checked its validity by using a Rayleigh test to identify deviations from a uniform distribution of the circular data. Neurons showing a P value less that 0.05 were deemed direction selective.

The polar curves shown in Figure 3A,B intend to provide a handy visualization of the direction dependency of the responses. They are based on fitting the function specified in equation (3) to the actual discharge rates in the test and baseline periods for each direction (βi are the free parameters; τ, the angle in radians, is the independent variable, N = 4): 

(3)
graphic

Velocity Tuning Paradigm

The direction with the most vigorous pursuit-related discharge as judged from the audiomonitor was chosen for assessing the velocity tuning of the neuron. For all directionally tuned neurons, this direction, based on qualitative and subjective criteria, turned out to correspond to the preferred direction as revealed by the quantitative analysis of directionality described before. All the trials obtained for a given neuron and for a given direction were sorted according to peak velocity (maximum velocity in the first 150 ms after pursuit onset) and divided into 4 groups of trials covering the range of peak pursuit velocities occurring. For every session, all the trials were sorted according to increasing peak velocity. Trials with peak velocity ranging between mean velocity (across all trials) minus 2 standard deviations and mean velocity plus 2 standard deviations of mean velocity were only considered to remove outlier velocities. The remaining trials were divided into 4 equal velocity groups (velocity bins) ranging from the lowest elicited eye velocity to the highest one. Following this, the average number of spikes during the first 200 ms following SPEM initiation (test) and 300 ms preceding target movement onset (baseline) were computed for each of the 4 groups. For each neuron, a normalized velocity modulation coefficient (Cv) was computed for each of the 4 (i = 1–4) velocity groups, using the following formula: 

(4)
graphic

Multiple Linear Regression Analysis of Discharge Rate

In order to quantitatively analyze the relationship between the neuronal activity and eye movement kinematics, we modeled the discharge rate spk(t) as a linear combination of eye position (pos(t)), eye velocity (vel(t)), and eye acceleration (acc(t)) at time (t): 

(5)
graphic

The 4 coefficients a, b, c, and d, and δ were estimated to minimize the deviation between the reconstructed discharge rate and the actual discharge rate as indicated by a maximal coefficient of determination (CD = r2) for the equation. The search range for the choice of the discharge latency δ ranged from –50 to 50 ms. The CD value corresponds to 1 minus the ratio of the error sum of squares (sse) and the total sum of squares (sst). The sse is the square of the difference between the reconstructed PC firing frequency and the observed firing frequency, and sst is the square of the difference between the observed PC firing frequency and the temporally averaged firing frequency of the PCs for the whole duration (a constant value). The CD value ranged between 0 and 1. The time period from 100 ms before SPEM onset to 200 ms after SPEM onset was used for the estimation of the coefficients. A Student’s t-test was applied to test the null hypothesis that the coefficient for each eye movement parameter is equal to zero. P values less than 0.05 indicate that a given coefficient is significantly different from 0.

To reveal the relative contributions of the 3 kinematic variables, we omitted 1 or 2 of the variables in equation (5) and compared the goodness of the resulting fits with the goodness of the 3-variable fits. The same analytical approach was applied to the population average of the neurons tested in their particular preferred direction (Fig. 9) and to the population averages obtained for each of the individual 8 directions (Fig. 10). The procedure describing how the population response was computed is described in the Results under “Population Velocity Tuning.”

Results

Types of Responses

We recorded the SSs of 200 PCs with pursuit-related responses. For 154 units out of this sample, the direction tuning could be assessed with more than 8 trials for each direction, for 117 units out of the 154 units a velocity tuning could be obtained with more than 8 trials for each target velocity. For 123 units out of the group of 154, we had a sufficiently large enough number of trials (n > 5) needed to categorize the unit according to response type (Fig. 1) and to use it for the analysis of population responses (see later). Classification of these units as PCs was based on the occurrence of CSs and consideration of their high spontaneous activity level. All the neurons in our sample exhibited spontaneous discharge rates as measured during fixation of a stationary target of more than 30 spikes/s, with the maximum spontaneous firing being as high as 200 spikes/s. No other cell type in the cerebellar cortex exhibits such high spontaneous firing levels (Armstrong and Rawson 1979; Prsa et al. 2009). Figure 1 exemplifies the different types of SS responses exhibited by OMV PCs during SPEM initiation. Figure 1A shows the example of a tonic SPEM-related increase in activity that persisted throughout the trial. Twenty-seven of the 123 PCs (21.95%) exhibited comparable tonic increases. Figure 1B,C depicts 2 neurons that demonstrated phasic increases in activity related to SPEM initiation. In the example shown in Figure 1B, the phasic response decayed back to spontaneous firing level within 200 ms, whereas the neuron shown in Figure 1C exhibited a tonically elevated discharge rate after the phasic burst. Almost half of the neurons in our sample showed similar phasic or phasic-tonic increases of their discharge rate (59 out of 123; 47.97%; see Materials and Methods for the quantitative analysis used to assign neurons to specific categories). Figure 1D presents the example of a neuron exhibiting a tonic decrease (decrease persisted beyond 200 ms) of its baseline activity level at SPEM onset. About 12.2% (15 out of 123) neurons displayed such responses. Figure 1E depicts an example neuron exhibiting phasic decrease in activity. Twenty-two out of the 123 neurons (17.89%) showed similar responses. Finally, as shown in Figure 1F, occasionally also sequences of phasic decrease and phasic increase responses in either order could be observed (6 PCs; not contributing to the group of 123 PCs that were analyzed further). Figure 2 shows the population averages for each of the category. Population averages were calculated by pooling all the trials across all the neurons and considering all velocities in the direction that exhibited the most vigorous firing (corresponding the preferred direction in the case of direction selectivity). Figure 2 depicts the average spike density function for every category of neurons.

Figure 1.

(AF) Types of responses: tonic increase (A), phasic increase (B), burst tonic (C), tonic activity decreases (D), phasic activity decreases (E), and activity decreases followed by burst (F). Each panel shows, from top to bottom, eye position records (horizontal), raster plots, and spike density function of the neuronal discharge. All the responses are for the preferred direction of the neuron, which was toward right in all the examples shown here. The vertical line indicates pursuit onset.

Figure 1.

(AF) Types of responses: tonic increase (A), phasic increase (B), burst tonic (C), tonic activity decreases (D), phasic activity decreases (E), and activity decreases followed by burst (F). Each panel shows, from top to bottom, eye position records (horizontal), raster plots, and spike density function of the neuronal discharge. All the responses are for the preferred direction of the neuron, which was toward right in all the examples shown here. The vertical line indicates pursuit onset.

Figure 2.

(AD) Examples of population spike density functions of different types of neurons. Burst + burst tonic (A), tonic increase (B), phasic pause (C), and tonic pause (D). Vertical line indicates onset of pursuit eye movement.

Figure 2.

(AD) Examples of population spike density functions of different types of neurons. Burst + burst tonic (A), tonic increase (B), phasic pause (C), and tonic pause (D). Vertical line indicates onset of pursuit eye movement.

To sum up, based on this qualitative examination, 70% of SPEM-related OMV PCs exhibited phasic or tonic increases in activity, whereas the others showed phasic or tonic decreases in activity in relation to SPEM initiation. Furthermore, SPEM-related responses were in 2 of 3 of the cases phasic (increase or decrease).

Direction Tuning

The directional selectivity for SPEMs in the frontoparallel plane was assessed for 154 PC SS units (58 from monkey A and 96 from monkey N). As explained in the Materials and Methods, neurons showing SPEM-related increases in activity (eq. 1) were treated separately from the neurons showing SPEM-related decreases in the activity (eq. 2). A Rayleigh test deployed to assess the nonuniformity of the circular data deemed 118 out of 154 neurons directionally selective. Thirty-six neurons, which showed a P value of more than 0.05 in this test, were labeled as nondirectional selective. The majority of neurons (76.62%) were designated as directionally selective and the mean direction of the circular data (X in eqs. 1 and 2) was taken as measure of the preferred direction. In this latter group, 82 showed activity increases during SPEMs and 36 showed activity decreases.

Figure 3A illustrates an example neuron with activity increases during SPEMs that had a clear directional tuning, preferring smooth pursuit to the upper right. Similarly, an example neuron with activity decreases during SPEMs, strongest for downward smooth pursuit, is depicted in Figure 3B.

We next asked if all the directions were equally represented or, alternatively, if there was a bias for cardinal directions in the OMV. This was not the case as indicated by the even representation of all directions between 0° and 360° (Fig. 3C; Rayleigh uniformity test, P > 0.05 for both the “activity decrease” and the “activity increase” groups of SPEM-related PCs).

Figure 3.

Directional selectivity of smooth-pursuit–related neurons. Neuronal activity is represented in the form of spike density functions for the 8 directions (4 cardinal and 4 oblique; A and B). Vertical bar indicates the onset of the pursuit eye movement. (A) Example neuron with SPEM-related “activity increase” showing directional preference toward the upper right. (B) Example neuron with SPEM-related “activity decrease” showing directional preference toward the downward direction. Smoothed polar plots (eq. 3) in A and B show the baseline activity (gray) and the activity during SPEMs (black) for all 8 directions. (C) Shows the distribution of preferred directions for all the neurons showing activity increases and activity decreases.

Figure 3.

Directional selectivity of smooth-pursuit–related neurons. Neuronal activity is represented in the form of spike density functions for the 8 directions (4 cardinal and 4 oblique; A and B). Vertical bar indicates the onset of the pursuit eye movement. (A) Example neuron with SPEM-related “activity increase” showing directional preference toward the upper right. (B) Example neuron with SPEM-related “activity decrease” showing directional preference toward the downward direction. Smoothed polar plots (eq. 3) in A and B show the baseline activity (gray) and the activity during SPEMs (black) for all 8 directions. (C) Shows the distribution of preferred directions for all the neurons showing activity increases and activity decreases.

Velocity Tuning

Out of 117 PCs tested, 88 (75%) showed a linear change of their SPEM-related response with velocity (linear regression of Cv as a function of eye velocity, P < 0.05). The percentages of activity increase PCs and activity decrease PCs exhibiting linear velocity tuning were comparable (64 out of 87 with activity increase and 24 out of 30 with activity decrease exhibited linear velocity tuning, P < 0.05). Figure 4A shows example neurons exhibiting different types of velocity dependencies as demonstrated by plots of their spike density function for the 4 velocities tested and plots of their Cv as a function of velocity. The upper 2 examples represent the linear dependencies discussed before, and the following 3 PCs exemplify the highly idiosyncratic nonlinear dependencies observed in the minority of the PCs tested. No attempt was made to fit them with particular functions.

Figure 4.

Velocity tuning of smooth-pursuit–related neurons. (A) Velocity tuning of 5 example neurons (top to bottom) with the 4 velocity bins for each neuron (vertical dotted line indicates pursuit onset) (left), the spike density functions with vertical lines indicating pursuit onset for the 4 velocity bins in increasing order (middle), and the Cv plotted as a function of 4 velocity bins (right). Grouped velocity tuning for neurons showing “activity increase” (B) and exhibiting “activity decrease” (C). The averaged Cv is plotted in B and C as a function of 4 velocity bins.

Figure 4.

Velocity tuning of smooth-pursuit–related neurons. (A) Velocity tuning of 5 example neurons (top to bottom) with the 4 velocity bins for each neuron (vertical dotted line indicates pursuit onset) (left), the spike density functions with vertical lines indicating pursuit onset for the 4 velocity bins in increasing order (middle), and the Cv plotted as a function of 4 velocity bins (right). Grouped velocity tuning for neurons showing “activity increase” (B) and exhibiting “activity decrease” (C). The averaged Cv is plotted in B and C as a function of 4 velocity bins.

At the group level, neurons with activity increase during SPEMs showed a significant increase of their velocity modulation coefficient with Cv (Fig. 4B; Friedman analysis of variance [ANOVA], P < 0.05) due to the dominance of individual PCs exhibiting a monotonic increase of their Cv with eye velocity. In contrast, activity decrease PCs did not show any consistent velocity tuning at the group level (Fig. 4C; Friedman ANOVA, P > 0.05).

Population Velocity Tuning

To see if there was any velocity tuning at the population level, we pooled the discharge rates of all the trials (8575 trials) of all 123 PCs studied irrespective of whether they belonged to the activity increase or decrease type. Individual trials were sorted into 10 velocity bins based on peak velocity (width: 1.4° /s, range from 6 to 20°/s; peak velocity determined for the first 150 ms after SPEM onset), irrespective of their affiliation with a particular PC. The number of trials contributed by each PC was between 65 and 80, minimizing the concern that cells contributing more trials might have a bigger influence on the population response. Next, we calculated the average collective spike density function for the trials contributing to each of the 10 velocity bins as a function of time relative to SPEM onset. The result is shown in Figure 5. This figure in pseudocolor demonstrates a significant velocity tuning at the population level, characterized by an obvious increase (red) in the strength of the population signal with increasing peak velocity. This impression was supported by a significant linear regression analysis (y = 1.1 + 0.008x; r = 0.89; P < 0.0005) of the ratio of the average discharge rate during SPEMs (the first 200 ms) divided by the average discharge rate during the fixation period (the 300 ms immediately preceding target movement onset) as a function of velocity (as represented by the 10 velocity bins in increasing order). The clear representation of SPEM velocity at the population level seems particularly noteworthy, given the variable and in general comparatively weak effect of velocity on the discharge of individual PCs mentioned earlier.

Figure 5.

Pseudocolor plot showing the population average of vermal PC SSs during SPEMs. Eye movements are sorted according to increasing peak velocity (6–20°/s). The abscissa (−200 ms to 0–200 ms) shows time with respect to SPEM onset. The white line indicates the onset of movement. The color bar at the right indicates the average discharge rate (spikes/s).

Figure 5.

Pseudocolor plot showing the population average of vermal PC SSs during SPEMs. Eye movements are sorted according to increasing peak velocity (6–20°/s). The abscissa (−200 ms to 0–200 ms) shows time with respect to SPEM onset. The white line indicates the onset of movement. The color bar at the right indicates the average discharge rate (spikes/s).

Correlation of Individual PC SSs with Kinematic Parameters

The comparatively weak influence of eye velocity on individual PCs could be a consequence of an additional—and perhaps even larger—influence of other kinematic parameters. In order to determine if this was the case, we next applied multiple regression analysis to explore how well the firing pattern of individual PCs could be predicted by various combinations of the 3 kinematic parameters, eye position, velocity, and acceleration using the linear model described by equation (5). Figure 6A shows the distribution of the resulting coefficients of determination (CDs) for all the 123 PCs considered. They ranged between 0.4 and 1, with a median of 0.822. All the kinematic parameters contributed significantly in the majority of the neurons. A total of 102 out of 123, 113 out of 123, and 93 out of 123 of the PCs showed significant coefficients for eye position, eye velocity, and eye acceleration respectively (t-test, P < 0.05). The average estimated kinematic coefficients were highly variable at their best δ (−4.7664 ± 99.46 spikes/s/degree for eye position; 1.23 ± 5.39 spikes/s/degree/s for eye velocity, and 0.049 ± 0.214 spikes/s/degree/S2 for eye acceleration). The time lag (δ) for obtaining best CD also had a broad distribution with an average lag of 6.6 ± 28.64 ms (a positive δ means that the discharge activity led the movement). The distribution of CDs, based on the 3–kinematic parameter model, and the distributions of the 3 kinematic parameters are shown in Figure 7.

Figure 6.

Representation of eye movement kinematics in the discharge of smooth-pursuit–related neurons (n = 123). (A) Distribution of CD (CD = r2) obtained after correlating the discharge profiles of individual neurons with a linear combination of eye position, velocity, and acceleration (eq. 5). (BG) Distributions of CDs obtained when discharge was correlated with reduced kinematic descriptions of the eye movement: eye velocity excluded (B), acceleration excluded (C), position excluded (D), only eye velocity correlated with the discharge profile (E), only eye acceleration (F), and only eye position (G).

Figure 6.

Representation of eye movement kinematics in the discharge of smooth-pursuit–related neurons (n = 123). (A) Distribution of CD (CD = r2) obtained after correlating the discharge profiles of individual neurons with a linear combination of eye position, velocity, and acceleration (eq. 5). (BG) Distributions of CDs obtained when discharge was correlated with reduced kinematic descriptions of the eye movement: eye velocity excluded (B), acceleration excluded (C), position excluded (D), only eye velocity correlated with the discharge profile (E), only eye acceleration (F), and only eye position (G).

Figure 7.

(A) Distribution of CD for individual smooth-pursuit–related PC SSs resulting from multiple regression of instantaneous discharge rate as a function of eye movement kinematics according to equation (5). (BD) distribution of acceleration sensitivity coefficients (B), distribution of velocity sensitivity coefficients (C), and distribution of position sensitivity coefficient (D).

Figure 7.

(A) Distribution of CD for individual smooth-pursuit–related PC SSs resulting from multiple regression of instantaneous discharge rate as a function of eye movement kinematics according to equation (5). (BD) distribution of acceleration sensitivity coefficients (B), distribution of velocity sensitivity coefficients (C), and distribution of position sensitivity coefficient (D).

We further tested the contribution of each individual kinematic parameter in equation (5) by either removing it from the equation or by explaining the temporal firing pattern of the neuron with only this particular parameter. Figure 6B–D shows the distribution of CD after removing eye velocity, eye acceleration, or eye position from equation (5), respectively. Removal of eye acceleration and eye position led to distributions of the CD (median CD without acceleration = 0.7681, median CD without eye position = 0.7674; Fig. 6C,D), which were not significantly different from the one obtained with all the parameters included (median CD = 0.822; U tests, P > 0.05 each). In contrast, the removal of the eye velocity term from equation (5) led to a significant decrease of the median CD to 0.6621 (U test, P < 0.05; Fig. 6B). In other words, it seems to be eye velocity that is most important for determining the SS firing pattern of PCs. This conclusion receives further support by trying to explain the spiking pattern with one kinematic parameter only. Restricting the linear model to eye velocity resulted in a median CD of 0.6109 (Fig. 6E), whereas eye acceleration (median CD = 0.143; Fig. 6F) and position (median CD = 0.389; Fig. 6G) yielded substantially smaller median CDs (for both, U test comparison with the CD for eye velocity, P < 0.05).

To summarize, the firing pattern of individual PCs is best explained by assuming a substantial influence of eye acceleration, velocity, and position, with velocity playing the most important role.

Correlation of the PC Population Response with Kinematic Parameters

We calculated the instantaneous PC population response as explained earlier. The contributions of individual PC responses in their respective direction exhibiting the most vigorous firing (preferred direction in the case of direction-selective neurons) and across all velocities were pooled for the population analysis. We will later come back to the question if this particular action is justified. The relationship of the population response to eye movement kinematics was then analyzed resorting to the same multiple linear regression approach also used for the analysis of individual PCs. Actually, the population response based on 123 PC SSs was perfectly correlated with eye movement parameters, as indicated by a CD of 0.9939 for a δ of 11 ms. We obtained almost identical results when instead of averaging across all the trials (n = 8575) of all the neurons, we first calculated the average mean instantaneous firing rate of individual neurons and then pooled the averaged activities across neurons to get the population response (CD of 0.992 for a δ of 13 ms). The CD characterizing the population response was higher than the CD for any of the individual PCs (maximum individual CD = 0.98 and median individual CD of the population = 0.822). The coefficients of all 3 kinematic parameters contributed significantly (t-test, P < 0.05) to the estimate of the population response. When we tested the contribution of each kinematic parameter by removing individual parameters or pairs as independent variables from the regression, surprisingly, it turned out that neither eye acceleration nor eye position was needed in order to obtain the high CD. Removing eye acceleration yielded a CD of 0.9819 and removing eye position yielded a CD of 0.9588. In contrast, removing eye velocity from equation (5) resulted in a substantially lower CD of 0.8172. It seems inconsistent that eye velocity alone can give an almost perfect description of the discharge pattern, whereas removal of eye velocity from the 3–kinematic parameter model causes an only mild decline of the CD. The explanation is that the 3 kinematic parameters are not linearly independent. Actually, a linear combination of acceleration and position provides a relatively precise prediction of eye velocity (CD = 0.94).

Correlating the population response with eye velocity alone yielded a quite high CD of 0.843. In contrast, correlating it with either eye acceleration or eye position as sole independent variables yielded low CDs of 0.1743 and 0.5045, respectively. In summary, at the population level, the linear combination of all 3 kinematic parameters results in the best prediction of the discharge. However, eye velocity seems to be the most relevant parameter. Basically, the same conclusion can be drawn from cross-correlating the population spike density function with mean eye velocity, acceleration, and position. The cross-correlation with velocity was substantially higher (r = 0.8) than the ones for acceleration (r = 0.65) and position (0.3) (Fig. 8).

Figure 8.

(AC) Cross-correlation between population spike density functions with average position profile (A), average velocity profile (B), and average acceleration profile (C). The more uneven trace depicts the population spike density function and the smooth traces reflect eye position, velocity, and acceleration in A, B, and C, respectively. To the right is the resulting cross-correlation function. Velocity correlates the best with population spiking and the maximum correlation is obtained at zero lag.

Figure 8.

(AC) Cross-correlation between population spike density functions with average position profile (A), average velocity profile (B), and average acceleration profile (C). The more uneven trace depicts the population spike density function and the smooth traces reflect eye position, velocity, and acceleration in A, B, and C, respectively. To the right is the resulting cross-correlation function. Velocity correlates the best with population spiking and the maximum correlation is obtained at zero lag.

In the multiple linear regressions analysis presented above, we had pooled trials across the full spectrum of eye velocities available, spanning a wide range of 6–20 degree/s. Hence, the question arises if the influence of eye velocity on the population response suggested by this analysis holds for the full range of velocities, rather than reflecting the particular influence of a subset of velocities. In order to decide this alternative, we divided the whole range of velocities into 10 velocity bins (bin-width: 1.4 degree/s) and calculated independent population responses for each velocity bin. The population responses were then subjected to multiple regression analyses of the instantaneous discharge rate as a function of the linear combination of the 3 kinematic parameters as described above. The resulting CDs summarized in Figure 9A were not different from the ones obtained for the population responses based on all velocities. In other words, the sensitivity to eye velocity is the same, independent of the particular range of eye velocity considered. The average coefficients for the 10 population velocity bins were 18 ± 9.95 spikes/s/degree (eye position), 2.1 ± 0.44 spikes/s/degree/s (eye velocity), and 0.024 ± 0.017 spikes/s/degree/S2 (eye acceleration). The kinematic coefficients obtained for each of the 10 population velocity bins are summarized in Table 1. Figure 9B shows the average CD for a range of δ (−50 to 50 ms) for all 10 population velocity bins, with the maximum-average CD obtained when the population response led the eye movements by 18 ms.

Table 1

Kinematic coefficients obtained when the 10-velocities–based population responses divided on the basis of increasing peak velocity were modeled with a linear combination of eye position, velocity, acceleration, and a bias term (eq. 5)

 a (spikes/s/degree) b (spikes/s/degree/s) c (spikes/s/degree/S2d 
Velocity bin 1 19.951 2.3284 0.06979 66.675 
Velocity bin 2 35.614 2.6291 0.018871 64.149 
Velocity bin 3 35.973 2.9873 0.010415 66.266 
Velocity bin 4 13.728 1.7924 0.015592 69.481 
Velocity bin 5 11.951 1.9479 0.020931 71.764 
Velocity bin 6 12.838 1.8858 0.018164 68.285 
Velocity bin 7 16.213 2.0818 0.014985 68.808 
Velocity bin 8 8.2084 1.5375 0.027446 71.66 
Velocity bin 9 15.975 2.162 0.0094182 65.294 
Velocity bin 10 9.5854 1.7159 0.037471 67.64 
 a (spikes/s/degree) b (spikes/s/degree/s) c (spikes/s/degree/S2d 
Velocity bin 1 19.951 2.3284 0.06979 66.675 
Velocity bin 2 35.614 2.6291 0.018871 64.149 
Velocity bin 3 35.973 2.9873 0.010415 66.266 
Velocity bin 4 13.728 1.7924 0.015592 69.481 
Velocity bin 5 11.951 1.9479 0.020931 71.764 
Velocity bin 6 12.838 1.8858 0.018164 68.285 
Velocity bin 7 16.213 2.0818 0.014985 68.808 
Velocity bin 8 8.2084 1.5375 0.027446 71.66 
Velocity bin 9 15.975 2.162 0.0094182 65.294 
Velocity bin 10 9.5854 1.7159 0.037471 67.64 
Figure 9.

(A) CDs obtained when correlating the instantaneous population discharge rate with eye movements kinematics according to equation (5) (Materials and Methods) or, alternatively, with various slimmed-down versions of this equation. Regressions are based on records of neuronal responses different velocities, sorted in 10 bins according to increasing peak velocity. The values of CD are shown in a color scale on the right. A consideration of all 3 kinematic eye movement parameters yielded better predictions of the population response than any of the slimmed-down kinematic descriptions. B shows the average CDs obtained for the 10 population responses for a range of δ (−50 to 50 ms; see eq. 5). Bold black curve shows the average CD at different δ and the gray shadow shows the standard deviation.

Figure 9.

(A) CDs obtained when correlating the instantaneous population discharge rate with eye movements kinematics according to equation (5) (Materials and Methods) or, alternatively, with various slimmed-down versions of this equation. Regressions are based on records of neuronal responses different velocities, sorted in 10 bins according to increasing peak velocity. The values of CD are shown in a color scale on the right. A consideration of all 3 kinematic eye movement parameters yielded better predictions of the population response than any of the slimmed-down kinematic descriptions. B shows the average CDs obtained for the 10 population responses for a range of δ (−50 to 50 ms; see eq. 5). Bold black curve shows the average CD at different δ and the gray shadow shows the standard deviation.

The population responses whose kinematic dependencies we discussed above were based on the responses of individual PCs tested in their respective preferred direction. One might rightly argue that this particular structure of the population response is arbitrary, rather than biologically plausible. Actually, as discussed elsewhere (see the Discussion), we think that PCs act as a population rather than as individual elements because they converge on individual target neurons in the deep cerebellar nuclei (DCN). Hence, the responses of these target neurons must inevitably reflect the collective PC input, that is, the population response. However, a single DCN neuron might be contacted by PCs with different preferred directions. Moreover, it may receive input from PCs with no SPEM relatedness, in addition to input from those related to SPEMs. In order to explore the consequences of this scenario, we also calculated population responses based on all 154 PCs whose directional tuning had been assessed and derived separate population responses for each of the 8 directions (single velocity at 10 degree/s), with all the 154 PCs contributing to each of the 8 population responses (Fig. 10A; “8-direction population responses”). These direction-specific population responses were then subjected to the multiple linear regression analysis of the influence of eye movement kinematics as described earlier. The resulting CDs (summarized in Fig. 10B for the various combinations of kinematic parameters) actually turned out to be very similar to the ones obtained for the population responses based on the respective preferred directions. We also tried to fit the 8-direction population responses resorting to the kinematic coefficients best fitting the former population response based on the responses to 10 different velocities in an individual best direction (“10-velocities–based population response”; see Table 1). Although the CDs obtained were somewhat smaller, the fits obtained were still very reasonable, supporting the view that the estimated kinematic parameters were not simply artifacts of a specific approach chosen for the analysis of the population data. A summary of the kinematic coefficients and CDs obtained for the 8-direction–based population responses as well as the CDs obtained with the fixed set of kinematic coefficients (CD_fixed) is given in Table 2.

Table 2

Kinematic coefficients (a, b, c, and d) and CDs obtained for the 8-direction–based population responses

 a (spikes/s/degree) b (spikes/s/degree/s) c (spikes/s/degree/S2d CD CD_fixed 
0° 2.5353 0.96045 0.0171 76.449 0.9595 0.8779 
45° 1.8227 0.83491 0.0182 78.623 0.8655 0.7623 
90° 0.0962 0.76628 0.0198 74.132 0.9230 0.8765 
135° 4.8452 1.0709 0.0104 92.092 0.9145 0.8487 
180° 10.448 1.4378 0.0106 85.606 0.9322 0.8457 
225° 11.136 1.5824 0.0129 87.167 0.8870 0.8530 
270° 2.725 0.6841 0.001 78.086 0.7635 0.7239 
315° 0.4217 0.5822 0.0106 75.192 0.8921 0.8661 
 a (spikes/s/degree) b (spikes/s/degree/s) c (spikes/s/degree/S2d CD CD_fixed 
0° 2.5353 0.96045 0.0171 76.449 0.9595 0.8779 
45° 1.8227 0.83491 0.0182 78.623 0.8655 0.7623 
90° 0.0962 0.76628 0.0198 74.132 0.9230 0.8765 
135° 4.8452 1.0709 0.0104 92.092 0.9145 0.8487 
180° 10.448 1.4378 0.0106 85.606 0.9322 0.8457 
225° 11.136 1.5824 0.0129 87.167 0.8870 0.8530 
270° 2.725 0.6841 0.001 78.086 0.7635 0.7239 
315° 0.4217 0.5822 0.0106 75.192 0.8921 0.8661 

Note: The last column of the table shows the CDs (CD_fixed) obtained when a fixed set of kinematic coefficient (the average kinematic coefficient obtained from the 10-velocities–based population response) was used to fit the 8-direction–based responses.

Figure 10.

(A) The instantaneous population discharge rate for all 8 frontoparallel directions based on all neurons (“activity increase” neurons and “activity decrease” neurons irrespective of their preferred direction). Arrowhead indicates the direction of movement. Note that the population activity for the downward pursuit is weaker than for pursuit in other directions (average activity in first 200 ms of pursuit eye movement for downward pursuit being 80.25 spikes/s and the average activity of rest of the 7 directions combined being 83.23 spikes/s). This difference reflects the lower peak velocity and peak acceleration for this particular direction when compared with pursuit in other 7 directions (average peak velocity and peak acceleration for downward pursuit being 10.2 deg/s and 115.79 deg/S2, respectively, and the average activity of rest of the 7 directions combined being 11.2 deg/s and 137.83 deg/S2, respectively). (B) CDs for population averages in 8 different directions (0°–315°). Rest same as Figure 9A.

Figure 10.

(A) The instantaneous population discharge rate for all 8 frontoparallel directions based on all neurons (“activity increase” neurons and “activity decrease” neurons irrespective of their preferred direction). Arrowhead indicates the direction of movement. Note that the population activity for the downward pursuit is weaker than for pursuit in other directions (average activity in first 200 ms of pursuit eye movement for downward pursuit being 80.25 spikes/s and the average activity of rest of the 7 directions combined being 83.23 spikes/s). This difference reflects the lower peak velocity and peak acceleration for this particular direction when compared with pursuit in other 7 directions (average peak velocity and peak acceleration for downward pursuit being 10.2 deg/s and 115.79 deg/S2, respectively, and the average activity of rest of the 7 directions combined being 11.2 deg/s and 137.83 deg/S2, respectively). (B) CDs for population averages in 8 different directions (0°–315°). Rest same as Figure 9A.

In summary, population responses of PC SSs are better correlated with the eye movement parameters as compared with the correlation obtained for individual PC SSs. Actually, independent of the specific way to calculate them, they are able to give an almost perfect account of the resulting kinematic profiles.

Our experimental paradigm allowed us to provide a reliable account of only pursuit initiation, the major reason being that the target ramp duration used in our experiments was only 500–600 ms. Taking out pursuit latency (150 ms), the period of pursuit eye movement available was 350–450 ms only. Out of this period, we are using 200 ms for the study of pursuit initiation, free of saccades. Unfortunately, the remaining period did not allow a satisfactory assessment of closed-loop behavior as it was contaminated by catch-up saccades occurring at variable times. In an attempt to obtain at least a preliminary insight into possible differences between pursuit initiation and closed-loop pursuit, we compared the correlation of population responses for 3 different time bins (−100 to 0 ms, 0 to 100 ms, and 100 to 200 ms) relative to pursuit onset. We carried out this analysis for the 10-velocities–based population responses described in Figure 9 as well as for the 8-direction–based population responses described in Figure 10. We restricted our analysis to a simplified version of equation (5) obtained by omitting the δ. Figure 11A shows the median and interquartile range of the CDs obtained for the 10-velocities population responses for the 3 time epochs relative to pursuit onset. Clearly, the CD for the first 100 ms after pursuit onset is higher than the 100 ms period preceding and following it (Wilcoxon matched-pairs test, P < 0.05). Almost the same conclusion can be drawn from the 8-direction–specific population responses shown in Figure 11B (Wilcoxon matched-pairs test, P < 0.05). Better correlations for a temporal window excluding closed-loop pursuit are in line with a preferential role of OMV PCs in pursuit initiation.

Figure 11.

(A) CDs (median and interquartile range) for characterizing the correlations between the 10-velocities population response (Fig. 9) and their respective kinematic variables (position, velocity, and acceleration) in 3 different time epochs (each of 100 ms) relative to pursuit onset. (B) CD (median and interquartile range) for population averages of 8-direction–based population responses (0°–315°; Fig. 10), with their respective kinematic variables in 3 different time epochs relative to pursuit onset.

Figure 11.

(A) CDs (median and interquartile range) for characterizing the correlations between the 10-velocities population response (Fig. 9) and their respective kinematic variables (position, velocity, and acceleration) in 3 different time epochs (each of 100 ms) relative to pursuit onset. (B) CD (median and interquartile range) for population averages of 8-direction–based population responses (0°–315°; Fig. 10), with their respective kinematic variables in 3 different time epochs relative to pursuit onset.

Discussion

In this study, we recorded SS activity from OMV PCs, while the monkey subjects were performing SPEMs elicited by step–ramp stimuli. We observed that PC SS units exhibited many different types of responses related to SPEM initiation, not only more or less tonic responses, seemingly related to eye velocity, but also phasic bursts, or conversely transient pauses. In any case, they were typically directionally selective with a uniform representation of all directions in our sample of PCs. Previous studies of SPEM-related responses of OMV PCs evoked by sinusoidal pursuit have emphasized tonic responses, seemingly related to velocity. However, the phasic, pursuit-related responses that were actually displayed by two-thirds of the neurons in our sample were most likely missed by previous studies because of the periodic character of the pursuit stimulus used. What could the source of the formidable variability of response profiles of individual PCs be? We think that part of the explanation may be the heterogeneity of mossy fiber sources of the OMV: The list includes the dorsomedial and dorsolateral pontine nuclei as well as the substantial parts of the ventral pontine nuclei, the nucleus reticularis tegmenti pontis, and the paramedian pontine reticular formation, many of them known to carry distinct visual- and pursuit-related signals to the OMV (Thielert and Thier 1993; Thier and Mock 2006). Moreover, studies of the oculomotor region in the dorsal pontine nuclei have demonstrated that already at the level of this specific input to the OMV, pursuit-related signals may exhibit a substantial degree of heterogeneity (Dicke et al. 2004). This preponderance of phasic responses is also reflected at the level of OMV target neurons in the caudal fastigial nucleus, which typically display an initial transient burst-like response during SPEM initiation (Fuchs et al. 1994). Tonic responses are more characteristic of the fastigial responses during steady-state SPEMs. A multiple linear regression analysis of the responses of individual units showed that a consideration of all 3 kinematic parameters, eye position, velocity, and acceleration, could predict the discharge profiles reasonably well, independent of the individual profile being phasic, tonic, or pausing. The fact that usually eye velocity was found to make the strongest contribution is in line with the aforementioned studies of OMV PC SS units during sinusoidal SPEMs also emphasizing eye or gaze velocity (Suzuki and Keller 1988a, 1988b; Shinmei et al. 2002).

Importantly, a profound improvement of the prediction was achieved when kinematic variables were used to predict the collective discharge of the whole sample of neurons, the population response, rather than the responses of individual neurons. Our population responses were calculated based on averaging the instantaneous discharge rates of all the trials contributed by all the PCs for a particular velocity bin, that is, it was a linear sum with equally weighted contributions from each unit. We used this simple averaging method for the sake of its simplicity and the existing literature does not indicate any other population averaging method (like response normalization to peak discharge rates) to be more suitable for PC SS units or the cerebellum in general. Actually, the perfect description this approach provided supports the notion that it reflects the computational principle employed by populations of PCs. The correlation of eye movement kinematics and the discharge profile of the population of the PC SSs were almost perfect and significantly better than any of the correlations obtained for individual neurons. In other words, the population response contains information not available at the level of individual neurons. The population coding hypothesis receives further support from the analysis of velocity preferences. Whereas individual PCs exhibited only weak velocity tuning, the population response based on our entire sample of PC SSs showed a very precise linear relationship between the average population activity and peak SPEM velocity. In other words, the population signal has all the information needed to completely describe SPEM initiation. Obviously, a regression analysis cannot establish causal relationships, although the high CD during SPEM initiation may suggest such a relationship. Actually, 3 considerations support the notion of a causal relationship. First, the kinematic coefficients obtained for the 3–kinematic parameters model for explaining the population response are very similar to that of oculomotor motoneurons (Keller 1973; Sylvestre and Cullen 1999). Sylvestre and Cullen (1999), in particular, obtained kinematic coefficients for step–ramp pursuit (at 20°/s) with a very similar range of coefficients (0.95–16.7 for eye position, 0.13–8 for eye velocity, and 0.05–1.8 for eye acceleration; Table 1). Second, the lead (δ = 18) of the population response vis-à-vis the eye movement for the maximum CD is close to the range of latencies (10–20 ms) of pursuit responses evoked by OMV stimulation (Krauzlis and Miles 1998). Third, lesions of the OMV (Takagi et al. 2000) as well as inactivation of the caudal fastigial nucleus, the immediate target of OMV PCs (Robinson et al. 1997), cause deficits in SPEM initiation. These findings together are in accord with the notion that the population signal reflects a computational step helping to improve the transformation of target motion into an appropriate pursuit response. Does this mean that we might understand the population signal as the neuronal basis of an “internal model”? Actually, we think that this conclusion would be premature as we lack a quantitative description of the input driving the PC population response and therefore knowledge of the transfer function underlying the population response. Hence, we cannot decide at this point if the transfer function involved corresponds to a specific type of internal model, reflecting specific physical features of the body such as an inverse dynamics model of the eyeball (Shidara et al. 1993).

The assumption of population coding yields a perfect match between eye movement kinematics and a neuronal signature. Yet, is the notion of population coding more than the reflection of a statistical trick that happens to yield better results without reflecting a relevant biological principle? Actually, we think that the assumption of population coding of PC SSs is an inevitable consequence of an important but nevertheless largely neglected feature of the corticonuclear projection, namely the convergence of hundreds of individual PC axons on single DCN neurons (Palkovits et al. 1977). This strong convergence has 2 implications: first, a single PC will have little influence on a given nuclear neuron, and second, the nuclear neuron will be unable to trace the origin of an individual synaptic input to a specific PC. Rather, it is the collective input from all PCs converging onto the nuclear neuron at issue that determines its response. As PC CSs do not have an appreciable effect at the level of nuclear neurons (Monsivais et al. 2005), this collective input corresponds to a PC SS population input. Of course, the population response, reconstructed in the present study from responses of individual PC SSs subjected to one and the same task, yet recorded sequentially, is little more than a first approximation of the true population input as there is no reason to assume that the recorded neurons would project to the same target neurons. In any case, population coding will smear differences between individual PC SS units and even straighten out the qualitative differences between responses such as tonic versus phasic responses or activity increases versus activity decreases. If, alternatively, each of these distinct response patterns were to be conveyed to the DCN level without losing their identity, then PC SSs with similar characteristics would have to converge onto functionally distinct DCN neurons, resulting in subsets of DCN neurons with specific, smooth-pursuit–related activity profiles. However, there is little evidence for functionally distinct subsets of neurons in the cFN as Fuchs et al. (1994) reported that they shared similar pursuit-related response profiles, characterized by a burst at pursuit onset followed by a tonic steady-state response later during smooth pursuit. Actually, the population response profile of OMV PCs looks very similar to the activity profile of a typical fastigial unit.

The OMV is but one of several regions of cerebellar cortex that have been implicated in smooth pursuit (Krauzlis 2004; Ilg and Thier 2008). Besides the OMV, the list of pursuit-related regions includes the flocculus and neighboring ventral paraflocculus, usually collectively referred to as the floccular complex, and the little explored hemispheric oculomotor region, centering on hemispheric folia VI and VII (Rambold et al. 2002; Medina and Lisberger 2007; Ohki et al. 2009). Unlike the floccular complex, whose role in the control of SPEMs seems to be a consequence of its role in the modification of vestibular and optokinetic reflexes, the OMV accommodates goal-directed saccades in addition to foveal smooth pursuit (Thier et al. 2000, 2002). A contribution of the OMV to both types of goal-directed eye movements is suggested by the presence of both saccade- and pursuit-related signals in the OMV and the clear effects of OMV lesions on both types of eye movements. Lesions of the OMV cause transient changes of saccade and pursuit metrics and a loss of short-term saccadic and pursuit adaptation (Takagi et al. 1998, 2000; Barash et al. 1999; Golla et al. 2008; Xu-Wilson et al. 2009). The pursuit deficit emphasizes the early, open-loop part of the pursuit eye movement and also involves the ability to adjust the velocity of this part of the SPEM (Takagi et al. 2000). In contrast to smooth-pursuit initiation, the later closed-loop SPEM is only mildly affected. Both the saccade and the pursuit initiation deficit can be understood as consequences of a misadjustment of parameters determining the precise metrics of motor responses, which are prompted by sensory stimuli but have to be carried out in the absence of immediate sensory feedback. In both cases, the misadjustment seems to reflect the loss of a precise description of eye movement kinematics provided by a PC population signal. The short-term adaptation of saccade metrics can be led back to suitable changes of the PC SS population signals (Catz et al. 2008). It is close at hand to assume that in a similar vein also smooth-pursuit adaptation, that is, the adjustment of the velocity of the early open-loop eye movement, may reflect suitable changes of the OMV PC SS population signal. This remains to be shown. It also needs to be clarified if pursuit and saccades rely on a common OMV population code, rather than 2 distinct ones involving different sets of OMV PCs. Actually, a common code would be compatible with the pursuit-related firing rates observed. The absolute changes of the pursuit-related PC population response amount to only 20 spikes/s (from 75 to 95 spikes/s) for the range of pursuit velocities studied (from 6 to 20°/s). This suggests that the remaining dynamic range of the population discharge should be large enough to accommodate also the much larger velocities of saccades. Independent of these open questions, our findings clearly strengthen the notion that the modulatory influence of cerebellar cortex on motor behavior is in general accommodated by a carefully adjusted PC SS population code.

In conclusion, PC population coding in cerebellar cortex can be understood as a general principle that is firmly embedded in anatomy rather than being an artificial construct. Apart from its role in precisely shaping the motor behavior across modalities, it also has important implications for cerebrocerebellar communication. A cerebellar population code must be a principle relevant for the cerebellar influence on cerebral cortex (Lindner et al. 2006; Handel et al. 2009; Ignashchenkova et al. 2009; Strick et al. 2009).

Funding

Deutsche Forschungsgemeinschaft (SFB 550 A7).

Conflict of Interest: None declared.

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