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1 Department of Neurosurgery, 2 Department of Physiology, and 3 Graduate Program in Neuroscience, University of Minnesota, Minneapolis, Minnesota 55455
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Fu, Q.-G., D. Flament, J. D. Coltz, and T. J. Ebner. Relationship of cerebellar Purkinje cell simple spike discharge to movement kinematics in the monkey. J. Neurophysiol. 78: 478-491, 1997. The simple spike discharge of 231 cerebellar Purkinje cells in ipsilateral lobules V and VI was recorded in three monkeys trained to perform a visually guided reaching task requiring movements of different directions and distances. The discharge of 179 cells was significantly modulated during movement to one or more targets. Mean simple spike rate was fitted to a cosine function for direction tuning, a simple linear function for distance modulation, and a multiple linear regression model that included terms for direction, distance, and target position. On the basis of the fit to the direction and distance models, there were more distance-related than direction-related Purkinje cells. The simple spike discharge of most direction-related cells modulated at only one target distance. The preferred directions for the simple spike tuning were not uniformly distributed across the workspace. The discharge of most distance-related cells modulated along only one movement direction. On the basis of the multiple linear regression model, simple spike discharge was also correlated with target position, in addition to direction and distance. Approximately half of the Purkinje cells had simple spike activity associated with only a single parameter, and only a small fraction of the cells with all three. The multiple regression model was extended to evaluate the correlations as a function of time. Considerable overlap occurred in the timing of the simple spike correlations with the parameters. The latency for correlation with movement direction occurred mainly in a 500-ms interval centered on movement onset. The correlations with target position also occurred around movement onset, in the range of 
200-500 ms. Distance correlations were more variable, with onset latencies from 500 to 1,000 ms. These results demonstrate that the simple spike discharge of cerebellar Purkinje cells is correlated with movement direction, distance, and target position. Comparing these results to motor cortical discharge shows that the correlations with these parameters were weaker in Purkinje cell simple spike discharge, and that, for the majority of Purkinje cells, the simple spike discharge was significantly related to only a single movement parameter. Other differences between simple spike responses and those of motor cortical cells include the nonuniform distribution of preferred directions and the extensive overlap in the timing of the correlations. These differences suggest that Purkinje cells process, encode, and use kinematic information differently than motor cortical neurons.
One step in understanding how a neural structure contributes to movement control is to define the relationship between the neuronal discharge and the relevant movement parameters (Georgopoulos 1986 Behavioral paradigm
The behavioral paradigm is similar to that used previously (Fu et al. 1993 Chamber implantation and electrophysiological recording
On demonstrating proficiency at the behavioral task, the animals were anesthetized with xylazine (1.0 mg·kg Data and statistical analyses
Neuronal discharge and kinematic data were aligned on movement onset, defined as the time at which tangential velocity exceeded 1.0 cm/s; correspondingly, we defined movement end as the time at which tangential velocity fell below this threshold. Averages of simple spike activity and kinematics were constructed from 5-10 movements for each of the 48 targets. We analyzed three time periods for each cell: 1) premovement time (PT), defined as the 200-ms interval before movement onset; 2) movement time (MT), defined as the period from movement onset to movement end; and 3) total time (TT), defined as the sum of PT and MT. To determine the presence of significant simple spike modulation, we used a one-way analysis of variance (ANOVA) for movements to all 48 targets, comparing firing rate with background activity (measured as the average simple spike discharge in the interval 1,200-500 ms before movement onset) for each time period. Cells whose modulation was not statistically significant for all three time periods were not included in the subsequent regression analyses.
Histology
Select recording locations and chamber coordinates were marked electrolytically. The three animals were killed [under deep pentobarbital sodium anesthesia (150 mg/kg ip)]. The animal was determined to be in a plane of surgical anesthesia before the thoracotomy. An intracardiac perfusion of Ringer solution was followed by Zamboni's fixative (4.3 g NaOH, 20 g paraformaldehyde, 18.8 g NaH2PO4, and 150 ml picric acid in 850 ml H2O). The cerebellum was removed and sectioned (40- or 50-µm sections) in the parasagittal plane with the use of a freezing microtome. The sections were stained with thionin.
Data base and location of Purkinje cells
We recorded the simple spike activity of 231 movement-related cerebellar Purkinje cells in three monkeys (27 cells in monkey LI, 31 in monkey BE, and 173 in monkey MA). Of the 192 Purkinje cells with receptive fields as tested by palpation and passive movement, 33% were related to the hand/wrist area, 31% to the forearm/elbow area, and 36% to the shoulder. The remaining cells were audibly modulated during reaching movements. Of the total population of cells, 179 (77.5%) had significant increases or decreases in firing rate relative to background discharge for one or more targets (ANOVA, P < 0.05) during one or more of the three time periods (125 in PT, 153 in MT, and 151 in TT). The remainder of the analysis was performed on the simple spike data obtained from this group of 179 cells.
Directional tuning of simple spike activity
For about half of the Purkinje cells, the simple spike activity significantly fitted a cosine function [69 cells (45.7%) in TT; 52 cells (41.6%) in PT; 75 cells (49.0%) in MT; see Table 1, "Direction" plus "Both"]. Figure 2 shows discharge histograms for a Purkinje cell whose simple spike activity in TT was strongly modulated with movement direction at distances of 3-6 cm. This cell's preferred directions were 134.3°, 105.7°, 123.7°, and 99.9°, respectively, for the aforementioned distances. The degree of modulation did not differ greatly among the four individual distances (Idir = 0.80, 0.81, 0.72, and 1.13; c1 = 17.60, 11.89, 11.62, and 13.80 spikes/s). This unit had a receptive field to passive rotation of the hand at the wrist.
Distance-related simple spike activity
The relationship of simple spike activity to movement distance was evaluated with the use of a simple linear regression model (Eq. 2). Of 151 Purkinje cells studied during TT, 55% (45 "Distance" plus 38 "Both") had simple spike activity that significantly correlated (R2 > 0.67) with movement distance (Table 1). During PT, 45% of the cells had simple spike activity that significantly correlated with distance, and during MT, 56% had such activity. Figure 5 shows the discharge of a Purkinje cell whose simple spike activity was correlated significantly with distance at one direction (0°). The receptive field for this cell was localized to the shoulder. The slope with distance for this direction was 2.91 spikes·s
Correlations with multiple movement parameters
Use of the simple distance and direction regression models revealed that the discharge of some cells correlated significantly with more than one parameter (Table 1). Therefore we extended the analysis by fitting the data to the multiple linear model (Eq. 3). Figure 7A shows the mean PRE for pairs of model comparisons. The PRE is an index that indicates which of several models best fits the data; a higher PRE indicates that more of the variability in simple spike discharge is accounted for by a particular model. Solid bars represent statistically significant improvements in mean PRE and unshaded bars represent nonsignificant improvements. Sequentially, the graphs illustrate that models 3 (Eq. 3) and 2 (Eq. 4) better predict the simple spike firing rate than model 1 (Eq. 1), and that model 3 better predicts the firing than model 2. For those cells in which the fit improved with the additional parameters, the mean PRE is quite large (i.e., ~30% in the comparison of models 1 and 3). Therefore distance and target position are important parameters that need to be included in the model. A determination of the optimal number of predictors also justifies the use of the larger model with six predictors. Figure 7B shows the relationship between the mean Mallows' Cp statistic and the number of predictors included in different models. The Cp statistic gives the standardized total mean squared error of estimation for the data. For the optimal number of predictors (p), a criterion of Cp 64 p is used. Using six predictors we obtained a Cp of 5.4, which justifies the use of a model with six predictors (Eq. 3). On the basis of this model, we calculated partial R2 values for direction, distance, and target position (R2dir, R2dis, and R2tar, respectively), and a total R2 based on the sum of these partial R2 values. Note that the partial R2s sum to the total R2.
Relations of parameter correlations to receptive fields
The majority of Purkinje cells analyzed in this study was found to have receptive fields involving the wrist/hand, elbow, and shoulder; a smaller number of cells were audibly modulated during movement, but with an indeterminate receptive field. Therefore we analyzed whether the correlations defined by the different parameters in either the simple models (direction and distance) or the multiple models were related to the receptive field location with the use of one-way ANOVAs. There were 69 Purkinje cells with direction tuning based on the cosine tuning model, and of these, 30 had receptive fields involving the shoulder, 8 had elbow receptive fields, 18 had hand receptive fields, and 13 had no clear receptive fields. Neither the presence of significant directional tuning (P > 0.05, F-test) nor the depth of modulation, Idir (P > 0.05, F-test), differed on the basis of the receptive field type. There were 83 cells with distance modulation based on the simple linear model, and of these, 30 had shoulder receptive fields, 17 had elbow receptive fields, 24 had hand receptive fields, and 12 cells had no clear receptive fields. Neither the frequency of significant distance modulation (P > 0.05, F-test) nor the slope (P > 0.05, F-test) was dependent on the receptive field type.
Temporal encoding of movement parameters
We evaluated whether the simple spike correlation with the different parameters exhibited any temporal parcellation (see Fu et al. 1993
Direction-related modulation in Purkinje cell simple spike discharge
For approximately half of the Purkinje cells studied, the simple spike discharge significantly fitted a cosine tuning function to movement direction. This same relationship has been used to describe the directional dependency of premotor, primary motor, and parietal cortical neurons (Caminiti et al. 1991 Distance and target position modulation in Purkinje cell simple spike discharge
The encoding of movement distance in the simple spike discharge of Purkinje cells has been largely ignored in previous cerebellar single-unit studies (Fortier et al. 1989 Temporal characteristics of multiple parameter correlations
In our previous studies of the primary and premotor cortices, there was a temporal parcellation of the cell discharge correlations with direction, distance, and target position (Fu et al. 1993 Kinematic coding differences between simple spike discharge and motor cortical discharge
Previous studies comparing cerebellar and motor cortical neuronal activity during these types of reaching movements emphasized some of the similarities (Fortier et al. 1993
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; Kalaska 1991). This approach has been successful in relating the firing of primary, premotor, and parietal cortical neurons to the kinematics of reaching movements (Caminiti et al. 1991; Fu et al. 1993, 1995; Georgopoulos et al. 1982, 1988; Kalaska et al. 1983; Lacquaniti et al. 1995; Schwartz et al. 1988). Unfortunately, the motor parameters encoded or controlled by the cerebellum during voluntary limb movements remain only partially defined. Movement direction may be the parameter most commonly studied in relation to the firing of cerebellar neurons. Purkinje cell simple spike discharge as well as dentate and interposed neuronal discharge display directionally sensitive discharge in single-joint (Frysinger et al. 1984; Thach 1970a,b, 1978; Wetts et al. 1985) and multijoint movements (Fortier et al. 1989, 1993). However, some investigators observed only minimal (Chapman et al. 1986; MacKay 1988) or no directional coding in the discharge of dentate neurons (Robertson and Grimm 1975), whereas others reported a large population of bidirectional cerebellar neurons during single-joint movements (Schieber and Thach 1985). Two recent studies of multijoint movements showed that the modulation with direction is not necessarily reciprocal, but instead graded, and can be modeled by a cosine tuning function (Fortier et al. 1989, 1993). This illustrates the need to evaluate systematically the discharge properties of cerebellar neurons over not only a large range of values for the parameter of interest, but also over the physical workspace.
; Mano and Yamamoto 1980; Marple-Horvat and Stein 1987) suggests that the time derivatives of movements are encoded. The discharge of cerebellar interposed neurons is correlated significantly with elbow angular velocity during forearm movements in the primate (Robertson and Grimm 1975) and during limb movements in the cat (Soechting et al. 1978). In the primate, Purkinje cell simple spike discharge varies with wrist velocity during manual tracking (Mano and Yamamoto 1980) and with hand velocity during the operation of a joystick (Marple-Horvat and Stein 1987). In the latter report, simple spike correlations with velocity were stronger than the correlations with acceleration. Some mossy fiber afferents, in addition to interpositus neurons, discharge in relation to movement velocity in the primate (van Kan et al. 1993a,b).
; Harvey et al. 1977; Thach 1978) and in the simple spike firing of Purkinje cells (Bauswein et al. 1983; Mano and Yamamoto 1980). However, some position-related simple spike discharge occurs in Purkinje cells (Marple-Horvat and Stein 1987). Simple spike firing is also related to the maintenance of a fixed wrist position against a torque load (Gilbert and Thach 1977; Thach 1970b).
, 1995). We used the same simple and multiple linear regression analyses to identify statistically the prevalence and strength of the simple spike correlation with the parameters. Therefore, in addition to defining characteristics of Purkinje cell simple spike discharge during reaching movements throughout a two-dimensional workspace, the task design and analysis permitted a detailed comparison with previous premotor and primary motor cortical findings. A preliminary account of these results has been presented in abstract form (Fu et al. 1994).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
, 1995). Three female rhesus monkeys (Macaca mulatta) weighing 5.0, 5.2, and 5.3 kg performed visually guided, multijoint arm movements in the horizontal plane with the use of a two-joint manipulandum. The animals sat in a primate chair and faced a vertically positioned color monitor (23.5 × 32 cm) placed ~45 cm from the animal's chest. Using the manipulandum, the animals superimposed a cross-hair cursor (0.75 cm) onto brightly colored squares (1 cm2) displayed on the screen. In each trial, the animals first superimposed the cursor onto a centrally positioned start box for a randomized period of time ranging from 0.5 to 1.5 s. The start box was then extinguished and 1 of 48 targets appeared. The targets were arranged circumferentially around the start box at 45° intervals (8 directions) and at six distances ranging from 1.0 to 6.0 cm, in 1.0-cm increments. To complete the trial successfully, the animals were required to move the cursor to the target within 2 s of its appearance and to maintain the cursor in the target for an additional 1.5 s. The successful completion of a trial was rewarded with the delivery of fruit juice.
1·h1) and ketamine (20 mg·kg1·h1) and implanted with stainless steel chronic recording chambers. The chambers were positioned stereotaxically on the animal's right side (monkey MA: posterior 6 mm, lateral 10 mm; monkey LI: posterior 6 mm, lateral 10 mm; monkey BE: posterior 6 mm, lateral 13 mm) and attached to the skull with screws and acrylic cement. In the immediate postoperative period the animals received an analgesic (Nubain, 0.05 mg/kg), and for several days they received prophylactic doses of antibiotics (Ampicillin, 250 mg·kg1·day1). After recovery, extracellular single-unit recordings were made with the use of paralyene-coated tungsten microelectrodes (3-10 M
). Purkinje cells were identified by the presence of spontaneous simple and complex spikes, which were discriminated with the use of time and amplitude techniques (Ojakangas and Ebner 1992). A description of the complex spike activity during this task will be included in a future report. Discriminator signals were converted to transistor-transistor logic pulses before being digitized and stored to computer at 1 kHz. Signals from potentiometers located at the manipulandum's joints were sampled and stored at 1 kHz for calculation of hand position and tangential velocity. Palpation and passive limb manipulation were used to determine whether a cell had a somatosensory receptive field of the hand, wrist, elbow, or shoulder girdle. Cells were also examined for modulation during active, spontaneous reaching movements with the manipulandum. Cells that did not respond to either active movements or passive manipulation were not studied further.
, 1995) to fit the simple spike firing to movement direction, distance, and target position. We used both simple and multiple linear regression analysis to identify correlations between simple spike discharge and movement parameters for two reasons. First, the multiple regression analysis requires that either direction or distance modulation in the discharge occur over a range of the workspace. This model could potentially fail to detect correlations that occur over a limited range of directions or distances. Use of the simple linear models was necessary to examine specifically for directional tuning along a single distance and distance modulation along a single direction. Second, use of both simple and multiple regression analysis permitted a full comparison with previously published motor cortical discharge studied with the use of the same paradigm (Fu et al. 1993, 1995).
as follows
which can be expressed as
(1)
where b0 represents the intercept of the regression equation, b1 and b2 the regression coefficients, c1 the change in firing rate of the cell as a function of direction (
![<IT>f = b</IT><SUB>0</SUB><IT> + c</IT><SUB>1</SUB>[cos (θ − θ<SUB>p</SUB>)]](/content/vol78/issue1/fulltext/478/img002.gif)
), and p the preferred direction. On the basis of the model F ratio (P < 0.05), an R2 greater than ~0.7 was required for a significant fit of the model to the data. An index of the depth of directional modulation (Idir = c1/b0) was used to assess the proportional increase or decrease over the mean level of activity (Georgopoulos et al. 1982). To test the hypothesis of uniformity of the cells' preferred directions, we used Watson's U2 method (Mardia 1972).
where a0 is the intercept and a1 is the slope.
(2)
Here, the interaction terms, sin (
![+ <IT>k</IT><SUB>5</SUB>[sin (θ)⋅<IT>d</IT>] + <IT>k</IT><SUB>6</SUB>[cos (θ)⋅<IT>d</IT>]](/content/vol78/issue1/fulltext/478/img005.gif)
(3)
)·d and cos ()·d, are the X and Y coordinates, respectively, of target position. The regression model used is the same as that described in Fu et al. (1993, 1995). Briefly, the development of this final model consisted of testing three preliminary models of increasing complexity. The first was the direction model described above (Eq. 1). The second model combined direction and distance terms as follows
The third model tested was given in Eq. 3 above, which included terms for direction, distance, and their interaction, target position. A proportional reduction in error (PRE) approach was used to compare the extent to which each of the three models accounted for the variability in firing rate (Judd and McClelland 1989
(4)
).
where d is movement distance, kn are the least-squares estimates, and
![+ <IT>k</IT><SUB>4</SUB>(<IT>t</IT>)<IT>d</IT><SUP>2</SUP><IT>+ k</IT><SUB>5</SUB>(<IT>t</IT>)[sin (θ)⋅<IT>d</IT>] + <IT>k</IT><SUB>6</SUB>(<IT>t</IT>)[cos (θ)⋅<IT>d</IT>]](/content/vol78/issue1/fulltext/478/img008.gif)
(5)
represents movement direction. The time increments were 20-ms bins. Before fitting the time regression model, the data were smoothed with the use of a three-point moving average.
; Georgopoulos et al. 1982; Schwartz et al. 1988), usually eight directions of movement were used (n = 8), whereas in our task eight directions and six distances were used (n = 48), increasing the likelihood of finding significant relationships with a smaller partial R2. For the temporal regression (Eq. 5), the criterion for the existence of a correlation was arbitrarily set to three consecutive time bins with a significant partial R2 to reduce the number of spurious correlations. Onset latency of a given parameter correlation was defined as the time at which the first of three consecutive bins had a significant partial R2 value.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
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FIG. 1.
A: regions where majority of recordings was obtained for each animal. 
, monkey BE; - - -, monkey MA; ···, monkey LI. B and C: examples of recovered recording tracts in monkey MA (B) and a lesion tract in monkey BE (C). Pf, primary fissure. Anterior is to the right in the parasagittal sections in B and C. Calibration bar: 1.3 mm.
View this table:
TABLE 1.
Parameter coding
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FIG. 2.
Example of Purkinje cell showing modulation of simple spike activity with movement direction. All data aligned on movement onset, marked by vertical dotted line. Histograms of average firing at 8 directions and 6 distances; each histogram was generated from 10 trials and plotted with 20-ms binwidths. Superimposed curve is velocity profile. Plot at bottom of each histogram set is average activity during total time (TT) vs. movement direction with superimposed cosine tuning curve. Significant directional tuning (F test, P < 0.05) was seen along 4 distances (3.0, 4.0, 5.0, and 6.0 cm). Average index of depth of directional modulation (Idir) = 0.87 ± 0.18 (SD) and average mean slope (c1) = 13.7 ± 2.8 for the 4 distances.
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FIG. 3.
Properties of cell discharge with significant directional tuning based on the cosine regression model. A: number of cells in each analysis period along movement distance. B: c1 for each movement distance and analysis period. C: Idir relative to baseline discharge for direction for each movement distance and analysis period. In B and C, each histogram bar indicates mean ± SD. PT, premovement time; MT, movement time.
). In Fig. 4C, the size of Idir at each segment is given. The distribution was found to be uniform (ANOVA, P > 0.05), although there was a slight reduction in the Idir in the 315-360° region. Therefore, although there were well-defined groupings of preferred directions for the population of Purkinje cells, the amplitude of the simple spike modulation for a given cell was not dependent on the preferred direction.
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FIG. 4.
Distribution of preferred directions. A: preferred direction for each unit, based on the discharge from all 6 distances combined. Length of each vector represents Idir. B: frequency of distribution of preferred directions in each 22.5° sector. Length of each sector is given by number of neurons whose preferred direction falls within each sector, weighted relative to number of target distances at which direction-related modulation is statistically significant. C: size of Idir distributed over workspace. Calibrations: A: Idir = 2; B: 3 units; C: Idir = 1.
; Marple-Horvat and Stein 1987). In this reaching task peak velocity is tightly correlated with movement amplitude (Fu et al. 1993); this speed-distance relationship has been extensively documented (Fitts 1954; see Georgopoulos 1986). Therefore one possibility is that the nonuniform directional tuning was related to variation in movement velocity as a function of direction. We evaluated this possibility on the basis of the peak velocity. For a given distance, peak velocity did not vary with direction (ANOVA, P > 0.05). Furthermore, the depth of modulation with direction, Idir, was not correlated with the peak velocity (r = 0.04, P > 0.05). Therefore the simple spike directional tuning was independent of the peak velocity.
1·cm1. Although there was a trend toward increasing simple spike discharge with increasing distance, the simple spike-distance relationships along the other seven directions were not significant (F test, P > 0.05).
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FIG. 5.
Movement distance-related simple spike activity of a Purkinje cell. Conventions as in Fig. 2, except each histogram set represents the activity for 6 distances at movement direction indicated. Below or next to each histogram, simple spike activity during TT is plotted as a function of movement distance. A least-squares regression line is drawn through points and coefficient of determination is given by R2. Significant distance-related modulation occurs only at a direction of 0°.
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FIG. 6.
Properties of cell discharge with significant distance-related modulation based on linear regression model. A: histogram showing number of cells whose discharge modulated with distance at 
1 movement directions for the 3 analysis periods. Majority of cells' simple spike discharge was distance modulated at only 1 direction. B: mean slope (a1 from Eq. 2) for each movement direction and analysis period.
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FIG. 7.
Summary statistics for development of multiple regression model. A: comparison of mean proportional reduction in error (PRE) for the 3 models evaluated. Black bars: significant improvement in PRE of model 3 over model 1, model 2 over model 1, and model 3 over model 2, respectively. White bars: nonsignificant improvements in PRE. B: relationship of Mallows' Cp to number of variables included in multivariate model. The 8 variables used included the 6 given in Eq. 3, plus sin2 ( ) andcos2 (). Cp calculated for 6 variables was 5.4.
View this table:
TABLE 2.
Discharge-parameter relationships
1·cm1 (n = 83) in TT. There were no significant differences in the mean slope (a1) with distance in any of the eight movement directions for any of the three time epochs (ANOVA, P > 0.05, Fig. 6B). The distribution of cells modulated with distance and direction only and with both parameters during the different time periods is summarized in Table 1. Direction modulation was equally likely to occur in any of the three analysis periods (
2 test, P > 0.05), as was distance modulation. Interestingly, distance modulation had a slightly higher overall incidence than direction modulation. As reviewed in the DISCUSSION, when considering distance modulation, the covariation of movement amplitude and velocity must be taken into consideration.
). The cell shown in Fig. 8A had particularly strong direction-related discharge during each of the three analysis periods, with a preferred direction of 234° for TT. Note that the direction-related discharge was reciprocal, with increases in firing rate above baseline for movements in the left hemifield of the workspace and decreases below baseline in the right hemifield. There were no significant relationships with distance or target position for any of the three time epochs. Although the general features of the simple spike responses were captured by the model, it is clear from the predicted polar contour plots that some properties of the spatial response profile were not. This discrepancy is consistent with the total R2 of ~0.6 obtained for this Purkinje cell; that is, 40% of the variability in the firing was not accounted for by the model.
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FIG. 8.
Polar contour plots for 3 cells with significant simple spike modulation during TT. Movement distance is plotted along radius and direction is given by the angle. Pseudocoloring represents modulation above or below background firing rate (spikes/s). Top plots: actual modulation. Bottom plots: predicted modulation. A: cell with significant direction modulation. Note spatially tuned modulation. Partial R2s during TT: R2dir = 0.56, R2dis = 0.02, R2tar = 0.00. B: polar contour plots for cell with significant modulation for distance. Areas with similar modulation (i.e., color) were found to occur over a relatively broad range of directions at a given distance. Partial R2s during TT: R2dir = 0.12, R2dis = 0.40, R2tar = 0.06. C: polar contour plots for cell with significant target position modulation. Partial R2s during TT: R2dir = 0.02, R2dis = 0.01, R2tar = 0.68.
).
, 1995). For units whose discharge was related to only one parameter based on the multiple regression model, we counted the number of cells with a significant partial R2 during each analysis period (Fig. 9A). The number of cells with a significant partial R2 for direction, distance, and target position tended to occur with near-equal frequency during each period. For the population of cells related to two or more parameters, the R2dir was greatest during MT and distance correlations were slightly more prevalent during PT (Fig. 9B). These observations differ from the findings in the motor cortices in which direction correlations dominated PT and distance correlations were most prevalent in MT (Fu et al. 1993).
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FIG. 9.
Number of cells whose highest partial R2 occurred for direction, distance, and target position as a function of the 3 analysis periods. A: distribution for cells whose discharge was fit significantly to only 1 parameter. B: distribution for cells whose discharge was significantly fit to 2 parameters, grouped on the basis of the dominant parameter (i.e., that with the highest partial R2).
80 and 520 ms.
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FIG. 10.
Partial R2s for direction, distance, and target position and total R2 over the 2,000-ms analysis period for 2 individual cells. A: example of cell modulated with direction and target position. B: example of cell modulated with direction, distance, and target position. Movement onset at time 0 (vertical dotted lines).
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FIG. 11.
Population analysis of partial R2s and latency for each parameter. A: averaged (mean ± SD) temporal profiles of partial R2 values for all units that showed significant modulation of discharge related to given parameter. Movement onset at time 0 (vertical dotted lines). B: frequency distribution of partial R2 onset latencies for all units with discharge significantly correlated to given parameter.
200 and 300 ms. The latency for target position occurred primarily between 200 and 400 ms, whereas the latency distribution for distance was extremely wide, with most cells falling in the range of 100-500 ms. The mean onset latencies were as follows: 190.6 ± 337 ms (direction); 147.7 ± 272 ms (target position), and 323.3 ± 421 ms (distance). There were no significant differences in the three distribution functions (Kruskal-Wallis test, P > 0.05). Therefore the overlap in the onset of simple spike correlations with the three parameters was pronounced. It should be pointed out that the wide variability in latency and timing of the correlations with the individual parameters can have the effect of reducing the amplitude of the mean partial R2 temporal profiles. This probably contributed to the low mean partial R2s shown in Fig. 11A.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
; Fu et al. 1993; Georgopoulos et al. 1982, 1984, 1988; Kalaska et al. 1983; Schwartz et al. 1988), as well as cerebellar neurons (Fortier et al. 1989, 1993). Earlier cerebellar studies that found limited or no directional coding emphasized primarily reciprocal changes in modulation and concentrated on single-joint movements (Chapman et al. 1986; Harvey et al. 1979; Schieber and Thach 1985). As discussed by Fortier et al. (1989), the directional tuning of cerebellar neurons is not limited to reciprocal changes in the simple spike discharge, but has more graded changes in the degree of modulation. The present study confirms earlier observations on the discharge of cerebellar cortical neurons, establishing that the simple spike discharge of a large population of Purkinje cells exhibits significant directional tuning. It should be noted that the present study differs from previous work (Fortier et al. 1989) in that only identified Purkinje cells were recorded and movements were performed at six distances in addition to the eight directions.
, 1995), there were several differences in the directional tuning. First, the fit of the simple spike discharge to the cosine tuning function was not maintained over several distances. Typically, this type of directional modulation was limited to only one distance. This result differed conspicuously from that in the primary motor and premotor cortices, in which the directional tuning and preferred directions were relatively constant over a range of distances (Fu et al. 1993).
for cerebellar units. However, in both the present and previous cerebellar studies the distribution of preferred directions was not uniform. Both studies had a predominance of preferred orientations for movements of the arm crossing the midline and away from the animal's body to the left (
135°). Additionally, in this study there were a large number of Purkinje cells with preferred orientations in the opposite direction, ipsilaterally and toward the animal's right side (315°). This nonuniformity is in distinct contrast to the motor (Georgopoulos et al. 1982, 1984, 1988) and premotor cortices (Caminiti et al. 1991; Fu et al. 1993, 1995), in which the preferred directions are uniformly distributed in two- and three-dimensional space. The modulation of the simple spike discharge of Purkinje cells with direction is markedly different from that in the motor cortical areas.
). The second possibility is that the preferred directions represent a type of coordinate axes for Purkinje cell simple spike discharge. Nonuniform preferred directions have been described for Purkinje cell simple spike discharge in the flocculus (Graf et al. 1988). A third possibility is that other, unsampled populations of Purkinje cells would have a different set of preferred directions. However, this also could be consistent with a coordinate axes representation in which preferred directional tuning is parcelled into anatomically distinct groups of Purkinje cells.
, 1993; Marple-Horvat and Stein 1987). In the present study, ~70% of the Purkinje cells had a significant partial R2 for distance based on the univariate regression analyses (Table 1). This percentage was actually slightly higher than the percentage of Purkinje cells (~60%) correlated with direction based on the cosine tuning regression model. The average slope approached 4.0 spikes·s1·cm1; therefore changes in distance were capable of extensively modulating simple spike discharge. The multiple regression model also yielded significant fits with distance, including a large number of Purkinje cells related to distance only as well as cells related to multiple parameters (Table 2). The model comparison results show that distance explains a significant amount of the variability in the simple spike firing for a fraction of the Purkinje cells. Furthermore, both the single and multiple linear regression models revealed considerable distance-related simple spike firing during PT and MT.
, 1995; Kurata 1993; Riehle and Requin 1989). The present study demonstrates that the simple spike discharge of Purkinje cells is correlated with movement distance. Although the slope of the regression (a1) was similar to that found in our previous study (Fu et al. 1993), there is an important difference. The simple spike discharge of many more Purkinje cells was significantly related only to distance. A similar difference was seen for target position, with 17% of cells having simple spike discharge correlated with this parameter only.
); therefore the correlations with distance could reflect velocity sensitivity (see Fu et al. 1993). This is of particular importance in the cerebellar cortex, where several studies have documented that the discharge of cerebellar neurons, including Purkinje cell simple spike firing, has velocity sensitivity during limb movements (Mano and Yamamoto 1980; Marple-Horvat and Stein 1987; van Kan et al. 1993b). Therefore, when referring to distance, this important caveat must be considered.
, 1995). Specifically, significant correlations with direction occurred first and preceded movement onset. These were followed closely by encoding of target position, with distance coding beginning sometime after movement initiation. For the Purkinje cell simple spike discharge, no temporal order was found. As shown in Fig. 9A, for cells related to a single parameter, only slight differences were found in the number of cells correlating significantly with direction, distance, or target position in PT and MT. For cells encoding multiple parameters, no clear order of the encoding emerged (Fig. 9B), although correlations with distance and target position occurred commonly in the premovement period. This question of temporal encoding was refined with the use of the temporal regression analysis applied previously to the motor cortices (Fu et al. 1995). Across the population of Purkinje cells recorded, the distributions of onset latencies for the three parameters overlapped extensively and no significant difference was obtained among the three distributions (Fig. 11). It would appear from the present results that in contrast with the serial elaboration of kinematic information found for the motor cortices (Fu et al. 1995), the simple spike discharge of Purkinje cells processes the same information in parallel. This tendency for parallel processing of the kinematic variables suggests that the cerebellar cortex is concerned with the entire spectrum of movement information at all times (i.e., premovement and postmovement).
). In this discussion we have concentrated on some of the differences in the correlations of movement kinematics between the discharge of cerebellar Purkinje cells and that of cells in the motor cortices. Two additional differences should be stressed. First, the degree to which the variability in simple spike firing is explained by movement direction, distance, and target position is ~57% of that observed in the primary and premotor cortices (mean total R2 = 0.35 in cerebellum vs. 0.61 in motor cortices). This is one of the more striking differences among the two populations of cells. Because a large component of the variability in simple spike discharge is unexplained, other parameters of movement may account for some of this variability. As described above, movement velocity is a likely candidate (Mano and Yamamoto 1980; Marple-Horvat and Stein 1987). Another possibility is that Purkinje cell simple spike discharge is modulated by the kinematics as it evolves in time, as opposed to simply the movement endpoints of direction, target position, and distance. We are presently evaluating this possibility.
, 1995) were significantly correlated with more than one parameter. Instead of representing multiple parameters within the discharge of a single cell, the parameters are represented in different Purkinje cells. Considering the lack of any definite temporal ordering in the correlations, these differences suggest that the cerebellum parcels kinematic information among different cells as opposed to temporally within a single cell.
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ACKNOWLEDGEMENTS |
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We thank L. King for help in typing the manuscript and M. McPhee for preparation of the figures and histology.
This work was supported by National Institute of Neurological Disorders and Stroke Grants NS-18338 and NS-31530.
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FOOTNOTES |
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Address for reprint requests: T. J. Ebner, University of Minnesota, Lions Research Building, Room 421, 2001 6th St. SE, Minneapolis, MN 55455.
Received 23 August 1996; accepted in final form 18 March 1997.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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