© 2006 Nature Publishing Group http://www.nature.com/natureneuroscience
ARTICLES
Force field effects on cerebellar Purkinje cell discharge
with implications for internal models
S Pasalar1,2, A V Roitman1, W K Durfee2 & T J Ebner1
The cerebellum has been hypothesized to provide internal models for limb movement control. If the cerebellum is the site of an
inverse dynamics model, then cerebellar neural activity should signal limb dynamics and be coupled to arm muscle activity.
To address this, we recorded from 166 task-related Purkinje cells in two monkeys performing circular manual tracking under
varying viscous and elastic loads. Hand forces and arm muscle activity increased with the load, and their spatial tuning differed
markedly between the viscous and elastic fields. In contrast, the simple spike firing of 91.0% of the Purkinje cells was not
significantly modulated by the force nor was their spatial tuning affected. For the 15 cells with a significant force effect, changes
were small and isolated. These results do not support the hypothesis that Purkinje cells represent the output of an inverse
dynamics model of the arm. Instead these neurons provide a kinematic representation of arm movements.
Prominent among recent theories of the cerebellum’s role in controlling
limb and eye movements is that the cerebellum acquires and stores
representations of the input-output properties of the motor apparatus
or their inverses1–3, so-called internal models. Inverse dynamics models
generate the joint torques/forces needed to achieve a desired trajectory3–7. Forward models predict the state of system, either the motor
variables or the sensory output, as a consequence of the current state of
the arm and the motor commands1,2. An advantage of internal models
is the reduced need for sensory feedback in order to perform accurate
and coordinated movements, overcoming the problem of long time
delays and low gains inherent to feedback loops3.
Internal models have gained wide acceptance as a fundamental
strategy used by the central nervous system in the control of movement,
based on psychophysical observations, including the anticipatory
changes in grip forces during predictable manipulations of object
load8,9 and the ability of humans to adapt and generalize reaching
movements to new dynamic environments10–12.
Several motor structures have been implicated as potential sites for
internal models for limb movements13–17. However, much of the
literature has centered on the cerebellum, with many researchers
hypothesizing that the cerebellum is the site of an inverse dynamics
model1–3,5–7,12,18–21. In support of this hypothesis, cerebellar patients
have difficulty adapting to visuomotor transformations22 and external
force fields19. However, these subjects generally master the new
environments over time, which raises questions about whether the
cerebellum is essential23,24. Functional imaging findings during motor
learning also suggest that the cerebellum participates in the acquisition
and storage of internal models17,20,21.
Electrophysiological support for an inverse dynamics model comes
from ventral paraflocculus/flocculus Purkinje cell recordings during the
ocular following response in monkeys5,6. In these studies, the simple
spike firing was reconstructed using a combination of position, velocity
and acceleration signals. The simple spike signals were interpreted in
terms of the dynamic counterparts of the kinematics, which are the
elastic, viscous and inertial forces needed to control the eye. These
conclusions have been challenged because the reconstructed kinematic
signals are not necessarily equivalent to the forces25.
Purkinje cells have been hypothesized to be a critical stage in the
transformation from kinematics to forces3,5–7. A direct prediction of
the inverse dynamics model hypothesis is that Purkinje cells provide
signals needed to specify the dynamics of a movement5–7. A corollary
prediction is that Purkinje cell firing is closely coupled to muscle
activity7,11. However, recordings of cerebellar neurons that support or
contradict the inverse dynamics model hypothesis for arm movements
are lacking. The present study tests these predictions for Purkinje cell
simple-spike firing in the monkey during manual tracking, by imposing two orthogonally directed force fields at a series of loads.
RESULTS
Hand kinematics and forces
Two monkeys intercepted and tracked a circularly moving target using
a two-jointed, robotic manipulandum under all force conditions
(Fig. 1a,b). An essential feature of this error-constrained tracking
task was that the kinematics were tightly controlled. Accordingly,
the average hand paths and hand speed closely matched those of
the target (Fig. 1c). Neither the hand path (measured as the average
radius of the tracking circle) nor the average hand speed during the
track period varied significantly with the direction of tracking, start
angle, type of force field or load (four-way analysis of variance
(ANOVA), P 4 0.05).
1Department of Neuroscience and 2Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA. Correspondence should be
addressed to T.J.E. ([email protected]).
Received 5 July; accepted 15 September; published online 8 October 2006; doi:10.1038/nn1783
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Figure 1 Schematic of the circular tracking task
Cue period: 180°
Hold
and sample hand kinematics. (a) The monkey
Viscous
period
+
controlled the cursor on the vertically mounted
2 cm
2 cm
computer screen by moving the robotic
+
+
4 cm s–1
manipulandum while the force fields were applied
2s
0.00 N
by the torque motors. (b) The trial sequence was
1.05 N
2.10 N
initiated when the monkey held the cursor (black
3.15 N
Elastic
Track period: 360°
Intercept period: 65°
4.20 N
cross-hair, 0.5 cm across) on the hold target (red
2 cm
+
circle, 2.5 cm diameter) for a random time
2 cm
4 cm s–1
between 2 s and 2.5 s (hold period). A cue target
+
2s
(yellow circle, 2.5 cm diameter) then appeared at
one of four positions (01, 901, 1801 or 2701) at a
radius of 5 cm and moved clockwise (CW) or
counterclockwise (CCW) around a circle centered on the hold target as the monkey maintained the cursor in the hold target (cue period). After traversing 1801,
the cue target changed color (to red) after which the monkey had 651 of target travel to intercept the target (intercept period); this was followed by 3601 of
target tracking (track period). Target speed was constant at 80 degrees s–1 (7 cm s–1) for all trials. At any point in the trial sequence, deviation of the cursor
from the hold or moving target aborted the trial. (c) Example hand trajectories and speed profiles (average of 5 repetitions) for different loads of viscous (top)
and elastic (bottom) force fields.
b
c
EMG activity
The EMG activities of the wrist, elbow and
shoulder muscles exhibited characteristics
NATURE NEUROSCIENCE VOLUME 9
[
Shift (°)
Shift (°)
Shift (°)
Shift (°)
Coefficient
Coefficient
Coefficient
Coefficient
Force (N)
Force (N)
Force (N)
Force (N)
Force (N)
Force (N)
Force (N)
In contrast, the forces at the hand reflected the magnitude and similar to the hand forces. The DOM and average EMG activity
direction of the external force fields (Fig. 2). The depth of modulation (AVG) increased significantly with increasing force magnitude irre(DOM) of the X and Y components of hand force scaled linearly with spective of the force-field type and tracking direction (Fig. 3 DOM and
the magnitude of the applied load for both force fields (Fig. 2, DOM). AVG for flexor carpi radialis and latissimus dorsi). We observed similar
Furthermore, the two force fields resulted in markedly different spatial results for all individual muscles in both monkeys, allowing us to
tuning profiles for the X and Y components, owing to the direction of average the DOM and average activity data across all muscles for each
each force field. The direction of force on the hand under the viscous force-field type (Fig. 4a,b).
The arm muscles also exhibited a shift in the position of maximal
field is opposite to that of the movement, and therefore, the force
profiles were different between the counterclockwise (CCW) and activity between CCW and CW tracking that was similar to that of the
clockwise (CW) tracking directions. In contrast, the elastic field is hand forces (Figs. 3 and 4, shift). The average shift for all muscles was
purely position dependent, with the force on the hand always directed 68.8 ± 30.81 under the null force condition as previously reported26 and
toward the center of the tracking circle, and is independent of tracking demonstrated that each muscle’s tuning depends on both position and
direction. Therefore, the force profiles were similar for CCW and CW movement direction. Similar to the hand forces, the type of force field
tracking directions. These directional properties were quantified as the and magnitude of the load significantly affected the shift between CCW
shift in the position of maximal force between CCW and CW tracking, and CW tracking (Fig. 3, shift for flexor carpi radialis and the latissimus
based on cross-correlating the force profiles at
each load (Fig. 2, cross-correlation), and were
X-force
a
compared between the two force fields at each
Cross-correlation
Shift
DOM
CCW
CW
6
180
1.0
10
load (Fig. 2, shift). On average, the shift in the
135
3
0.5
90
0.0
0
5 CCW
position of maximal X and Y hand forces
Viscous
45
–0.5
–3
CW
between CCW and CW tracking was 157.4 ±
0
–6
0
–1.0
1.05 N
0.00
N
2.10
N
5.81 (all values are mean ± s.d.) at the highest
180
1.0
10
6
4.20 N
3.15 N
135
0.5
3
load (4.2 N) of the viscous field and 2.5 ± 1.91
90
0.0
5 CCW
0
Elastic
45
at the highest load of the elastic field.
–0.5
–3
CW
0
0
–1.0
–6
Therefore, the force fields had three effects
0.0
2.1
4.2
0 90 180 270 360 0 90 180 270 360
0 90 180 270 360
0.0
2.1
4.2
Force
(N)
Shift
(°)
Force (N)
Position (°)
Position (°)
on the X and Y hand forces: (i) the amplitudes
Y-force
scaled proportionally with the force load,
b
Cross-correlation
Shift
CCW
CW
DOM
(ii) the spatial tuning profiles for the two
6
180
1.0
10
135
3
0.5
tracking directions were out of phase under
90
5 CW
0
0.0
Viscous
the viscous field, and (iii) the spatial tuning
–3
45
–0.5
CCW
0
–6
0
–1.0
profiles for the two tracking directions were in
1.05
N
0.00 N
2.10 N
1.0
6
180
10
4.20 N
3.15 N
phase under the elastic field. In contrast, the
3
0.5
135
magnitude and type of force field had no
0.0
0
90
5
Elastic
CW
–0.5
45
–3
significant effect on the hand path or speed.
CCW
0
–6
0
–1.0
0.0
2.1
4.2
0
90
180
270
360
0
90
180
270
360
0.0
2.1
4.2
0
90
180
270
360
These results allowed us to evaluate the effects
Force (N)
Force (N)
Position (°)
Position (°)
Shift (o)
of increasing force load and altering the forcefield type on the electromyographic (EMG) Figure 2 Force applied by the monkey, measured at the handle. (a) X coordinate of the hand force for
activity and neural data, independent of CCW (left) and CW (right) tracking, under viscous (top) and elastic (bottom) force fields. Each trace is
the average of 20 repetitions (5 repetitions at each start angle, aligned to match tracking position). Also
the kinematics.
Force (N)
© 2006 Nature Publishing Group http://www.nature.com/natureneuroscience
a
shown are plots of DOM (peak-to-peak of the force profiles) as a function of force load, cross-correlations
between force profiles of CCW and CW tracking for all loads of both force fields, and the shift in the
position of maximal force as a function of force type and load obtained from the maximum of the crosscorrelation. (b) Similar plots for the Y coordinate of hand force. The error bars in this and all the figures
represent mean and s.d. of the corresponding values obtained from four different start angles (Methods).
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Elastic
90 180 270 360 0
Position (°)
90 180 270 360
Position (°)
Latissimus dorsi
CCW
CW
0.0
0.00 N
3.15 N
1.0
1.05 N
4.20 N
2.10 N
0.5
0.5
CW
0
90 180 270 360 0
Position (°)
90 180 270 360
Position (°)
0.0
2.1
4.2
Force (N)
0.5
CCW
180
135
90
45
0
1.0
0.0
2.1
4.2
Force (N)
180
135
90
45
0
CW
0.0
0.0
CW
2.1
4.2
Force (N)
Shift
0.0
AVG
CCW
CW
0.0
CCW
CW
0.5
CCW
0.0
0.5
1.0
1.0
0.5
1.0
0.0
CCW
0.0
180
135
90
45
0
CW
0.0
2.1
4.2
Force (N)
DOM
1.0
0.5
0.0
CCW
0.0
Normalized units
1.0
Viscous
CW
0.0
0
b
0.5
CCW
Shift (°)
0.5
1.0
0.5
Shift (°)
2.10 N
CCW
Shift (°)
1.0
1.05 N
4.20 N
0.0
CW
180
135
90
45
0
Shift (°)
0.0
0.5
AVG
1.0
Normalized units
0.5
0.00 N
3.15 N
DOM
1.0
0.0
Normalized units
2.1
4.2
Force (N)
Shift
0.0
2.1
4.2
Force (N)
Figure 3 Example EMG data for two muscles. (a) EMG activity of the flexor carpi radialis under different loads of viscous (top) and elastic (bottom) force fields
for CCW and CW tracking directions. Each trace is the average of 20 repetitions, full-wave rectified and normalized to the maximum activity of the muscle
during the recording session. The DOM increased with a slope of 0.120 ± 0.032 nu N–1 (nu ¼ normalized units) across the two tracking directions and the
two force fields (R2 ¼ 0.85 ± 0.03). The average EMG activity also increased with a slope of 0.050 ± 0.013 nu N–1 (R2 ¼ 0.94 ± 0.03). The CCW-CW shift
was 50.0 ± 4.91 at the null force and increased to 133.5 ± 5.31 at the highest load of the viscous force field (4.2 N) and decreased to 34.25 ± 7.01 at the
highest load of the elastic force field. (b) Similar EMG data for latissimus dorsi. The slopes were 0.124 ± 0.035 nu N–1 (R2 ¼ 0.92 ± 0.02) and 0.051 ±
0.008 nu N–1 (R2 ¼ 0.93 ± 0.03) for DOM and the average EMG activity (AVG), respectively. The shift was 55.0 ± 5.81 under the null condition; this
increased to 117.5 ± 12.61 under the viscous field and decreased to 22.5 ± 5.01 under the elastic force field.
dorsi). All muscles exhibited similar changes in their position and
movement-direction tuning. Increasing the force load resulted in a shift
of 150.6 ± 18.11 for the highest load of viscous field (4.2 N) and 27.0 ±
10.01 for the highest load of elastic field (Fig. 4, shift). Therefore, the
dependence of the muscle activity on the direction of movement was
accentuated with the viscous field and the position dependence was
accentuated with the elastic field.
was present during cue and track periods, for 86.8% of cells (n ¼ 144)
the DOM during the cue period was not significantly different from
control (ANOVA, P 4 0.05). In contrast, for all task-related Purkinje
cells, the track period DOM was different from the hold period DOM.
In addition, for all but one of the cells with significant cue period
modulation (n ¼ 22), the DOM during the cue period was significantly
less than that during the track period (ANOVA, P o 0.001). Therefore,
the simple spike modulation during the track period is coupled to the
arm movement and not to the visual stimulus26.
The task-related Purkinje cells were highly modulated during the
track period. The DOM was 63.2 ± 32.7% of the average baseline firing
of 60.4 ± 36.1 spikes s–1. The simple-spike firing of 151 (91.0%) of the
Simple-spike discharge
We recorded the simple-spike firing of 229 Purkinje cells (160 in
monkey H, 69 in monkey N) during the performance of the task.
Histology in monkey H confirmed that the recordings were primarily in
the intermediate and neighboring lateral zones
of lobules IV–VI and the cells recorded in
DOM
AVG
Shift
monkey N were targeted to the same region.
a
b 1.0
c 180
1.0
Of the 229 cells, we selected 166 (117 in
135
0.5
0.5
Viscous
90
monkey H, 49 in N) as being task-related
45
(that is, track-period DOM or average firing
0.0
0.0
0
was significantly different from hold-period
1.0
180
1.0
firing; ANOVA, a ¼ 0.05); these consisted of
135
0.5
90
Elastic
0.5
92 cells studied under the viscous field, 21
45
under the elastic field and 53 under both fields.
0.0
0.0
0
0.0 1.05 2.1 3.15 4.2
0.0 1.05 2.1 3.15 4.2
0.0 1.05 2.1 3.15 4.2
To test whether the observed simple-spike
Force (N)
Force (N)
Force (N)
modulation during the track period was due
to target motion rather than the arm move- Figure 4 Muscle population data. (a–c) DOM, average activity and CCW-CW shift of EMG activity for all
ment, we compared the DOM during the cue muscles under viscous and elastic force fields. The DOM and average EMG activity for all muscles
period to that during the hold period increased with slopes of 0.113 ± 0.053 nu N–1 (R2 ¼ 0.71 ± 0.21) and 0.049 ± 0.033 nu N–1
(control). Although the same target motion (R2 ¼ 0.79 ± 0.17), respectively.
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Shift (°)
Normalized units
Normalized units
© 2006 Nature Publishing Group http://www.nature.com/natureneuroscience
Elastic
Normalized units
Viscous
CW
Normalized units
Flexor carpi radialis
CCW
1.0
Normalized units
a
[
NOVEMBER 2006 NATURE NEUROSCIENCE
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100
0
CCW
CW
–1
75
50
25
Elastic
50
25
1.05 N
4.20 N
–1
0.0
DOM
CW
25
0
90 180 270 360 0
Position (°)
180
135
90
45
0
2.1
4.2
Force (N)
0.0
AVG
75
CCW
50
CCW
25
CW
180
135
90
45
0
180
135
90
45
0
0
50
25
90 180 270 360
Position (°)
75
–1
75
50
0
CW
0
90
45
0
2.1
4.2
Force (N)
Shift
2.10 N
–1
0.00 N
3.15 N
75
Shift (°)
50
2.1
4.2
Force (N)
75
CCW
100
0
spikes s
–1
0
CW
0.0
90 180 270 360
Position (°)
spikes s
Viscous
spikes s
–1
b
90 180 270 360 0
Position (°)
CCW
50
0
150
–1
–1
50
0
150
spikes s
100
CCW
50
Shift (°)
2.10 N
0
spikes s
CCW
CW
*
50
CCW
25
CW
0
0
0.0
2.1
4.2
Force (N)
0.0
2.1
4.2
Force (N)
0.0
2.1
4.2
Force (N)
Figure 5 Simple spike firing of two example Purkinje cells. (a) Simple-spike firing of a Purkinje cell recorded under both viscous and elastic force fields from
monkey N. The firing histograms, DOM, average firing and CCW-CW shifts were generated using the same conventions as the previous figures. There were no
significant changes in the DOM, average firing or CCW-CW shift as function of the force load. (b) Simple-spike firing of another Purkinje cell recorded under
both force fields from monkey H. The average firing decreased under the elastic force field during CCW tracking from 41.1 ± 4.6 spikes s–1 (null field) to
32.9 ± 2.1 spikes s–1 (4.2 N) with a slope of –1.96 spikes s–1 per N (R2 ¼ 0.59) and is indicated by an asterisk.
166 task-related cells did not show a change in any of the three
measures as a function of force load. The simple-spike discharge of
an example cell shows a combination of position and movementdirection tuning (Fig. 5a). For either direction of tracking under the
viscous or elastic fields, the DOM, average firing and position of
maximal activity did not change significantly as the load increased.
Of the 15 cells with a significant force effect (8 from monkey H,
7 from N), 14 showed a significant change in only one of the three
measures; the 15th showed a significant change in two measures. The
sample Purkinje cell (Fig. 5b) exhibited one of the larger significant
changes in the average firing (AVG, CCW, elastic) due to the force
loads. However, the DOM and CCW-CW shift did not change
significantly as a function of the load, nor did the average firing change
significantly during CW tracking or under the viscous field. The DOM
significantly changed for eight cells (Fig. 6a; seven increased, one
decreased). For four other Purkinje cells, the average firing significantly
changed (two increased, two decreased). The CCW-CW shift changed
significantly for four cells (three increased, one decreased).
Therefore, the simple-spike firing was affected by the force load for
15 of 166 cells, and the changes were generally small and isolated to a
single aspect of the discharge and to only one direction of tracking.
Figure 6 Population data for Purkinje cells. (a) Number of cells with a
significant increase (+) or decrease (), or no significant change in the DOM,
average activity and CCW-CW shift for viscous and elastic force fields. The
cells recorded under both force fields are counted both under the viscous
and elastic in the plots. For the cells with a significant force effect, the
absolute value of the regression slope was 0.055 ± 0.025 nu N–1 (R2 ¼
0.52 ± 0.12) for the DOM and 0.026 ± 0.005 nu N–1 (R2 ¼ 0.62 ± 0.09)
for the average activity. (b) Map of the penetration sites for the reported
cells for monkey H, showing the locations at which viscous, elastic and both
fields were studied. The diamonds are the penetrations in which a cell
had a significant force effect.
NATURE NEUROSCIENCE VOLUME 9
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Finally, the cells with force effects on the simple-spike firing did not
show any spatial clustering in monkey H (Fig. 6b). Similarly, for
monkey N, on the basis of chamber-recording coordinates, there was
no evidence of clustering of the seven cells that exhibited significant
force effects (data not shown).
The next analysis focused on the position of maximal firing/EMG
activity. The simple-spike discharge during tracking under all loads
exhibited tuning to both position of the hand and direction of movement26. This was evident in the shift in the position of maximal firing as
a function of tracking direction (Figs. 3 and 5) and was quantified
based on the peak of the cross-correlation. The shifts for the simplespike discharge were distributed widely around the circle (Fig. 7a,b)
and did not show a specific preference under either force field (Rayleigh
test, P 4 0.05). For the 53 Purkinje cells studied under both force fields
(gray lines in Fig. 7a,b), the mixture of positional and directional
a
Number of
cells
© 2006 Nature Publishing Group http://www.nature.com/natureneuroscience
Elastic
spikes s
–1
150
1.05 N
4.20 N
CW
100
Shift
180
135
Shift (°)
0
0
0.00 N
3.15 N
CCW
50
CW
Shift (°)
100
spikes s
50
AVG
150
–1
100
DOM
150
spikes s
spikes s
Viscous
spikes s
–1
–1
CW
spikes s
CCW
150
spikes s
a
b
DOM
150
50
0
5 2
+
50
No
change
0
Shift
150
100
100
0 1
–
AVG
150
Viscous
Elastic
100
2 1
1 1
+
–
50
No
change
0
2 1
1 1
+
–
No
change
PF
Viscous Elastic Both
5 mm
Cells with significant force modulation
Right
1407
a
b
Viscous
90
Cells
c
Elastic
90
60
120
120
60
120
90
60
30
150
150
30
150
30
0°
180
210
180
0
0 180
CCW – CW shift (°)
d
90
120
Muscles
tis
us
sim
Figure 7 Distribution of shifts in the position of
maximal activity for the CCW versus CW direction
across population of cells and muscles. (a,b) The
CCW-CW shift for the highest load of viscous and
elastic force field for all Purkinje cells. Gray lines,
the 53 cells studied under both fields.
(c) Differences in the CCW-CW shift of these
53 Purkinje cells between the highest loads of the
two force fields. (d–f) Similar plots of the CCWCW shift for the muscles. The muscles are listed
in order of increasing shift (that is, for the viscous
field, the shift for the latissimus dorsi is 122.51
and the shift for the spinodeltoid is 166.11).
La
150
rs
do
i
Spin
ode
lt
e
Latissimus dorsi
Biceps
Cleidodeltoid
Flexor carpi ulnaris
Flexor carpi radialis
Extensor carpi radialis
Triceps
Brachioradialis
Acromiodeltoid
Extensor carpi radialis
Pectoralis
Spinodeltoid
Brachioradialis
Pectoralis
90
Extensor carpi ulnaris
Biceps
Extensor carpi radialis
Acromiodeltoid
Spinodeltoid
Flexor carpi radialis
Flexor carpi ulnaris
Triceps
Cleidodeltoid
Latissimus dorsi
330
240
CCW – CW shift (°)
f
120
60
270
90
300
60
30
150
La
tis
us
sim
d
i
ors
30
180
lis
radia
chio
Bra
0°
210
330
oid
tuning was also not dependent on the field
0
180
0 180
240
300
270
CCW – CW shift (°)
CCW – CW shift (°)
type, with an average shift between the two
force fields of 3.6 ± 23.41 at the highest force
load (Fig. 7c). This was in contrast with the
EMG activity: the muscles had distinct preferences for each force-field DISCUSSION
type (Fig. 7d,e) and had an average shift between the two force fields of The main observation of this study is that the simple-spike discharge of
122.6 ± 15.71 at the highest force load (Fig. 7f). Moreover, for 97.6% of lobule IV–VI Purkinje cells is little affected by external force fields or
the 166 Purkinje cells, the shift between the firing profiles of the two loads for this circular tracking task. For 91% of Purkinje cells, the
average firing, DOM and spatial tuning did not change significantly
tracking directions did not change significantly across force loads.
The above results were for the task-related Purkinje cells; the selection with increasing force load of either field type. In contrast, the DOM
of these cells was based on the modulation during the track period of the X and Y hand forces and the arm EMG activity increased
under the null field. This raises the possibility that the 63 neurons not markedly with increasing the force load. Similarly, the average EMG
related to the task under the null field became modulated with the
external force fields and provided information on the force fields or
CCW
CW
a 80
0.00 N
loads. We tested for changes in DOM and average firing as a function of
60
force in these cells. None of these cells showed any significant effect as a
40
function of force (ANOVA, P 4 0.05).
20
Modeling results
The last analysis used to test for force effects was based on modeling the
simple-spike discharge using a von Mises tuning model, fitting the
simple-spike firing with a highly flexible model both with and without
force terms. The goal was to use this additional analysis to determine if
and how the DOM and average firing were affected by the force. Fitting
the models to the simple-spike histograms showed that models with
and without force information captured almost equal amounts of the
variability in the firing (Fig. 8). For the example Purkinje cell, there was
only a small increase in the coefficient of determination (R2) even
though three force terms were added to the model (Fig. 8a). Across the
population of Purkinje cells, the results of modeling were similar and
there was no significant difference in the adjusted R2 with or without
the force terms for the viscous or elastic fields (Student’s t-test, P 4
0.05, Fig. 8b). These results confirm that the original analysis based on
DOM, average firing and shift in the position of maximal firing did not
miss any major force modulation.
0
80
1.05 N
60
40
20
0
80
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2.10 N
60
40
20
0
80
3.15 N
60
40
20
0
80
No force
Force
4.20 N
60
40
Figure 8 Modeling the simple-spike firing. (a) The simple-spike firing of a
Purkinje cell recorded under the elastic field was modeled using two bimodal
von Mises models (Methods), one with force parameters (solid line) and one
without force parameters (dotted line). The firing for each tracking direction
was fitted separately. The adjusted R 2s for the no-force model were 0.79
(CCW) and 0.88 (CW), compared to 0.81 (CCW) and 0.91 (CW) for the force
model. (b) The improvement to the adjusted R 2s by adding the force terms
was small across the population of cells. For the model with no force terms,
the adjusted R2 was 0.60 ± 0.17 for the recordings under viscous force field
and 0.56 ± 0.18 for the recordings under elastic force field. Adding the force
terms slightly improved the fit to an adjusted R2 of 0.65 ± 0.16 for the
viscous force field and 0.61 ± 0.17 for the elastic force field.
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activity increased for all muscles with load. Moreover, the positions of
maximum force and EMG activity between CCW and CW tracking
became out of phase under viscous loads and in phase under elastic
loads, consistent with the movement-direction and positional dependence of these fields. In contrast, the type of force field and the
magnitude of the load had almost no effect on the positional and
directional tuning of the Purkinje cells. Together these observations
lead to the conclusion that this population of Purkinje cells does
not encode forces, nor is the simple spike activity coupled to arm
muscle activity.
Implications for internal models
It has been hypothesized that Purkinje cells are involved in an inverse
dynamics model, providing signals that specify the dynamics of the arm
movement5–7,12. This hypothesis also predicts that Purkinje cell activity
is strongly coupled to the arm EMG activity7,11. The lack of significant
effects of force-field type or load on the simple-spike discharge for the
vast majority of Purkinje cells and the dissociation between the changes
in arm EMG activity and the simple-spike discharge are incompatible
with the hypothesis that these Purkinje cells are the output of an inverse
dynamics model of the arm2,3,5,6,18.
The results of this study can be used to reinterpret previous eye
movement findings that the simple-spike discharge encodes for an
inverse dynamics model5,6. In those studies it was argued that the
observed position, velocity and acceleration signals of flocculus/paraflocculus Purkinje cells during the ocular following response represent
dynamics as opposed to kinematics. If instead those signals were
interpreted to represent the kinematics of the eye, this would be
consistent with the position, movement-direction and speed modulation observed in this and other studies of manual tracking26,27, as well
as in studies of smooth pursuit eye movements28.
We are unaware of previous studies in which Purkinje cell activity in
the awake monkey was evaluated under various loads and force fields.
More information is available on Purkinje cell modulation in relation
to isometric prehensile or grip forces. For example, approximately 14%
of Purkinje cells modulate with grip force or its derivatives during
thumb and forefinger prehension29,30, and approximately 25% modulate with force during grasp31. However, in the study described in
ref. 31, in which the grasp forces were systematically varied, the overall
effect was small (less than 3 spikes s–1 N–1). It remains to be determined
whether this level of force-related modulation is consistent with an
inverse dynamics model of the hand.
There are two limitations to the present findings. First, the recordings were performed in highly trained monkeys that had mastered the
force fields and loads. Accordingly, the results address the storage of an
inverse dynamics model and not the question of whether these Purkinje
cells participate transiently in the acquisition of an inverse dynamics
model13,15,17,20. Second, the conclusions are restricted to Purkinje cells
within the recorded areas, primarily lateral and intermediate zones in
lobules IV–VI (Fig. 6b), a region known to contain Purkinje cells that
are highly modulated during limb movements26,27,32,33. It is possible
that Purkinje cells in other regions are modulated in relation to force
and/or are coupled to EMG activity of the arm. One possible target is
more posterolateral regions34. However, Purkinje cells in more posterolateral regions exhibit modulation to visual inputs and oculomotor
behaviors in addition to limb movements35–37, making these regions
more likely to be involved in higher-order aspects of visuomotor
control. Other motor structures, particularly the motor cortical areas
in which force coding and/or coupling to EMG activity has been
observed may be better candidates than the cerebellum for the site of an
inverse dynamic model of the limbs14–16,38–40.
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From the perspective of internal models, we consider two possibilities for how this kinematic representation could be used. First, this
kinematic signal could be the input to an inverse dynamics model,
downstream of the Purkinje cells. One potential site for the transformation of kinematics to limb forces/torques is the cerebellar nuclei.
However, the reports of nuclear neurons being modulated in relation to
force or being coupled to EMG are variable41–44. Second, the kinematic
properties of the simple-spike discharge are also consistent with the
output of a forward internal model that predicts the movement
consequences from the motor commands and the current state of the
arm2,3,18. Although both these possibilities need further testing, the
absence of force/EMG signal and the presence of predominantly
kinematic signals clarifies the roles Purkinje cells do and do not have
in internal models.
Conclusion
The present and previous findings26 demonstrate that Purkinje cell
simple-spike discharge is tuned to the kinematics of the arm movement
but not to arm dynamics. The behavior of these Purkinje cells is best
described as being modulated in relation to the geometry of the
movement, specifying combinations of hand position and movement
direction. When combined with their speed-related scaling properties,
Purkinje cell simple-spike discharge provides a representation of the
spatial and temporal features of arm movements26. Previous studies
show that the discharge of Purkinje cells in similar tracking tasks
leads arm kinematics by approximately 100 ms (refs. 26,27), consistent
with the cerebellum’s participation in planning/generating the
desired trajectory.
METHODS
Behavioral task. Animal care and experimentation were conducted in accordance with US National Institutes of Health guidelines and were approved by
the Institutional Animal Care and Use Committee of the University of
Minnesota. Two monkeys (H and N, female, Macaca mulatta, 6–7 kg)
were trained to move a two-jointed, robotic manipulandum (InMotion2,
Interactive Motion) in the horizontal plane to control a cursor on a vertically
mounted computer screen in front of them (Fig. 1a). The gain was set to unity
so that 1 cm of hand movement resulted in 1 cm of cursor movement. The task
required interception of a circularly moving target from a centrally located
‘hold’ target and subsequent visually guided pursuit of the target for one
rotation (Fig. 1b).
Except for control trials with no external force (null force), one of two
external force fields was applied to the monkey’s hand by the manipulandum45.
The first was a velocity-dependent viscous force field opposing the movement.
The second was a position-dependent elastic force field directed toward the
center. Five force magnitudes were studied for each field type with the same
range (0–4.2 N, in 1.05 N increments). For most of the recordings from
monkey H, only the viscous (118 of 160 cells) or elastic (29 of 160 cells) force
field was tested. In the remaining recordings from monkey H (13 of 160 cells)
and all recordings from monkey N (69 cells), we tested the effects of both fields,
using randomly intermixed trials. Task parameters (load, force-field type, start
angle and tracking direction) were independently varied in a randomized,
blocked fashion. For each combination of task parameters, we obtained five
repetitions for a total of 200 trials per recording session for a single force field
(5 loads 4 start angles 2 directions 5 repetitions). During sessions under
both force fields, we used nine force loads (null and four force magnitudes at
each force-field type), totaling 360 trials per session.
Behavioral, neural and EMG data acquisition. We used the robot’s optical
encoders to acquire the hand position at 200 samples s–1; this was used to drive
the cursor position on the monitor and to determine the hand velocity/speed
by numerical differentiation26. We also acquired the force applied by the
monkey to the robot at 200 samples s–1, using a six-degrees-of-freedom
transducer (ATI) at the handle.
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The recording chamber was placed over the parietal cortex ipsilateral to the
tracking arm (left for monkey H and right for monkey N), using antiseptic
conditions and full surgical anesthesia26,27. The chamber was stereotaxically
positioned to target the electrode recordings in the intermediate and neighboring lateral zones of lobules IV–VI where arm-related Purkinje cells have been
reported32,33. We used one of three types of microelectrodes to record from
Purkinje cells extracellularly: parylene-coated tungsten (10–15 MO, FHC),
four-core quartz-platinum/tungsten (tetrode, 0.5–1.5 MO, Thomas Recording),
or single core electrodes with same specifications as the tetrodes. Purkinje cells
were identified by the presence of complex spikes. At each recording session,
two electrodes were independently driven into the cerebellum using a hydraulic
positioning system (Narishige). We used conventional techniques to amplify
the spike waveforms33. The discrimination of the simple spikes was performed
online using the Multiple Spike Detector system (Alpha-Omega Engineering)
and offline using MClust software (A.D. Redish, University of Minnesota). The
resulting spike train data were digitized and stored at 1 kHz. The raw
waveforms were also recorded at 32 kHz and used to verify discrimination
or cell identification when needed.
We obtained bipolar intramuscular EMG recordings from 12 different
shoulder, elbow and wrist muscles during several experimental sessions from
both monkeys (Fig. 7d,e). The EMG signals were band-pass filtered online
(0.1–3 kHz) and amplified, then digitized and stored at 6 kHz. The EMG data
were then digitally full-wave rectified and normalized by the maximal activity
of each muscle during each session. The latter permitted a direct comparison of
the activity among muscles.
Upon conclusion of the recordings in monkey H, electrolytic lesions were
made at selected chamber coordinates. The monkey was killed and perfused,
the cerebellum removed, processed for histology, and then sectioned26,27. The
lesions and electrode tracks were identified to establish recording locations. The
recordings in monkey N were targeted to the same region of the cerebellum
using the same stereotaxic coordinates.
Trial averaging and kinematics and force data analysis. For each recording
session, we averaged kinematics, force, spike train and EMG data from the track
period over similar trials (n ¼ 5) and collapsed these data into 125-ms bins
(equal to ten degrees of tracking), resulting in a total of 36 bins for the track
period. Depending on the start angle and direction of tracking, the track period
could start and end at different positions around the circle. Therefore, all data
were shifted and aligned to begin at 01 and continue CCW to 3601. In our
previous study, we demonstrated that the start angle did not affect the task
kinematics or the neural firing26. In this study, task dynamics was also not
affected by the start angle (Results). Therefore, trials with the same force and
direction conditions but different start angles were considered similar and
either used as repetitions for the analysis and statistical testing, or averaged to
generate tuning plots and to fit the models as described later (n ¼ 20 for each
force-direction condition).
We evaluated the hand paths, speed profiles and forces (X and Y) for
differences across force-field types and loads, tracking directions and start
angles (four-way ANOVA, a ¼ 0.05). We used the average radius of the tracking
circle to test for differences in the hand paths and the peak-to-peak difference
of the force profiles (DOM) to test for differences in the hand force. If the
ANOVA revealed a significant difference for one of the dependent variables at
different force loads, then we conducted a post-hoc analysis to test for changes
as functions of force load. This was done by fitting a linear regression model to
the data determining the slope of the fit and the significance (F-test, a ¼ 0.05).
We evaluated the shifts in the position of maximal forces between CCW and
CW tracking, in a similar manner to that used for the simple spike and EMG
data (described below).
activity, DOM and the shift in the position of maximal activity between CCW
and CW tracking (CCW-CW shift). The simple spike firing and EMG data for
the track period (36 bins for the 3601 of tracking) was smoothed using a 3-bin
sliding window. The average activity was simply the mean over the 3601 of
tracking. The DOM was defined as the difference between the maximum and
minimum of the smoothed data. The average firing and DOM were obtained
for each force-direction condition.
The CCW-CW shift was based on a previous observation that the position of
maximal firing and maximal EMG activity depended on tracking direction26.
To determine the shift, we performed a circular cross-correlation analysis on
the data from the two tracking directions. The cross-correlations were calculated over the angular positions (±1801), the peak in the cross-correlogram
determined, and the shift associated with the peak used as a measure of the shift
in the position of maximal simple-spike firing or EMG activity between the two
tracking directions. The absolute value of the shifts was used in the analysis.
This is called the ‘angular distance’, the smaller angle between the two directions
(between 0 and 1801). Therefore, the CCW-CW shift values are not circular
variables and were treated using linear statistics46. The shifts were obtained at
each force load. We used an identical analysis to determine the shift in the
X and Y hand forces.
We performed an ANOVA to examine if any of the three measures differed
significantly (a ¼ 0.05) with the force load, using data from different start
angles as repetitions. If a significant difference was observed, then we used a
post-hoc analysis based on a linear regression to determine whether the relationship was linear and to determine the slope. For the Purkinje cells recorded under
both types of force fields, this statistical testing was performed separately for the
three measures under each force field. Therefore, for these cells, we used twice as
many statistical tests compared to Purkinje cells recorded under a single force
field, and the significance level was corrected accordingly (a ¼ 0.025).
Modeling. Finally, the data was modeled using two bimodal von Mises
distributions46. The goal was not to develop a physiologically relevant
model of the simple spike firing, but instead to capture as much as
possible of the profile of the simple spike firing during the track period,
including any nonlinearities26,47. The first model included seven parameters
to capture the two modes and the positional/directional tuning:
f ¼ b0 + b1 ek1 cosðym1 Þ + b2 ek2 cosðym2 Þ The parameter b0 defines a baseline
firing rate, b1 and b2 scale the tuning for each mode, and k1 and k2 determine
the concentration of the von Mises distribution. The variable y is the position
along the circle and m1 and m2 are the positions of maximal response for the
two modes. The second model incorporated force (F) by adding an additive
force term to the baseline firing and force multiplicatives to the directional
tuning terms:
f ¼ b0 + b1 F + ðb2 + b3 FÞek1 cosðym1 Þ + ðb4 + b5 FÞek2 cosðym2 Þ
The simple spike data across the five force loads were fit to the model at each
direction of tracking and the adjusted R2 values were compared. For the
Purkinje cells recorded under both types of force fields, the data from each
force field was modeled separately. The findings demonstrated that the CCWCW shift of the simple spike modulation did not change as a function of force
load (Results); therefore, the assumption in this model that the preferred
positions (m’s) do not rotate with force was justified.
ACKNOWLEDGMENTS
We thank M. McPhee for assistance with graphics and S. Allison for assistance
with programming. This work was supported in part by the US National
Institutes of Health (grant RO1-NS-18338) and a grant from the Minnesota
Medical Foundation.
Simple spike and EMG analysis. We analyzed the simple spike firing during
the cue period to determine whether any modulation was due to the visual
component of the task. As for the track period, the cue period data were
averaged over the four start angles. Therefore, the firing modulation over the
entire 3601 movement of the cue was constructed and compared to the
modulation during the track period.
To examine the effects of the external force fields on the simple-spike firing
and EMG activity, we analyzed three aspects of the track period data: average
AUTHOR CONTRIBUTIONS
S.P. and A.V.R. conducted the experiments and performed the analyses, and also
participated in the design of the experiments. All authors contributed to
discussions of the data and to writing the paper. T.J.E. was instrumental in the
design of the experiments and supervised the project including experimentation,
data analysis and writing.
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COMPETING INTERESTS STATEMENT
The authors declare that they have no competing financial interests.
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reprintsandpermissions/
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