Purkinje Cells in Posterior Cerebellar Vermis
Encode Motion in an Inertial Reference Frame
Tatyana A. Yakusheva,1Aasef G. Shaikh,1Andrea M. Green,1,3Pablo M. Blazquez,2J. David Dickman,1
and Dora E. Angelaki1,*
1Department of Anatomy and Neurobiology
2Department of Otolaryngology
Washington University School of Medicine, St. Louis, MO 63110, USA
3Present address: De ´partement de Physiologie, Universite ´ de Montre ´al, Montre ´al, QC H3C 3J7, Canada.
The ability to orient and navigate through the
terrestrial environment represents a computa-
tional challenge common to all vertebrates. It
arises because motion sensors in the inner
ear, the otolith organs, and the semicircular
canals transduce self-motion in an egocentric
reference frame. As a result, vestibular afferent
information reaching the brain is inappropriate
for coding our own motion and orientation rela-
tive to the outside world. Here we show that
cerebellar cortical neuron activity in vermal
lobules 9 and 10 reflects the critical computa-
tions of transforming head-centered vestibular
afferent information into earth-referenced self-
motion and spatial orientation signals. Unlike
vestibular and deep cerebellar nuclei neurons,
where a mixture of responses was observed,
population that encodes inertial motion. They
carry the earth-horizontal component of a spa-
tially transformed and temporally integrated
rotation signal from the semicircular canals,
which is critical for computing head attitude,
thusisolating inertiallinear accelerationsduring
Orienting and navigating relative to the world, both of
which constitute fundamental tasks that we experience
daily, pose an important computational challenge: sen-
soryinformation (visual,vestibular, somatosensory) istyp-
ically encoded in a local (e.g., eye, head) reference frame.
Terrestrial life, however, depends on an allocentric (iner-
tial) reference frame that is often defined by the force of
gravity. As a result, a set of either implicit or explicit refer-
ence frame transformations is necessary for both spatial
perception and sensorimotor transformations. Coding of
space in allocentric coordinates has been suggested
(Dean and Platt, 2006; Fitzpatrick et al., 2006; Van Pelt
et al., 2005), yet the neural signature of these behavioral
observations has remained obscure.
Important sensory information about our motion and
orientation relative to the world arises from labyrinthine
receptors in the inner ear. However, interpretation of
cular canals and the otolith organs, faces two interdepen-
the ‘‘reference frame problem,’’ arises because vestibular
sensors are physically fixed in the head. Thus, duringrota-
tion primary semicircular canal afferents detect endo-
lymph fluid motion relative to the bony ducts, coding
angular velocity in a head-centered reference frame but
providing no information about how the head moves
relative to the outside world (Goldberg and Fernandez,
1975). For example, a horizontal (yaw) rotation in upright
orientation activates semicircular canal afferents similar
to a yaw rotation in supine orientation (Figure 1A). Yet
these two movements differ in inertial (earth-centered)
space. The second, referred to as the ‘‘linear acceleration
problem,’’ is due to a sensory ambiguity that arises be-
cause of physical laws (Einstein’s equivalence principle).
As a result, otolith afferents detect net linear acceleration
but cannot distinguish translational from gravitational
components (Figure 1B; Fernandez and Goldberg,
1976a). As a result, displacement to the right activates
otolith afferents similarly as a leftward tilt.
The brain thus faces the task of computing inertial
motion and spatial orientation using multimodal integra-
tion. In general, visual, somatosensory and efference
copies of the motor command signals can provide useful
cues for supplementing vestibular afferent activity during
navigation. However, even in the absence of these extra-
vestibular cues (e.g., during passive motion in darkness),
a solution to both of these computational problems can
be achieved by combining signals from the two vestibular
sensors (see the Supplemental Data available with this
article online; see also Angelaki et al., 1999; Glasauer
and Merfeld, 1997; Green and Angelaki, 2004; Green
et al., 2005; Merfeld and Zupan, 2002; Zupan et al.,
2002). Recent neurophysiological studies have suggested
that labyrinthine-receiving areas in the vestibular (VN) and
cerebellar (fastigial, FN) nuclei carry convergent otolith
Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc. 973
and semicircular canal signals that could provide a
population solution to the inertial motion detection prob-
lem (Angelaki et al., 2004; Green et al., 2005; Shaikh
et al., 2005a). However, little is currently known about
where this decoding takes place or whether and how
spatially transformed signals are represented in the firing
rates of individual neurons.
Here we explore the hypothesis that inertial motion is
explicitly coded by single Purkinje cells in the cortex of
the nodulus (lobule 10) and uvula (lobule 9; collectively
VN (Barmack, 2003; Naito et al., 1995; Newlands et al.,
2003). We report that, unlike vestibular and cerebellar
nuclei neurons, where a mixture of responses was ob-
lation that encodes inertial motion. Consistent with recent
computational model predictions (Green and Angelaki,
2004),wealsoshowthatNUPurkinje cellscarry aspatially
the semicircular canals that is used to compute head
attitude (i.e., angular position in world coordinates). We
conclude that the output of the two most posterior lobules
to both computational problems (Figures 1A and 1B) nec-
essary for allocentric orientation and inertial navigation.
Computational Solution to Inertial Motion Detection
Several studies have emphasized that a unique mathe-
matical solution to the inertial motion detection problem
can exist using exclusively vestibular afferent information
(Angelaki et al., 1999; Green and Angelaki, 2003, 2004;
Green et al., 2005; Glasauer and Merfeld, 1997; Merfeld,
1995; Merfeld and Zupan, 2002; Mergner and Glasauer,
1999; Zupan et al., 2002). The mathematical solution,
schematized in Figure 1C, consists of two interdependent
steps (see Supplemental Data for details). First, rotational
signals from the semicircular canals (u, coded in head-
centered coordinates) must be processed by a gravity
signal to construct an estimate of angular velocity in
earth-centered coordinates (Figure 1C, dashed black
arrow). Such an interaction can be used to decompose
angular velocity into two spatially defined components:
an earth-vertical (i.e., parallel to gravity) component,
uEV, and an earth-horizontal (perpendicular to gravity)
component, uEH(Figure 1C, solid gray arrows). Impor-
tantly, only the latter, uEH, signals a change of orientation
relative to gravity. As a result, temporal integration of uEH
(!uEH) can yield an estimate of spatial attitude or ‘‘tilt’’
(Figure 1C, dashed gray arrow). In a second computa-
tional step this tilt signal, !uEH, can be combined with
the linear acceleration component that is due to transla-
tion, t (Figure 1C, solid black arrows). Notice that the com-
igation are not independent, but intimately coupled, as
rotational velocity cannot be interpreted in a spatial frame
without knowledge of head orientation relative to gravity.
Similarly, parsing net linear acceleration into tilt (gravita-
tional) and translational components requires knowledge
about the integral of rotational velocity in an earth-
centered reference frame (Green and Angelaki, 2004).
Here wehave characterized the simple spike responses
of NU Purkinje cells during rotational and/or translational
motion in darkness to test the hypothesis that they repre-
sent the output of the computational steps illustrated in
kinje cells receive signals from both types of vestibular
sensors, such that their firing rates selectively encode
inertial (translational) motion (t). The schematic diagram
of Figure 1C postulates that, for coding translation, NU
Purkinje cells must carry not only an otolith-driven signal
(a), but also a spatially and temporally transformed semi-
circular canal signal (!uEH). We have organized the results
into three sections, testing each of the following hypothe-
ses: (1) NU Purkinje cells encode translation (rather than
net linear acceleration like otolith afferents; Fernandez
cular canal-driven signal that is spatially transformed to
reflect solely the earth-horizontal component of rotation
Figure 1. Schematics Illustrating the ‘‘Reference Frame’’ and
‘‘Linear Acceleration’’ Problems, along with the Proposed
(A) The ‘‘Reference frame’’ problem is illustrated by an example of two
yaw rotations that are identical in head coordinates but differ in earth-
centered coordinates. Yaw rotations in upright and supine orientations
differ relative to the direction of gravity (gs, defining here the earth ref-
erence frame), yet elicit identical semicircular canal afferent responses
that encode rotation, u, in head-centered coordinates.
(B) The ‘‘Linear acceleration’’ problem is described by schematizing
that hair cells and otolith afferents encode net linear acceleration, a,
thus respond identically to either translational, t, or gravitational, g,
(C) Proposed computational solution, schematized as two steps (for
details about the underlying mathematics, see Supplemental Data).
To solve the ‘‘Reference frame’’ problem, neural estimates of g must
be used by the brain to decompose the head-fixed canal activation,
u, into earth-vertical (uEV, parallel to gravity) and earth-horizontal
eration’’ problem, a change in angular orientation can be computed by
temporal integration of uEH. This signal (!uEH) can then be combined
with net linear acceleration from otolith afferents to extract translation.
974 Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc.
Cerebellum Detects Inertial Motion
(i.e., that which changes head orientation relative to grav-
ity); and (3) this canal-driven, spatially transformed signal
hasalsobeen temporally integrated,thuscoding headpo-
sition relative to gravity (rather than rotational velocity, as
do semicircular canal afferents; Fernandez and Goldberg,
Purkinje Cells Encode Translation Rather Than Net
To test whether NU Purkinje cells selectively encode
translation and ignore changes in head orientation relative
to gravity (i.e., tilting movements that activate otolith
afferents similarly as translation), we recorded neural
activities during combinations of sinusoidal (0.5 Hz) tilt
(rotation) and translation stimuli (Angelaki et al., 1999,
2004). The peak amplitude of the sinusoidal tilt was
adjusted to produce a 0.5 Hz linear acceleration compo-
nent(dueto changesinheadorientation relativetogravity)
and translation motions were delivered either in isolation
(Figures 2A and 2B) or together (Figures 2C and 2D). To
facilitate interpretation of cell responses during tilt, trans-
lation, and their combinations, net linear acceleration (the
stimulus encoded by otolith afferents; Fernandez and
Goldberg, 1976a, 1976b) has also been plotted in Figures
2A–2D (‘‘Net Acceleration’’ traces).
Combination stimuli differed in terms of the relative
directions of tilt and translation (i.e., the relative phase of
the two sinusoidal movements). Whenever a head tilt to
the right occurred simultaneously with translation to the
left, gravitational and inertial accelerations were oppo-
sitely directed and, if appropriately matched in amplitude,
canceled out, and neither component was transduced to
the brain (Figure 2C; ‘‘Tilt ? Translation’’). This occurs
because during Tilt ? Translation net acceleration is
zero, and otolith afferents cease to modulate (Angelaki
(A–D) Instantaneous firing rate of a typical
Purkinje cell during Translation (A), Tilt (B),
Tilt ? Translation (C), and Tilt + Translation (D)
(0.5 Hz). Data are shown along four stimulation
axes (cartoon drawings), with the translation/
tilt position (bottom traces) being matched in
both amplitude and direction to elicit an identi-
cal net acceleration in the horizontal plane.
Straight black and curved gray arrows denote
translation and tilt axes of stimulation, respec-
tively. Vertical dotted lines mark the peak
(E and F) Summary of peak firing rate modula-
tion amplitude (E)and phase(F) as afunctionof
stimulus orientation, q. Data are shown sepa-
Tilt (open squares, dashed lines), Tilt ? Trans-
lation (filled triangles, solid lines), and Tilt +
Translation (open triangles, dashed lines).
Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc. 975
Cerebellum Detects Inertial Motion
et al., 2004). In contrast, whenever a head tilt to the right
occurred simultaneously with translation to the right, the
two accelerations summed, resulting in net linear acceler-
ation that was double that for each movement alone
(Figure 2D; ‘‘Tilt + Translation’’). Unlike otolith afferent
responses, a cell that selectively encodes translation
should modulate similarly during Translation, Tilt ? Trans-
lation, and Tilt + Translation, with little or no modulation
during Tilt (Figures 2A–2D, ‘‘Translation’’ traces).
The top rows of Figures 2A and 2B illustrate the simple
spike responses from a typical Purkinje cell. Each row
plots responsesduringmotion alongoneoffourdirections
spaced 45?apart, including lateral translation/roll tilt (q =
0?; 2nd row) and fore-aft translation/pitch tilt (q = 90?;
4th row). In contrast to otolith afferents (Figures 2A–2D,
‘‘Net Acceleration’’ traces), the amplitude of NU Purkinje
cell responses was large during translation but small
during tilt (compare peak-to-trough sinusoidal modulation
of firing rate in Figures 2A and 2B). Peak response modu-
lation during translation varied according to the cosine of
the angle between the motion direction and the cell’s
preferred direction (Figure 2E, solid squares and solid
line). Also, typical of cosine-like tuning, response phase
(i.e., timing of peak neural response relative to stimulus
peak) shifted ?180?for motion directions on either side
of the minimum response direction that occurred at q =
45?(Figure 2F, solid squares and solid line). In contrast,
tilt responses were small for all stimulus directions
(Figure 2E, open squares and dashed line) despite an
identical net linear acceleration stimulus to otolith affer-
and tilt were presented simultaneously: responses during
Tilt + Translation and Tilt ? Translation were similar to
those during Translation (Figures 2C–2F, compare trian-
gles versus solid squares).
Peak response amplitudes from 72 Purkinje cells have
been summarized in Figure 3. Responses to tilt were sig-
nificantly attenuated compared to those during translation
[repeated measures ANOVA, F(1,71) = 171, p << 0.001]. In
contrast to the ‘‘afferent-like’’ prediction (i.e., identical
responses to tilt and translation; Figure 3A, unity-slope
dashed line), most data fell close to the abscissa, as
expected for neurons selectively responsive to translation
(Figure 3A, ‘‘translation-coding’’ prediction; solid line
parallel to abscissa). Similar conclusions were also drawn
from the combined stimuli (Figures 3B and 3C). There was
a significant correlation between responses to the com-
bined stimuli and those during translation, with slopes
of 1.00 (95% confidence interval: [0.81, 1.24], r = 0.86,
p << 0.001) and 0.99 (95% confidence interval: [0.73,
1.19], r = 0.76, p << 0.001) for Tilt ? Translation and Tilt +
Translation, respectively. These slopes were thus indis-
tinguishable from unity (‘‘translation-coding’’ predictions;
Figures 3B and 3C, solid black lines) and different from
a slope of 0 or 2 (‘‘afferent-like’’ predictions; Figures 3B
and 3C, dashed lines). For all stimuli, the cells appeared
to selectively modulate in response to translation but
failed to modulate strongly during the tilt movement.
Of particular relevance is the fact that Purkinje cells
modulate during Tilt ? Translation, although primary oto-
lith afferents do not respond to this stimulus (because
the net horizontal plane linear acceleration is zero;
responses thus reflect an extraotolith signal whose origin
was confirmed here to arise from the semicircular canals.
In particular, after surgical inactivation (plugging) of all six
semicircular canals, Purkinje cell modulation in the Tilt ?
Translation condition decreased significantly from that in
labyrinthine-intact animals (Student’s t test, t89 = 6.7;
p << 0.001). This is illustrated in Figure 4, which plots
responses from atypical Purkinje cell after canal plugging.
The format is similar to that of Figure 2, illustrating
cell responses from two stimulus directions, lateral
translation/roll tilt (q = 0?; 1st row) and fore-aft translation/
pitch tilt (q = 90?; 2nd row). Notably, despite a clear
modulation during Translation (Figure 4A), Tilt ? Transla-
of responses in labyrinth-intact animals, which followed
that of ‘‘Translation’’ (Figures 2A–2D), Purkinje cell
responses after canal plugging followed net acceleration
(Figures 4A–4D). Accordingly, they modulated similarly
Figure 3. Summary of Purkinje Cell Responses
Summary of neural responses during Tilt (A), Tilt ? Translation (B), and
Tilt + Translation (C), plotted as a function of the corresponding
response during Translation (0.5 Hz) (n = 72). Dashed gray and solid
black linesillustratethepredictionsfor‘‘afferent-like’’and ‘‘translation-
coding’’ neurons, respectively.
976 Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc.
Cerebellum Detects Inertial Motion
during Translation and Tilt but did not modulate during
Tilt ? Translation.
These data are summarized for 19 Purkinje cells in
canal-plugged animals in Figures 4E and 4F. Like otolith
afferentsbut unlike responses
responses to Tilt and Translation were similar [repeated
measuresANOVA, F(1,36) =0.64,p=0.43],with acorrela-
tion slope of 0.9, indistinguishable from unity (95% confi-
dence interval: [0.71, 1.13], r = 0.98, p << 0.001;
Figure 4E). In addition, unlike the predictions for transla-
tion-coding neurons, Tilt ? Translation versus Translation
data fell close to the abscissa, as expected for afferent-
like neurons encoding net acceleration (Figure 4F). The
ratio of Tilt ? Translation to Translation responses
decreased from 0.78 ± 0.14 in normal animals to 0.10 ±
0.07 after canal plugging.
The observations in Figures 3 and 4 were further quan-
tified using a partial correlation analysis in which the
responses of each cell to all four stimuli (Translation, Tilt,
Tilt + Translation, and Tilt ? Translation) were simul-
taneously fitted with ‘‘afferent-like’’ and ‘‘translation-
in intact animals,
coding’’ models (see Experimental Procedures). To sim-
plify plotting and visual interpretation, the variances of
these partial correlation coefficients were normalized
using Fisher’s r-to-z transform (Angelaki et al., 2004;
Smith et al., 2005). Figure 5A plots the z-transformed
partial correlation coefficients of the translation model
against those of the afferent-like model. Data in the
labyrinthine-intact animals fell mostly in the upper left
(and none in the lower right) quadrant defined by the
dashed lines corresponding to a 0.01 level of significance
(Figure 5A, black circles). Thus, Purkinje cells in labyrin-
thine-intact animals were significantly better fit with the
translation-coding as compared to the afferent-like
model. The reverse was true after canal inactivation,
when translation z scores decreased from 13.4 ± 5.6 to
1.8 ± 1.4 (ANOVA, p << 0.001) and data fell in the lower-
right quadrant (illustrating significantly better fit with the
afferent-like model; Figure 5A, gray-filled symbols).
Because canal signals were no longer available to
estimate the component of linear acceleration due to
changes in head orientation relative to gravity, after canal
Figure 4. Data after Canal Plugging
(A–D) Instantaneous firing rate of a typical
Purkinje cell during Translation, Tilt, Tilt ?
Translation, and Tilt + Translation (0.5 Hz).
Same format as in Figures 2A–2D.
(E and F) Summary of neural responses during
Tilt and Tilt ? Translation plotted as a function
of the corresponding response during Transla-
tion (n = 19). Dashed gray and solid black lines
illustrate the predictions for ‘‘afferent-like’’ and
‘‘translation-coding’’ neurons, respectively.
Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc. 977
Cerebellum Detects Inertial Motion
plugging Purkinje cells responded similarly to tilt and
Thus, by combining signals from both the otolith organs
and the semicircular canals, NU Purkinje cell responses
reflect the solution of the linear acceleration problem
and selectively encode translation. This is consistent
with the schematic diagram of Figure 1C, with the vermal
cortex conceptually lying within the bottom/right part of
the computational scheme. Notably, NUPurkinje cell pop-
ulation z scores differed from those in VN/FN neurons,
where data spanned the whole range and many had affer-
ent-like properties [Figure 5B, filled circles versus open
triangles; MANOVA, F(2,206) = 6.0, p = 0.003; Angelaki
et al., 2004].
The conceptual diagram of Figure 1C also recapitulates
that canal signals on Purkinje cells should have been
processed relative to canal afferent information in two
important aspects (Green and Angelaki, 2004; see also
Supplemental Data): First, the canal-driven component
of Purkinje cell responses should be in an earth-centered
(as opposed to a head-centered) reference frame. Sec-
ond, it should also be temporally integrated, thus reflect-
ing a tilt position (i.e., angular orientation) rather than an
angular velocity signal. Using Purkinje cell responses
duringTilt? Translation,wenextinvestigate eachofthese
predictions. Note that we used Tilt ? Translation to inves-
tigate these predictions because it is only during this
motion that the dynamic acceleration stimulus to the
otoliths is zero, and Purkinje cell modulation arises exclu-
sively from semicircular canal activation (as shown after
canal plugging in Figure 4).
Purkinje Cell Responses to Earth-Vertical
and Earth-Horizontal Axis Rotations: Evidence for
Reference Frame Transformation of Canal Signals
To appreciate the expected differences in firing rates
based on an earth-centered or head-fixed reference
frame, let’s revisit the example cell in Figure 2. During
earth-horizontal axis rotations, this cell carried a vertical
canal-borne signal with a preferred direction halfway
between roll and pitch (Figure 2C, ‘‘Tilt ? Translation’’
stimulus; a rotation is described as ‘‘earth-horizontal’’ or
‘‘earth-vertical’’ based on the relative orientation of the
rotation axis and gravity; see Experimental Procedures).
If this canal-driven signal is afferent-like in the sense that
it encodes rotation in a head-fixed reference frame (signal
u in Figure 1C), responses should be independent of the
spatial orientation of the rotation axis relative to gravity.
ilarly during earth-vertical axis rotations that activate the
vertical semicircular canals (e.g., roll responses in upright
orientation should be the same as roll responses in supine
only the earth-horizontal rotational component, uEH(as
hypothesized in the scheme of Figure 1C), they should
not modulate at all during earth-vertical axis rotations.
That the latter was indeed the case is shown in Figures
6A–6C, which plots earth-vertical axis rotation responses
from the same example cell as in Figure 2. There was no
stimulus-driven sinusoidal modulation during rotation
with the animal either upright (Figure 6A; when mainly
the horizontal semicircular canals were stimulated) or
tilted by as much as ±45?(Figures 6B and 6C; when not
onlythe horizontal but also the vertical semicircular canals
were stimulated). Such absence of modulation during
vertical canal stimulation (either in roll [Figure 6B] or pitch
[Figure 6C]) when the rotation axis was earth-vertical
contrasts with the robust responses seen during roll/pitch
when the axis of rotation was earth-horizontal (Figure 2C).
Figure 6D summarizes these results. Here, peak
response modulation during earth-vertical axis rotation
with the animal statically tilted relative to the rotation
axis (thus activating vertical semicircular canals) has
been plotted as a function of the response that would
in a head-centered reference frame (i.e., under the as-
sumption that the same canal-derived angular velocity is
encoded regardless of the relationship between the axis
of rotation and gravity). If the canal response component
of NU Purkinje cells was afferent-like and expressed in
a head-centered reference frame, data points should
have fallen along the unity-slope, dashed line (‘‘Head
coordinates’’). In contrast, as illustrated in Figure 6D,
data fell near the abscissa (‘‘Earth coordinates’’) and
were significantly lower than the corresponding predic-
tions for a head-centered estimate [ANOVA with repeated
measures, F(1,62) = 101, p << 0.001]. Thus, Purkinje cells
of semicircular canal afferent activation, a spatially
Figure 5. Scatter Plots of z Scores Corresponding to the
Partial CorrelationCoefficientsfor FitsofEachCell Response
with the ‘‘Translation-Coding’’ and ‘‘Afferent-like’’ Models
(A) Data from n = 72 cells in labyrinthine-intact (black circles) and
n = 19 cells in canal-plugged animals (gray circles) during 0.5 Hz
(B) NU Purkinje cell data (solid circles) are compared with those
previously recorded in VN/FN neurons (open triangles). The superim-
posed dashed lines divide the plots into three regions: an upper left
area corresponding to cell responses that were significantly better fit
(p < 0.01) by the translation-coding model, a lower right area that in-
cludes neurons that were significantly better fit by the afferent-like
model, and an in-between area that would include cells that were
not significantly better fit by either model. Data shown for the cell’s
best-responding translation direction.
978 Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc.
Cerebellum Detects Inertial Motion
Next we describe the temporal properties of this
Purkinje Cell Responses to Earth-Horizontal Axis
Rotations: Evidence for Distributed
The second prediction from the computational scheme of
Figure 1C is that the canal-driven component of Purkinje
cell responses should be temporally integrated, thus
reflecting a tilt position (i.e., angular orientation) rather
than an angular velocity signal. Because our stimulus
was not a transient displacement but a sinusoidal motion,
responses at a single frequency cannot specify whether
cell firing rate follows velocity (like canal afferents) or
position (as predicted from the computational scheme of
Figure 1C). To test whether Purkinje cells encode angular
velocity or its integral, responses at different frequencies
need to be characterized. How peak modulation and
phase vary with frequency can then be used to distinguish
the temporal properties of these responses.
Specifically, if the canal-driven Purkinje cell responses
encode angular velocity, velocity gains (computed as the
ratio of peak cell modulation amplitude relative to peak
stimulus velocity) should be independent of frequency
(Fernandez and Goldberg, 1971). Similarly, the phase of
velocity-coding neurons should be 0?. In contrast, if the
canal-driven response component of NU Purkinje cells
encodes angular position, velocity gains should decrease
with unity slope as a function of frequency. Equivalently,
position gains (computed as modulation amplitude rela-
tive to peak stimulus position) should be independent of
frequency. To encode tilt position, the phase difference
between response and stimulus velocity should be ?90?
across all frequencies.
Figures 7A and 7B plot velocity and position gains as
decreased with frequency, with a slope of ?1, which
was indistinguishable from unity (CI = [?1.12, ?0.88],
r = ?0.73; p << 0.001), the signature of temporal integra-
tion. In contrast, position gains were independent of
frequency [Figure 7B, dashed lines; repeated measures
ANOVA, F(2,57) = 1.8, p = 0.19]. Response phase (re
velocity) was also independent of frequency [repeated
measures ANOVA, F(2,57) = 2.6, p = 0.16] and on average
close to ?90?, compatible with temporal integration. Yet
the canal-driven response components of individual NU
Purkinje cells were nevertheless characterized by phases
that spanned a broad range. Next we explain why such
a cell-to-cell variability in response phase is required for
the detection of inertial motion.
Spatiotemporal Matching of Convergent Signals
To understand this spread of response phase, we need to
revisit therationale behind thesepredictions. Inthesimpli-
fied scheme of Figure 1C, a temporal integration would be
necessary to convert angular velocity into position (i.e., an
angular orientation or tilt signal approximately propor-
tional to the gravitational acceleration for small tilt angles;
see Supplemental Data and Green and Angelaki, 2004).
During tilt such canal-driven angular position signals
would then ‘‘cancel’’ the gravitational component of the
otolith afferent response coding net acceleration. An im-
plicit assumption here is that the otolith-driven responses
of NU Purkinje cells, like primary otolith afferents, encode
linear acceleration. However, several studies have shown
that central responses also encode linear velocity and in
general exhibit a broad distribution of phase relationships
relative to linear acceleration (Angelaki and Dickman,
2000; Angelaki et al., 2004; Chen-Huang and Peterson,
2006; Green et al., 2005; Musallam and Tomlinson,
2002; Shaikh et al., 2005b).
This property, which is generally thought to reflect spa-
tiotemporal convergence and the distributed nature of the
temporal processing required to distinguish tilt and trans-
lation (Angelaki and Dickman, 2000; Green and Angelaki,
2004), has been illustrated for NU Purkinje cells in
Figure 8A. The plot shows the 0.5 Hz phase relationship
between the canal-driven (Tilt ? Translation) and otolith-
driven (Translation) response components for each NU
Purkinje cell. Unlike primary otolith afferents, where
0.5 Hz phases are tightly clustered (Fernandez and
Figure 6. Canal-Driven Responses of Purkinje Cells Encode
Rotation in an Earth-Centered Reference Frame
(A–C) Instantaneous firing rate of the Purkinje cell of Figure 2 during
earth-vertical axis rotation (coding of uEV) with the monkey either
upright ([A], Yaw rotation) or statically tilted ±45?, bringing the plane
of rotation half-way between yaw and roll (B) or pitch (C) (see cartoon
(D) Peak response modulation during earth-vertical axis rotation with
the animal tilted ±30?and/or ±45?(as in [B] and [C]) plotted as a
function of the corresponding prediction under the assumption that
Purkinje cells encode rotation in a head-centered reference frame. If
cerebellar neurons encode rotation in head coordinates, data should
fall along the unity slope, dashed line (‘‘head coordinates’’). Alterna-
tively, if they selectively modulate only during earth-horizontal (but
not earth-vertical) axis rotation, data should fall along the abscissa
Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc. 979
Cerebellum Detects Inertial Motion
Goldberg, 1976b; Angelaki and Dickman, 2000), the
phase of the otolith-driven response component in NU
Purkinje cells varied widely from cell to cell. The canal-
driven component also varied accordingly such that it
matched the corresponding otolith-driven response on
a cell-by-cell basis (paired Student’s t test, t72= 2.0;
p = 0.04). The large cell-to-cell variability in canal-driven
response phase illustrated in Figure 7C can thus be
explained by the requirement to temporally match canal-
and otolith-derived signals on cells that extract inertial
Finally, the semicircular canal and otolith signal contri-
butions to Purkinje cell firing should not only be temporally
but also spatially matched. This was indeed the case, as
illustrated in Figure 8B, which plots the distribution of an-
gular differences in preferred direction between the canal-
driven (Tilt ? Translation) and otolith-driven (Translation)
signal components. Preferred response orientations
were computed by fitting a spatiotemporal model (Ange-
laki, 1991; Green et al., 2005) to spatial tuning curves
contributions to NU Purkinje cells were appropriately
matched spatially (preferred direction differences < 30?).
These results illustrate that the canal-driven component
of Purkinje cell responses provides a temporally and spa-
tially matched complement to the otolith-driven compo-
nent. This ‘‘matched’’ convergence is a necessary condi-
tion for a computational solution to the inertial motion
We have shown here that the simple spike activities of
Purkinje cells in the vermal cortex, lobules 10 (nodulus)
and 9(uvula),encode inertial motion and reflect anelegant
solution to both computational problems of Figures 1A
and 1B. In particular, (1) unlike vestibular and deep cere-
bellar nuclei neurons, where a mixture of translation-
coding and afferent-like responses was observed, NU
Purkinje cells seem to comprise a more uniform popula-
tion that encodes inertial motion. (2) NU Purkinje cells
carry a semicircular canal-driven signal that is spatially
transformed to reflect solely the earth-horizontal compo-
nent of rotation (i.e., they only modulate during rotations
that change head orientation relative to gravity); and (3)
this canal-driven, spatially transformed signal has also
been temporally integrated, thus coding head position
relative to gravity (rather than rotational velocity as do
semicircular canal afferents; Green and Angelaki et al.,
2003; Fernandez and Goldberg, 1971). Such an earth-
centered estimate of head attitude could then be sub-
tracted from net linear acceleration provided by the
otoliths and used to estimate inertial linear accelerations
Inertial Navigation: Data and Theory
The role of otolith and semicircular canal cues in inertial
motion detection and spatial orientation motivated many
pioneering studies (for reviews see Guedry, 1974; Mayne,
Figure 7. Evidence for Temporal Integra-
tion of Canal-Driven Signals
Purkinje cell gain (A and B) and phase (C)
during the Tilt ? Translation stimulus condition
(i.e., isolating the canal-driven response com-
ponent) plotted as a function of frequency.
Gain (in spikes/s per degree/s) and phase (in
degrees) in (A) and (C) are expressed relative
to the head velocity stimulus. Thin lines and
symbols illustrate data from single neurons
tested at different frequencies (n = 23; shown
only for best-responding stimulus direction);
thick lines indicate population averages. (B)
shows the mean (±SD) of velocity and position
gains (solid black and dashed gray lines, re-
spectively). Velocity gains are expressed in
units of spikes/s per degree/s. Position gains
are expressed in spikes/s per degree.
Figure 8. Spatiotemporal Matching of Canal-Driven and
(A) Response phase during the 0.5 Hz Tilt ? Translation stimulus
(canal-driven component) is plotted as a function of the respective
phase during Translation (otolith-driven component) (n = 72; data
along the best-responding stimulus direction). Phase has been
expressed relative to tilt velocity.
(B) Distribution of the difference in preferred directions between the
0.5 Hz Tilt ? Translation and Translation stimulus conditions. Data
(n = 16) from cells tested at multiple orientations (e.g., Figure 2) and
fitted with a spatiotemporal model to compute preferred directions
(Angelaki and Dickman, 2000).
980 Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc.
Cerebellum Detects Inertial Motion
1974; Young, 1984). The problem can be summarized as
follows. As in man-made inertial guidance systems, iner-
tial self-motion detection involves computation of rota-
tional and translational components expressed relative
to an earth-fixed reference. However, because our motion
sensors are fixed to the head, they measure the linear
acceleration and angular rotation within a reference frame
that is head- and not earth-centered (Figures 1A and 1B).
As a result, the unprocessed output of the peripheral
vestibular sensors neither distinguishes attitude (orienta-
tion) from inertial (translational) motion nor signals our
true rotation in space (Angelaki et al., 1999; Green and
Angelaki, 2004; Green et al., 2005; Glasauer and Merfeld,
1997; Merfeld, 1995; Merfeld and Zupan, 2002; Mergner
and Glasauer, 1999; Zupan et al., 2002).
Several behavioral studies have shown that the brain
estimates a solution to both computational problems
introduced in Figures 1A and 1B. For example, behavioral
evidence that the brain can discriminate translational from
gravitational accelerations using canal cues has come
from both eye movement and perception studies (Ange-
laki et al., 1999; Green and Angelaki, 2003; Glasauer,
1995; Merfeld et al., 2005a, 2005b; Stockwell and Guedry,
1970). In addition, evidence that the brain computes the
earth-referenced components of rotation can be found
in both eye movement (Angelaki and Hess, 1994; Angelaki
et al., 1995) and perceptual responses (Day and Fitzpa-
trick, 2005). Notably, after lesion of the NU, reflexive eye
movement responses during rotation no longer show
evidence for spatial (earth-centered) reference frame
transformations (Angelaki and Hess, 1995a; Wearne
et al., 1998).
The schematic of Figure 1C (see also Supplemental
Data) summarizes the concept of how vestibular signals
According to these concepts, (1) resolution of both the
reference frame and linear acceleration problems implies
a convergence of sensory information from the otolith
organs and the semicircular canals. (2) The two problems
are interdependent. That is, detection of self-rotation
relative to the outside world requires an internal neural
estimate of gravity. Concurrently, discrimination between
an internal estimate of gravity and translational accelera-
tion requires knowledge of the temporal integral of uEH,
emphasizing the functional need for spatially and tempo-
rally transformed semicircular canal information. Such
spatiotemporally transformed, canal-driven signals (that
canbeisolated andcharacterized duringTilt–Translation)
are functionally important for computing translation by
‘‘eliminating’’ the component of dynamic otolith afferent
activation associated with head reorientations relative to
gravity. Here we have shown that NU Purkinje cell activity
reflects the output of these transformations.
Role of the NU
The NU has direct projections to the vestibular and fasti-
gial nuclei (Barmack, 2003; Bernard, 1987; Wylie et al.,
1994). Several studies, including lesion, neuroanatomical,
and single-unit recording experiments, have implicated
the cerebellar NU in the central processing of otolith sig-
nals (Marini et al., 1975; Fushiki and Barmack, 1997;
Ono et al., 2000). In the rabbit, where NU responses
have been characterized in detail, both simple and com-
plex spike responses seem to reflect vertical canal and
otolith system activation (Barmack and Shojaku, 1995;
Fushiki and Barmack, 1997), as well as optokinetic stimu-
simple spike responses during translation are always
larger (often more than 10-fold; Figures 2A and 2B and
Figure 3A) than the corresponding tilt responses. Interest-
ingly, although the area receives projections from the
horizontal semicircular canals, no Purkinje cell modulation
has ever been observed during yaw rotations (see Bar-
mack, 2003 for a review). The scheme in Figure 1C pro-
vides an explanation: as long as yaw testing is done in
upright orientation (an uEVstimulus), NU Purkinje cells
will not respond, as they carry only the uEHcomponent
of the canal activation. If, however, yaw rotation is deliv-
ulus), we expect that there would be a robust response
(Green and Angelaki, 2004; Green et al., 2005).
Finally, although a role of the NU in tilt/translation dis-
crimination has yet to be explored using causal manipula-
tions (e.g., electrical microstimulation or inactivation),
there is clear evidence that lesions of the nodulus affect
the expression of coordinate transformations of rotation
signals during the vestibulo-ocular reflex (Angelaki and
Hess, 1995a, 1995b; Barmack et al., 2002; Cohen et al.,
1992; Wearne et al., 1998; Wiest et al., 1999). Similar con-
clusions were reached using electrical stimulation (Heinen
et al., 1992; Solomon and Cohen, 1994). Whether these
computations occur within the cerebellar cortex itself or
through feed-forward and feedback connections with
the vestibular and fastigial nuclei remains to be explored.
For example, ‘‘translation-coding’’ VN/FN neurons might
be the ones connected with the NU, possibly receiving
direct projections. Alternatively, the computation can
involve the whole circuitry, particularly given the strong
interconnectivity between these areas: NU efferents pro-
ject to VN areas that receive afferents from the contralat-
eral FN (Walberg et al., 1962; Angaut and Brodal, 1967). In
addition, NU Purkinje cells regulate the output of NU-pro-
jecting VN neurons (Xiong and Matsushita, 2000), and
electrical stimulation of the nodulus inhibits vestibulocere-
bellar pathways (Precht et al., 1976).
Frequency Bandwidth of These Computations:
Need for Extravestibular Signals
The effectiveness of semicircular canal signals for the
of the mechanical properties of the vestibular apparatus,
canal afferents do not provide a veridical estimate of
angular velocity at low frequencies (Fernandez and Gold-
berg, 1971). Thus, the ability to discriminate between
tilt and translation based solely on vestibular cues (e.g.,
during passive motion in darkness) deteriorates at low
Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc. 981
Cerebellum Detects Inertial Motion
frequencies (Glasauer, 1995; Kaptein and Van Gisbergen,
2006; Merfeld et al., 2005a, 2005b; Seidman et al., 1998).
In fact, it is typically at these low frequencies that percep-
tual illusions occur (‘‘somatogravic illusion’’; Graybiel,
1952; Clark and Graybiel, 1963, 1966; Graybiel et al.,
1979; Tormes and Guedry, 1975).
Thus, it is important to emphasize that in general central
estimates of inertial motion and spatial orientation are
likely to rely on multiple sets of sensorimotor cues includ-
ing vestibular, visual, and somatosensory signals, as well
as efference copies of the motor commands for active
movements. Extravestibular rotation cues are likely to be
of particular importance at low frequencies (e.g., < 0.1 Hz)
or below vestibular detection thresholds (Guedry, 1974).
For example, visual rotational cues have been shown to
contribute to translational motion estimation (Zupan and
that visual cues can significantly influence our percept of
head orientation relative to gravity (Dichgans et al., 1972;
Howard, 1986; Howard and Hu, 2001). How much each
of the sensory cues contributes to inertial motion percep-
tion might depend on their relative reliability, as recently
shown for statistically optimal multisensory cue integra-
tion (e.g., Ernst and Banks, 2002). Visual inputs and effer-
ence copy signals may play a large role in solving these
computational problems during active navigation. Thus,
the fact that a solution is reflected in cerebellar neuron
responses during passive motion in darkness is even
more surprising. Whether the cerebellar vermis is also
involved in multisensory cue integration during active
navigation remains to be explored.
Animals and Experimental Setup
Two juvenile fascicularis monkeys (Maccaca fascicularis) and one
were prepared under aseptic conditions and general anesthesia. A
circular delrin ring was surgically attached to the skull with stainless
steel T bolts and dental acrylic to immobilize the animal’s head in the
stereotaxic position during recording. A delrin platform with staggered
rows of holes was stereotaxically secured inside the head ring. To pro-
vide better access to the midline, the platform in two animals wastilted
were also chronically implanted with scleral search coils to measure
eye movements. After an adequate recovery period, animals were
trained to follow a small target light during fixation and pursuit. These
behavioral protocols allowed identification of the eye position and
velocity sensitivity of cells in the abducens, vestibular, and fastigial
nuclei (Angelaki et al., 2004; Dickman and Angelaki, 2002; Shaikh
et al., 2005b). The surgical and experimental procedures conformed
to the guidelines of the US National Institutes of Health and were
approved by the Animal Care and Use Committee at Washington
In one animal, neural activities were also collected after bilateral
plugging of all six semicircular canals (for details, see Angelaki et al.,
1999; Shaikh, et al., 2005a). This was done in one operation by expos-
membranous duct was then cut with the tip of a sharp knife. Subse-
quently, the hole was firmly filled with bony chips and covered with
a piece of muscle fascia. This procedure does not damage the otolith
organs.Data were collected within the first 2monthsafter surgery. The
efficacy of canal plugging was verified by an absent angular vestibulo-
ocular reflex (VOR) during 0.5 Hz yaw, pitch, and roll rotations in dark-
ness throughout the period of recordings (the translational VOR was
During experiments the monkeys were comfortably seated in a
primate chair secured inside the inner gimbal of a vestibular stimulator
composed of a three-axis rotator mounted on a 2 m linear sled (Acu-
tronics Inc., Pittsburgh, PA). The animal was positioned such that all
three rotation axes (yaw, pitch, and roll) were aligned with the center
of the head and the horizontal stereotaxic plane was aligned with the
earth-horizontal. The linear acceleration stimulus was measured by
a 3D linear accelerometer attached to the inner frame of the turntable,
while angular motion was measured using angular position/rate feed-
back from the rotator. The eye coil signals and the stimuli were filtered
(200Hz; 6-pole Bessel) and digitized at a rate of 833.33 Hz (model
1401, CED, 16-bit resolution; Cambridge Electronics Design, Cam-
NU Purkinje neurons were recorded extracellularly using epoxy-
coated tungsten microelectrodes (4–6 MU impedance; FHC, Bow-
doinham, ME). Each electrode was positioned into a 26-gauge guide
tube that was inserted through a predrilled hole in the skull into the
cerebellum and advanced using a remote-controlled microdrive. Re-
corded action potentials were amplified, filtered (300–6 kHz), discrim-
inated with a window-slope trigger, and stored on a computer using
the event channel of the 1401 for offline analyses. Neuronal data
were also acquired using an analog channel of the 1401 (40 KHz).
The data were analyzed offline using Spilke2 (Cambridge Electronic
Design) to extract the complex and simple spikes from the raw neuro-
nal data. We sorted spikes based on principal component analysis
using a clustering approach.
The nodulus-uvula was identified using stereotaxic coordinates as
well as the location of the abducens, vestibular, and fastigial nuclei
in each animal (see Figures S1, S2, and S3 for recording locations).
Recordings were restricted to the Purkinje cell layer, where both
simple and complex spikes could be observed online. All but 15 cells
were further identified as Purkinje cells offline using the following crite-
ria: first, simple spikes (SS) and complex spikes (CS) were identified
visually by their characteristic waveforms. Second, peri-CS-triggered
SS histograms were used to show that SS activity paused for 15 ms
after the occurrence of a CS. Because we found no difference in
response properties between identified and putative Purkinje cells,
the two groups have been considered together in all analyses.
To characterize the properties of NU neurons, the following experi-
mental protocol was delivered in complete darkness. Neural re-
sponses were characterized during combinations of tilt and translation
stimuli that have been used previously to independently manipulate
inertialand netgravitoinertial accelerations (Figure2;seealsoAngelaki
et al., 1999, 2004). These stimuli consisted of either pure translation
uli(Tilt?Translationmotionand Tilt+Translationmotion).Thetilt stim-
in the horizontal plane with a peak magnitude of approximately 0.2 G
(G = 9.81 m/s2). The amplitudeof the translation stimulus was adjusted
rotational and translational stimulation, inertial and gravitational accel-
ion depending on the relative directions of the two stimuli. As a result,
doubled (Tilt + Translation) or was nearly zero (Tilt – Translation), even
though the actual translation of the animal remained the same.
Each cell was usually characterized at a minimum of two horizon-
tal plane orientations (q = 0?and q = 90?), corresponding to lateral
motion/roll tilt and fore-aft motion/pitch tilt, respectively (see
982 Neuron 54, 973–985, June 21, 2007 ª2007 Elsevier Inc.
Cerebellum Detects Inertial Motion
Figures 2A–2D, 2nd and 4th rows). If neural isolation was maintained,
this 0.5 Hz protocol was also delivered along two additional direc-
tions, half-way in-between the lateral and fore-aft directions (q = ?45?
and q = 45?; see Figures 2A–2D, 1st and 3rd rows). Along their best-
responding direction, several cells were also tested during these four
protocols (Translation, Tilt, Tilt ? Translation, Tilt + Translation) at two
different frequencies, 0.16 Hz (±0.1 G, corresponding to tilt and trans-
corresponding to tilt and translation amplitudes of 5?and 2.16 cm,
respectively). Note that the highest- and lowest-frequency/amplitude
parameters were determined by the mechanical limitations of the
pitch/roll rotator and sled, respectively.
Finally, a few cells were also tested during earth-vertical axis rota-
tions. Notice that we describe rotations based on their ‘‘axis,’’ as
defined bythe right-hand rule.Forexample, yawwhileupright (rotation
axis parallel to gravity) was considered an ‘‘earth-vertical axis’’ rota-
tion, whereas yaw while supine (rotation axis perpendicular to gravity)
was considered an ‘‘earth-horizontal axis’’ rotation (Figure 1A). Simi-
larly, pitch/roll while upright were considered ‘‘earth-horizontal axis’’
rotations, whereas pitch/roll while ear-down/supine were considered
‘‘earth-vertical axis’’ rotations. In these experiments, earth-vertical
axis rotations (0.5 Hz, ±10?) were delivered with the animal positioned
upright, pitched 30?(or 45?) nose-up/down (rotations producing
combinations of horizontal and torsional VOR) and rolled 30?(or 45?)
right/left ear-down (rotations producing combinations of horizontal
and vertical VOR).
Data analyses were performed offline using Matlab (Mathworks Inc.,
Natick, MA). Instantaneous firing rate was computed offline as the
inverse of interspike interval. Data from multiple cycles of sinusoidal
motion were folded into a single cycle by overlaying neural responses.
Response amplitudeand phaseweredetermined byfitting asinefunc-
tiontothecumulativeresponsesduring eachof thetranslation, tilt, and
combined stimuli (Angelaki and Dickman, 2000; Dickman and Ange-
laki, 2002). Response amplitude refers to half the peak-to-trough
modulation, whereas response phase has been expressed relative to
translation (or tilt) stimulus velocity.
Todetermine whether eachindividual cellencoded translation or net
linear acceleration, linear regression analyses were used to simulta-
neously fit the cumulative cycles of cell modulation during each of
the translation, tilt, and combined stimuli using an ‘‘afferent-like’’ and
‘‘translation-coding’’ model. Briefly, these models assume that neural
firing rate modulation is either due to the net acceleration or due to the
translational acceleration component (for details, see Angelaki et al.,
2004; Green et al., 2005). How well each of these two models fitted
the data was evaluated using a partial correlation analysis. To remove
the influence of correlations between the predictions themselves, we
calculated partial correlation coefficients RAand RTusingthe following
ð1 ? r2
TÞð1 ? r2
ð1 ? r2
AÞð1 ? r2
where rAand rTare the simple correlation coefficients between the
data, and each of the model predictions and rAT= 0.68 describes the
correlation between the two models.
Partial correlation coefficients were subsequently converted to z
scores using Fisher’s r-to-z transform in order to facilitate the interpre-
tation of statistical significance independently of the number of data
points (Angelaki et al., 2004; Smith et al., 2005). The advantage of
this comparison is that when z scores for one model are plotted versus
the respective z scores for the other model, the plot can be easily sep-
arated into regions in which data points can be distinguished as being
better correlated with one model as compared to the other at a partic-
ular level of significance. Because all NU neurons fell in the upper left
quadrant (i.e., reflecting the fact that the translation-coding model pro-
vided statistically significant better fits), intermediate models (Angelaki
et al., 2004) were not considered here. Correlations between indepen-
dent variables were obtained by minimizing the perpendicular offset of
the data to the line (using a nonlinear least squares algorithm based on
the interior-reflective Newton method), with 95% confidence intervals
computed using bootstrapping with replacement. Other statistical
comparisons of neural responses used analyses of variance and
Student’s t tests.
The Supplemental Data for this article can be found online at http://
The work was supported by grants from NASA (NNA04CC77G) and
NIH (F32 DC006540, R01 EY12814). We would like to thank Shawn
Newlands for the canal-plugging operation.
Received: February 2, 2007
Revised: May 2, 2007
Accepted: June 5, 2007
Published: June 20, 2007
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