Abstract
Many daily behaviors rely on estimates of our body's motion and orientation in space. Vestibular signals are essential for such estimates, but to contribute appropriately, two key computations are required. First, ambiguous motion information from otolith organs must be combined with spatially transformed rotational signals (e.g., from the canals) to distinguish head translation from tilt. Second, tilt and translation estimates must be transformed from a head- to a body-centered reference frame to correctly interpret the body's motion. Studies have shown that cells in the caudal cerebellar vermis (nodulus and ventral uvula, NU) reflect the output of the first set of computations to estimate translation and tilt. However, it remains unknown whether these estimates are encoded exclusively in head-centered coordinates or whether they reflect further transformation toward body-centered coordinates. Here, we addressed this question by examining how the 3D spatial tuning of otolith and canal signals on translation- and tilt-selective NU Purkinje cells in male rhesus monkeys varies with changes in head-re-body and body-re-gravity orientation. We show that NU cell tuning properties are consistent with head-centered otolith signal coding during translation. Furthermore, while canal signals in the NU have been transformed into a specific world-referenced rotation signal indicating reorientation relative to gravity (tilt), as needed to resolve the tilt/translation ambiguity, the resulting tilt estimates are encoded in head-centered coordinates. Our results thus suggest that body-centered motion and orientation estimates required for postural control, navigation, and reaching are computed elsewhere, either by further transforming NU outputs or via computations in other parallel pathways.
Significance Statement
Estimates of body motion and orientation are essential for daily activities. Vestibular signals contribute vitally to such estimates but must first undergo transformations to distinguish translation from tilt and convert head-centered estimates into body-centered representations. Previous studies implicated the caudal cerebellar vermis (nodulus and ventral uvula, NU) in computing estimates of translation and tilt. However, here we show for the first time that NU cells encode such estimates exclusively in head-centered coordinates. The NU thus reflects motion estimates appropriate for head and gaze stabilization but not the body-centered representations relevant for tasks such as body postural control and reaching. We suggest that head- versus body-centered motion and orientation estimates may be computed via at least partially distinct cerebellar pathways serving different functional roles.
Introduction
Daily tasks such as navigating, controlling posture, and coordinating voluntary movements require estimates of our spatial motion and orientation. Vestibular signals are essential for such estimates, but to contribute appropriately at least two key problems must be resolved. First, because our otolith organs transduce inertial (translational) and gravitational (tilt) accelerations equivalently (Fernandez and Goldberg, 1976a,b; Angelaki and Dickman, 2000), distinguishing translation from tilt requires combining otolith signals with rotational signals that provide an independent estimate of reorientation relative to gravity (Merfeld et al., 1999; Green and Angelaki, 2004, 2007; Laurens and Angelaki, 2017). Second, while the vestibular sensors provide essential estimates of head motion, the way they are activated by a given body motion depends on the head's movement and orientation with respect to the body. Vestibular and neck proprioceptive signals must thus be integrated to correctly estimate body motion (Kleine et al., 2004; Shaikh et al., 2004; Brooks and Cullen, 2009; Luan et al., 2013; Martin et al., 2018; Zobeiri and Cullen, 2022).
A brainstem–cerebellar network has been implicated in resolving both problems (Green and Angelaki, 2010). Neurons in the vestibular (VN) and rostral fastigial (rFN) deep cerebellar nuclei (Angelaki et al., 2004; Green et al., 2005; Shaikh et al., 2005b; Mackrous et al., 2019) as well as thalamic (Meng et al., 2007) and cortical areas (Liu et al., 2011) to which they project reflect population-level translation estimates. Furthermore, a solution to the otolith “tilt/translation ambiguity” is reflected in individual neurons of the caudal cerebellar vermis (nodulus and ventral uvula, NU; lobules X, IXc,d) where distinct translation- and tilt-coding Purkinje cells have been identified (Yakusheva et al., 2007; Laurens et al., 2013; Stay et al., 2019; Hernández et al., 2020). Consistent with theoretical predictions (Green and Angelaki, 2004, 2007), NU neurons combine otolith signals with canal signals that have been spatially transformed into estimates of the earth-horizontal component of rotation signaling head reorientation relative to gravity (i.e., tilt; Yakusheva et al., 2007; Laurens et al., 2013). Such estimates of head translation and tilt are essential for gaze and head stabilization and visual–vestibular integration for spatial perception. However, for tasks such as maintaining balance or reaching, these vestibular-derived estimates must be integrated with proprioceptive cues to estimate body motion and orientation.
Compelling evidence suggests the rFN plays an important role in encoding such body motion estimates. Many rFN neurons integrate vestibular and proprioceptive signals to distinguish head from body motion (Brooks and Cullen, 2009, 2013) and reflect the required transformation of head-centered vestibular signals toward body-centered coordinates (Kleine et al., 2004; Shaikh et al., 2004; Martin et al., 2018). Recently, Martin et al. (2018) examined this transformation in three dimensions (3D), showing that fully body-centered representations in 3D could be linearly decoded from small populations of rFN cells. Based on this and other observations, the rFN was suggested to reflect a late stage in the transformation, with the required nonlinear computations largely occurring upstream in the cerebellar cortex. Indeed, regions of the anterior vermis (AV) that integrate vestibular and proprioceptive signals and project to the rFN have been implicated in transforming vestibular rotation signals toward body-centered coordinates (Manzoni et al., 1999). Yet, most translation-responsive rFN cells also reflect at least a partial solution to the tilt/translation ambiguity (Angelaki et al., 2004; Green et al., 2005; Shaikh et al., 2005b; Martin et al., 2018; Mackrous et al., 2019) and thus the output of computations thought to be performed largely in the NU of the posterior vermis. Because many motion-sensitive NU cells also receive convergent input from neck proprioceptors (Sheliga et al., 1999; Mildren et al., 2025), a key question arises: Does the NU disambiguate tilt and translation only in head-centered coordinates or have tilt and translation estimates been further transformed toward body-centered coordinates? Here, we addressed this question by examining for the first time how the spatial tuning for translation and tilt in the NU varies with changes in head-re-body orientation.
Materials and Methods
Animal preparation
Data reported here were collected from three male rhesus monkeys (Macaca mulatta, 7–12 kg, 5–11 years old) that were prepared for chronic recording of eye movements and single-unit activity. In the first surgery, animals were chronically implanted with a 7 cm diameter Delrin head-stabilization ring that was anchored to the skull using hydroxyapatite-coated inverted T-bolts and neurosurgical acrylic bone cement (Martin et al., 2018). Supports for a removable Delrin recording grid (3 × 5 cm) were stereotaxically positioned inside the ring and secured to the skull with acrylic. The recording grid consisted of arrays of holes spaced by 0.8 mm arranged in staggered rows. Holes on each side of the grid were slanted relative to the horizontal plane 10° upward from lateral to medial to provide bilateral access to medial cerebellar regions. In the second surgery, animals were chronically implanted with a scleral search coil for recording eye movements in 2D (Robinson, 1963). After surgical recovery, animals were trained to fixate and pursue visual targets within a ±1.5° window for fluid reward using standard operant conditioning techniques. All surgical procedures were performed aseptically and under anesthesia. Surgical and experimental procedures were approved by the institutional animal research review board (Comité de déontologie de l’expérimentation sur les animaux) and were in accordance with national guidelines for animal care.
Experimental setup
During experiments, the animals were comfortably seated in custom-built primate chairs that were designed to permit the head to be secured in different positions relative to the body by means of a movable head-restraint system (Martin et al., 2018). This head-restraint system, which attached to the animal's ring implant at three points via setscrews, allowed the head to be manually reoriented along three independent orthogonal axes and locked in different head-on-trunk positions (Fig. 1A). In particular, the head could be reoriented in vertical planes toward nose-down (pitch reorientation by up to 45°; Fig. 1Aii,Dii) and right-/left-ear-down (roll reorientation by up to 30°; Fig. 1Aiii,Diii) about horizontal axes located at approximately the level of the second cervical vertebra. The head could also be reoriented in the horizontal plane about a vertical axis passing through the head center (yaw-axis reorientation by up to 45°; Fig. 1Aiv,Div). To prevent changes in torso and limb position, the animal's torso was secured with shoulder straps and a waist restraint, and his limbs were gently secured to the chair using soft forearm and ankle sleeves.
Experimental methods. A, Custom primate chairs used to test cell tuning with the head upright (Ai) as well as after manual repositioning of the head relative to the body in the vertical plane by up to 45° toward nose-down (Aii) or 30° toward right-ear-down (Aiii) and in the horizontal plane by up to 45° to the left (Aiv). B, Schematic illustration of the motion delivery system consisting of a custom two-axis rotator (Actidyn) mounted on top of a six-degree-of-freedom motion platform (Moog). The primate chair and eye monitoring system (field coil) were mounted to the innermost axis of the rotator system. C, Illustration of the 13 axes along which sinusoidal translation stimuli (blue and green arrows; 0.5 Hz, ±9 cm, ±0.09 G) and the three axes about which sinusoidal rotation stimuli (orange arrows; 0.5 Hz, ±10°, ±31.4°/s) were applied to characterize cell response tuning. D, Cell tuning for translation was characterized with the head upright (Di), after vertical-plane head reorientation relative to the body by either 45° toward nose-down (Dii) or 30° toward ear-down (Diii) and/or after horizontal-plane reorientation 45° to the left (Div). The predicted PD for body-centered (blue squares) versus head-centered (pink circles) encoding of translation is illustrated for a cell with a head upright PD (PDUP) along the x-axis (0° azimuth, 0° elevation). E, Tilt and translation stimulus combinations used to test a subset of cells along the four horizontal-plane axes (green arrows in C). These included sinusoidal tilts (Eii; 0.5 Hz, ±5.19°, ±0.09 G) matched in amplitude to the translation stimulus (Ei; 0.5 Hz ±9 cm, ±0.09 G) as well simultaneous translation and tilt stimuli combined in either an additive (Eiii; T + T, 0.5 Hz, ±0.18G) or subtractive (Eiv; T − T, 0.5 Hz, ±0G) fashion. F, Cells were tested during earth-vertical-axis rotation (EVAR; orange) and for the stimuli in E applied along the horizontal-plane axis closest to the cell's PD for the T − T stimulus when upright (Fi), as well as after the whole body was reoriented relative to gravity by 45° along the axis perpendicular to the cell's T − T PD (e.g., after body reorientation toward right-/left-ear-down for testing along the 0° azimuth PD axis; Fii) and after head reorientation by 45° to the left (Fiii). G, NU Purkinje cells were identified by the presence of both simple spikes (SSs) and complex spikes (CSs; top) and by showing that SS activity paused for at least 10 ms after the occurrence of a CS (bottom). H, Schematic representation of the theoretically predicted trajectory of PDs (green curve) between body-centered (blue square) and head-centered (pink circle) coding predicted for an example cell with a PDUP of (45°, 45°). The cell's tuning reflects a new PD (PDNEW; red x) of (25°, 30°) when the head is reoriented 45° toward nose-down (inset). The extent of shift from PDUP to PDNEW along the “ideal” (green) trajectory was quantified by a DI (x corresponds to a DI of 0.5). The extent of shift orthogonal to this trajectory was quantified by an angular error ε (purple arrow illustrates an ε of −8.5°) defined as the angle between PDNEW (red x) and the closest point along the ideal trajectory (PDPRED; black x).
The primate chair was secured to a motion system that was used to provide 3D translational and rotational motion stimuli. In initial experiments, motion stimuli were delivered using a six-degree-of-freedom motion platform described previously (6DOF2000E, Moog; Martin et al., 2018). This system was subsequently extended to incorporate a custom-built gimballed two-axis rotator system (Actidyn) that was integrated with and mounted on top of the motion platform (Fig. 1B). The gimballed rotator system consists of an inner “yaw-axis” rotator mounted inside an outer “pitch-axis” rotator. The primate chair was secured to the innermost frame of the rotator such that the animal's body-vertical axis was aligned with the inner yaw rotation axis and the center of the animal's head (intersection of his interaural and naso-occipital head axes) was positioned at the intersection of the two rotator axes (i.e., center of the gimballed rotator system). Consequently, rotation of the innermost axis of the rotator reoriented the animal about his body-vertical axis, while rotation about the outer pitch axis reoriented his body in a vertical plane with respect to gravity. Importantly, the complete 3D motion system allows delivery of different combinations of 3D translational and rotational motion stimuli across a broad range of different body orientations with respect to gravity.
The motion stimuli delivered to the animal were measured using a navigational sensor composed of a three-axis linear accelerometer and a three-axis angular velocity sensor (Tri-Axial Navigational IMU, Kistler), which was mounted to the chair support inside the innermost frame, just adjacent to the animal's head. Eye movements were measured with a three-field magnetic search coil system (24 in. cube; Riverbend Instruments) that was mounted on the innermost frame of the rotator such that the monkey's head was centered within the magnetic field. Visual targets were backprojected onto a vertical screen mounted in front of the animal (30 cm distance) using a wall-mounted laser and x–y mirror galvanometer system (Cambridge Technology). Stimulus presentation, reward delivery, and data acquisition were controlled with custom scripts written in the Spike2 software environment using the Cambridge Electronic Design (model power 1401) data acquisition system. Eye coil voltage signals and 3D linear accelerometer and angular velocity measurements of the motion stimuli delivered to the animal were antialias filtered (200 Hz, four-pole Bessel; Krohn-Hite), digitized at a rate of 833.33 Hz, and stored using the Cambridge Electronic Design system.
Neural recording
Single-unit extracellular recordings in the caudal cerebellar vermis (lobules IX and X; NU) were performed with epoxy-coated, etched tungsten microelectrodes (3–5 MΩ, FHC) that were inserted into the brain using 26 gauge guide tubes that were passed through the recording grid and small predrilled burr holes in the skull. A remote-controlled mechanical microdrive (Hydraulic Probe Drive; FHC) mounted on the animal's head-stabilization ring was then used to advance electrodes. Neural activity was amplified, filtered (30 Hz to 15 kHz), and isolated online using a time–amplitude dual window discriminator (BAK Electronics). Single-unit spikes triggered acceptance pulses from the window discriminator that were time stamped and stored using the event channel of the Cambridge Electronic Design data acquisition system. In addition, raw neural activity waveforms were digitized at 30 kHz and stored using the Cambridge Electronic Design system for off-line spike discrimination.
In initial penetrations, the abducens nuclei and rostral fastigial nuclei were localized bilaterally. The regions of interest in the NU were then identified on the basis of their stereotaxic location in relation to the abducens nuclei, fastigial nuclei, and fourth ventricle (Yakusheva et al., 2007). Recordings were restricted to neurons in the Purkinje cell layer where both simple spikes (SSs) and complex spikes (CSs) could be observed and heard on the audio monitor. Among recorded cells, 76% (72/95) were explicitly identified off-line as Purkinje cells by the capacity to identify the characteristic waveforms of both SSs and CSs and by showing that SS activity paused for at least 10 ms after the occurrence of a CS (Fig. 1G; Barmack and Shojaku, 1995). Units for which both SSs and CSs were present in the recording, but clear SS pausing was not observed, were considered putative Purkinje cells. Because we found no differences between identified and putative Purkinje cell spontaneous firing properties and responses to motion stimuli across the conditions tested (see below), the two groups have been presented together in the results. All cells described here were characterized as eye movement insensitive by their failure to exhibit changes in modulation during horizontal and vertical smooth pursuit (0.5 Hz, ±10 cm) as well as during saccades and fixation (up to ±20° horizontally and vertically). Cell responses to motion stimuli were recorded in darkness, and eye position was uncontrolled.
After a putative NU Purkinje cell was isolated, its responses to motion stimuli were first characterized with the animal's head facing straight ahead and with the head and body in an upright orientation. The cell's 3D spatial tuning for translation was characterized by recording responses to sinusoidal translation (0.5 Hz, ±9 cm, ±0.09 G) along 13 different axes. These axes were defined along fixed directions in 3D space (i.e., world-centered coordinates that were aligned with body coordinates when the body was upright) and described in a spherical coordinate system in terms of combinations of azimuth and elevation angles in increments of 45° spanning 3D space (Fig. 1C, blue and green arrows). The cell's 3D rotation tuning was also characterized during sinusoidal rotation (0.5 Hz, ±31°/s, ±10°) about the x, y, and z axes (Fig. 1C, orange arrows). The majority of neurons (N = 69/95) were further characterized along the four horizontal-plane axes (azimuth 0, 45, 90, and 135° for elevation 0°; Fig. 1C, green arrows) for different combinations of matched translation and tilt stimuli. These stimuli have been used in previous studies (Fig. 1E; Angelaki et al., 2004; Green et al., 2005; Yakusheva et al., 2007, Mackrous et al., 2019; Hernández et al., 2020) to evaluate how central neurons integrate otolith and canal signals to distinguish components of the net gravitoinertial acceleration (GIA), sensed by the otoliths, due to translational motion from those due to head reorientation relative to gravity. In addition to the purely translational motion stimuli described above, these stimuli consisted of pure tilts matched to the translation stimulus (see below; Fig. 1Eii) as well as simultaneous translational and tilt motion stimuli combined in either an additive [tilt + translation (T + T); Fig. 1Eiii] or subtractive [tilt − translation (T − T); Fig. 1Eiv] fashion. In particular, pure tilts consisted of 0.5 Hz sinusoidal rotations from upright with a peak amplitude of ±5.19° (±16.3°/s), producing a peak GIA stimulus to the otoliths that was matched in magnitude (0.09 G) to that produced by the pure translation. During combined tilt and translation stimuli, inertial and gravitational components of linear acceleration combined along a given axis either additively to produce double the net GIA (T + T stimulus; 0.18 G) or subtractively such that the net GIA was close to zero (T − T stimulus; 0 G). Importantly, because the T − T stimulus produces little activation of otolith afferents (i.e., net GIA close to 0; Angelaki et al., 2004), it provides a means of isolating semicircular canal contributions to central neural activities during earth-horizontal-axis rotations that dynamically reorient or tilt the head with respect to gravity.
To examine the reference frames in which translation-sensitive NU cells encode otolith signals, spatial tuning for translation was subsequently characterized in one or more additional head-re-body positions obtained by statically reorienting the head in vertical and/or horizontal planes (Fig. 1D). In particular, head reorientation in the vertical plane consisted of either pitch toward 45° nose-down or roll toward 30° right-ear-down, depending on the cell's preferred translation direction when upright and the axis of reorientation predicted to result in larger differences between head- and body-centered tuning (i.e., the axis further away from the cell's preferred upright translation direction; Fig. 1Dii vs Diii). Reorientation of the head in the horizontal plane involved displacement of the head to the left by 45° (Fig. 1Div). After statically positioning the head in a new orientation, neural responses were characterized for the same set of body-centered translation directions that were examined with the head upright and facing forward. Because tuning shifts that can distinguish between reference frames are predicted to be largest in the plane of head reorientation, translation directions in this plane were always tested first to maximize the potential to use partial datasets. After characterizing cell response tuning in each new head orientation, the head was returned to the upright and straight forward position, and responses along one or more directions close to the cell's preferred response direction (PD) were retested to confirm cell isolation before further characterization of the cell's activity.
To examine the reference frames in which canal-derived estimates of tilt are encoded within the NU, additional tests were performed on a subset of recorded neurons whose responses were characterized across different body-re-gravity and/or head-re-body orientations for the matched tilt and combined tilt/translation stimuli described above. In particular, we sought to (1) explicitly confirm that the canal signals carried by these cells had been spatially transformed into a true 3D estimate of tilt relative to gravity and (2) investigate the reference frames in which such tilt signals are encoded. Cells carrying true canal-derived tilt estimates should respond similarly to the T − T stimulus (i.e., which isolates canal signals during earth-horizontal-axis rotation) across different whole-body orientations relative to gravity. Consequently, to address the first issue, we reoriented the whole body of the animal relative to gravity by 45° along the horizontal-plane axis (i.e., azimuth 0, 45, 90, or 135°) closest to perpendicular to its preferred direction (PD) for the T − T stimulus (e.g., toward right-ear-down for a PD closest to 0°; Fig. 1Fi,ii). The cell's responses to earth-vertical-axis rotation (EVAR) as well as to translation, tilt, T − T, and T + T along the preferred T − T direction were then retested. Three cells were also retested for whole-body reorientation along the same axis but in the opposite direction (e.g., toward left-ear-down for a PD of 0°). Of particular relevance is the fact that across all body orientations (i.e., upright and body tilted), translation and tilt stimuli were applied along the same horizontal-plane axis in head/body coordinates (e.g., 0° azimuth in Fig. 1Fi). Consequently, the dynamic stimulus to the otoliths was similar in both whole-body orientations. In contrast, stimuli involving rotation activated different sets of canals in each body orientation. For example, tilts stimulated mainly the vertical canals when upright but both horizontal and vertical canals after body reorientation. Conversely, EVAR stimulated mainly the horizontal canals when upright and both vertical and horizontal canals after body reorientation. Importantly, cells carrying canal signals that had been spatially transformed into an estimate of the earth-horizontal component of rotation, signaling dynamic tilt—a signal referenced to world coordinates by the direction of gravity (i.e., world-/gravity-referenced signal)—should not reflect these different sensory activation patterns. Instead, they should exhibit similar responses to the T − T stimulus and remain unresponsive to EVAR across the different whole-body orientations.
Finally, to address the second issue (i.e., reference frames in which canal-derived estimates of tilt are encoded), head and body reference frames were dissociated by reorienting the head relative to the body by 45° to the left in the body upright orientation (Fig. 1Fiii). Responses to the translation, tilt, and combined tilt and translation stimuli were then retested.
Data analysis
Data analysis was performed off-line using scripts written in MATLAB (The MathWorks). Spike times were converted into instantaneous firing rate (IFR) by taking the inverse of the interspike interval (ISI) and assigning this value to the middle of the interval. For each neuron confirmed to be insensitive to eye movements and visual target presentation, we quantified baseline activity by calculating the cell's median IFR and firing regularity during 30–120 s samples of spontaneous activity obtained as the monkey sat quietly in darkness and/or made saccades to and fixated visual point targets in an otherwise dark room. Firing regularity was quantified by calculating the median CV2 where CV2 = |ISIn + 1 − ISIn|/(ISIn + 1 + ISIn). This measure is similar to the coefficient of variation (CV) but considers only adjacent ISIs and is thus less susceptible to large variation due to changes in the firing rate (Holt et al., 1996; Meng et al., 2015). It was previously used to quantify the properties of macaque NU Purkinje cells and cerebellar interneurons in the study of Meng et al. (2015), and we used the same measure to facilitate comparison with their results.
To quantify cell responses to motion stimuli, the gain and phase of the neural IFR response to each motion stimulus in a given direction and head/body orientation were obtained by fitting 5–20 well-isolated cycles of both the response and the stimulus with a sine function using a nonlinear least squares minimization procedure (Levenberg–Marquardt). Confidence intervals (CIs) on estimates of neural response gain and phase were obtained using a bootstrap method in which bootstrapped gain and phase estimates were obtained by resampling (with replacement) the response cycles used for the sine function fits 600 times. A cell was considered to exhibit a significant modulation for a given motion stimulus if at the time of peak response (estimated from the nonbootstrapped fit across response cycles), 95% CIs on the firing rate were greater than a minimum of two spikes/sinusoidal cycle. For translation stimuli, response gain was expressed in units of spikes/s/G (where G = 9.81 m/s2) and phase as the difference (in degrees) between peak neural modulation and peak translational acceleration. For rotational stimuli, gain was expressed in units of spikes/s/deg/s and phase as the difference between peak neural modulation and peak angular velocity. To facilitate comparison of cell responses to translation with those due to tilt relative to gravity, earth-horizontal-axis rotation responses were also calculated relative to the linear acceleration stimulus to the otoliths caused by tilt in units of spikes/s/G with phase expressed as the difference between peak neural modulation and peak acceleration.
Cells were subsequently classified based on their horizontal-plane response gains and phases as predominantly encoding the net GIA (i.e., like the otoliths), translation, tilt, or having composite properties (i.e., not better correlated with either translation or tilt). Using a multiple linear regression analysis, neural responses to translation, tilt, and combined tilt/translation stimuli (whenever possible) across directions in the horizontal plane were first fit with a general model that assumes that cell responses can be described as a weighted combination of acceleration components due to translation and tilt. Specifically, we fit the model Response = H1Transx + H2Transy + H3Tiltx + H4Tilty, where Response is a vector of the observed response amplitudes and phases (expressed compactly as a complex number) for the different stimuli, and Transx, Transy, Tiltx, and Tilty are the corresponding accelerations due to translation and tilt associated with each stimulus along the x (azimuth 0°) and y (azimuth 90°) axes. Regression coefficients, H1–H4, are complex numbers embedding both gain and phase information that provide estimates of the cell's responsiveness to translation and tilt along each axis. In addition to the general model, we also fit two simpler models including a “translation model,” which assumes that the neuron responds selectively to translation (i.e., H3, H4 = 0), and a “tilt model,” which assumes that the neuron responds selectively to tilt (i.e., H1, H2 = 0). Each model was fit 600 times using the bootstrapped response gains and phases for each stimulus, described above, to obtain distributions of model parameters (H1–H4). These were in turn used to compute distributions of tuning functions describing cell spatiotemporal sensitivities to translation and/or tilt (Angelaki, 1991).
To identify cells whose responses were consistent with encoding the net GIA, we compared the tuning functions for translation versus tilt that were obtained from fits using the general model. Specifically, we calculated distributions of differences in tuning function parameters (gains, phases, and PD) for translation versus tilt. Cells whose 95% CIs (percentile method) for gain, phase, and PD differences included zero were classified as GIA encoding. For comparison, we also calculated distributions of gain, phase, and PD differences for translation versus tilt obtained by fitting responses to pure translation and pure tilt stimuli only using the simpler translation and tilt models and obtained the same results.
Cells not classified as GIA encoding were then further examined to determine whether they could be considered statistically better correlated with either translation or tilt. We compared the fits of first-order translation and tilt models by calculating the correlation between the data and each set of model predictions as well as the correlation between the model predictions themselves. These were used to compute partial correlation coefficients that were then converted to normalized partial correlation scores (Z-scores) and used to assess significant differences in the model fits (see below, Statistical analysis). Cells that were significantly better correlated with the translation than the tilt model were classified as translation coding. Cells were classified as tilt encoding if they were both significantly better correlated with the tilt model and had responses to vertical-axis translations that were either negligible or smaller than those for horizontal-plane translations. All other cells were classified as composite.
The spatial tuning of each cell was subsequently characterized across one or more head orientations. The tuning profiles of cells classified as being responsive to translation (i.e., all cells except those identified as preferentially encoding tilt) were visualized in 3D by plotting response gains as a function of the azimuth and elevation of translation direction (Fig. 3A–C). A precise estimate of the cell's PD for translation was obtained by fitting response gains and phases across directions using a 3D spatiotemporal convergence (STC) model (Fig. 3D; for details, see Chen-Huang and Peterson, 2006; Martin et al., 2018) that is more general than cosine tuning and can account for the observation that many brainstem and cerebellar neurons exhibit translation responses that vary in terms of both gain and phase with motion direction (Siebold et al., 1999; Angelaki and Dickman, 2000; Shaikh et al., 2005a; Chen-Huang and Peterson, 2006; Martin et al., 2018). These fits yielded estimates of the cell's maximum response gain, phase, and direction (i.e., PD). In addition, we calculated the ratio of minimum to maximum response gain (STC tuning ratio), which provides a measure of the extent to which a cell's response reflects simple cosine-tuned changes in gain across motion directions (STC ratio = 0) versus dynamic properties that vary with motion direction (STC ratio > 0), consistent with the convergence of vestibular signals with different PDs and phases relative to the stimulus (Angelaki, 1991; Chen-Huang and Peterson, 2006). The majority (96%) of cells responsive to translation (i.e., cells other than tilt-selective cells) were fit with a 3D STC model with the head upright. In addition, 84% of datasets collected after either horizontal or vertical-plane head reorientation were fit with this model. For the remaining datasets, insufficient data were collected after head reorientation to fit the full 3D model. Such partial datasets were included only if we were able to complete testing across four directions in the plane of head reorientation. In these cases, preferred tuning was estimated by fitting responses across motion directions in that plane using a 2D STC model (Angelaki, 1991). In addition, since tilt, by definition, implies rotation about an earth-horizontal-plane axis, the spatial tuning for tilt was characterized in the horizontal plane using a 2D STC model. We defined the tilt PD as the horizontal-plane direction along which body tilt produced the maximum response.
To examine the extent to which cells encoded motion in a head- or body-centered reference frame, we quantified how their spatial tuning varied across changes in head-re-body orientation. Because translation directions were defined along axes fixed to the body and world (i.e., in body-/world-centered coordinates as opposed to head-centered coordinates), cells encoding motion in a body-centered reference frame should exhibit spatial tuning that remains invariant to changes in head-re-body orientation (Fig. 1D, blue squares). In contrast, head-centered cells should shift their spatial tuning with changes in head position to an extent that could be predicted based on the cell's PD and the amplitude and plane of head reorientation. For cells whose tuning properties were characterized fully in 3D across multiple head orientations, we quantified such spatial tuning shifts using a 3D displacement index (DI). This index, defined as the ratio of the actual change in spatial tuning compared with that predicted for head-centered tuning (ΔPDactual/ΔPDhead-centered), simultaneously took into account both the azimuth and elevation components of observed and predicted shifts (i.e., full 3D shifts in tuning) for head reorientation in a given plane (for details, see Martin et al., 2018). No shift in PD with changes in head orientation thus yielded a DI of 0 (body-centered tuning), whereas a PD shift consistent with the predictions for head-centered tuning yielded a DI of 1. In brief, the DI was obtained by first calculating an “ideal trajectory” of predicted PDs that would be obtained if the neuron's tuning shifted by different fractions of the way toward the full shift predicted for a head-centered cell (Fig. 1H, green trace). The cell's DI for head reorientation in a given plane was then obtained by computing the dot product between the actual PD observed after head reorientation (Fig. 1H; PDNEW, red cross) and each of the predicted PDs along the trajectory to find which predicted PD (corresponding to a particular DI) was the closest match to the observed PD (Fig. 1H; PDPRED, black cross). Because a given PD shift could also have components along a direction orthogonal to the “ideal trajectory,” we also estimated the angular deviation of the observed PD away from the closest predicted PD. This was done by calculating an angular error, ε, between these two directions as
To establish the significance of tuning shifts, we computed CIs for each DI (and ε values, when applicable) by using a bootstrap method based on resampling of residuals (Efron and Tibshirani, 1993). In brief, bootstrapped tuning functions for each head orientation were obtained by resampling (with replacement) the residuals of the STC model fit to the data, adding the resampled residuals to the model predicted response to create a new synthetic dataset and then fitting this dataset with the STC model to obtain a new set of model parameters. This procedure was repeated 1,000 times to obtain a distribution of tuning functions and corresponding distributions of DIs (and ε values) in each head orientation from which 95% CIs were obtained (percentile method). A DI (or ε) was considered significantly different from a particular value if its 95% CI did not include that value.
The DI analysis yielded an estimate of the extent of transformation toward body-centered coordinates for head reorientations in a given plane. In addition, to determine whether a cell could be considered more consistent with head- versus body-centered encoding of translation, we performed a second model-fitting analysis. Specifically, we simultaneously fit data collected across multiple head orientations with two different 3D STC models. These included a body-centered reference frame model in which response gains and phases were expressed in terms of motion directions defined in body-centered coordinates and a head-centered model in which gains and phases were instead expressed in head-centered coordinates. The fitting procedure was similar to that used to quantify 3D spatial tuning in a single head orientation (see above) but when extended across multiple head orientations incorporated an additional gain scaling factor to take into account any global changes in cell response gain (i.e., a general gain increase/decrease across all motion directions) associated with different head orientations (for details, see Martin et al., 2018). We then estimated the goodness of fit of each model by computing the correlation (R) between the model prediction and the data. Because the two models are themselves correlated, we removed the influence of this correlation by computing partial correlation coefficients (ρ; Eqs. 1, 2 in Statistical analysis below), which were then normalized using Fisher's r-to-Z transform. Score differences equivalent to p < 0.05 (see below) were considered significant. To visualize the results of this analysis, we constructed a scatterplot of Z-scores for the head-centered versus body-centered model fits and separated the plot into regions in which one model fit was significantly better than that of the other (Fig. 5).
Statistical analysis
All statistical tests were performed in MATLAB (The MathWorks). Bootstrap methods were used to evaluate the significance of cell modulation in response to a given stimulus as well as to evaluate the significance of tuning shifts. In brief, to establish CIs on the estimates of neural response gain and phase obtained from sine function fits to the firing rate modulation for a given motion stimulus and direction (see above), we used a bootstrap method in which bootstrapped gain and phase estimates were obtained by resampling (with replacement) the response cycles used for the sine function fits 600 times. A cell was considered to exhibit a significant modulation for a given motion stimulus if at the time of peak response, 95% CIs on the firing rate modulation were greater than a minimum of two spikes/sinusoidal cycle. The significance of changes in response tuning (i.e., estimated using STC models) was evaluated by using a bootstrap method based on resampling of residuals (Efron and Tibshirani, 1993) to create distributions of 1,000 tuning functions for each head orientation. These were used to compute corresponding distributions of PD response gain and phase changes, STC ratio changes, DIs, and ℇ values from which 95% CIs could be derived (for details, see above; Martin et al., 2018). A given parameter was considered significantly different from a particular value if the 95% CI did not include that value.
To test whether neural responses were better described by a “translation” versus “tilt” model as well as whether cell responses across head orientations were better correlated with a “head-centered” versus “body-centered” tuning model, we used partial correlation analyses that took into account correlations between the competing models themselves. In particular, to distinguish between competing models, we first computed the correlation between each model and the data. We then removed the influence of correlations between the two competing models by computing partial correlation coefficients according to the following equations:
We tested the uniformity of translational PDs (i.e., circular distributions of azimuth and elevation angles) in our sampled neural populations using Rao's spacing test (Berens, 2009). The Wilcoxon rank-sum test was used to test for significant differences between median firing rate, median CV2, and DI distributions. The Wilcoxon signed-rank test was used to compare distribution medians to specific values (e.g., DI medians to either 0 or 1). Hartigan’s dip test (Hartigan and Hartigan, 1985) was used to test distributions for multimodality. Correlations between DI and other cell tuning properties (Fig. 6) and between response gains across body orientations (Fig. 9A) and recording locations were evaluated using linear regression. For all statistical tests, p-values of <0.05 were considered statistically significant.
Results
The responses of 95 confirmed or putative Purkinje cells in the NU of the caudal vermis (42 in Monkey A, 27 in Monkey B, and 26 in monkey C) were recorded within ±4.4 mm of the midline (93% within 3 mm), 4.8–12.8 mm posterior to the abducens nuclei and at depths of 3.9 mm above to 2.1 mm below the abducens (Fig. 2A). All cells were insensitive to eye movements but responsive to passive movement stimuli provided by a 3D motion system (Fig. 1B). Quantification of the amplitude and variability of their baseline spontaneous (i.e., not motion stimulus-driven) firing activity in terms of median firing rate (mFR) and median CV2 (mCV2; see Materials and Methods; Fig. 2B) showed that our recorded cells exhibited unimodal distributions of mFR and mCV2 values (Hartigan’s dip test; mFR: dip = 0.024, p = 0.99; mCV2: dip = 0.026, p = 0.96) with ranges and means (mean [ ± SD] mFR: 48.4 ± 20.4 spikes/s; mCV2: 0.43 ± 0.11) similar to those reported previously for macaque NU Purkinje cells (Fig. 1 of Meng et al., 2015). Importantly, putative Purkinje cells (Fig. 2A,B, squares) were intermingled with and had spontaneous firing properties that could not be distinguished from those of identified Purkinje cells (Fig. 2A,B, circles; Wilcoxon rank-sum test; mFR: p = 0.54; mCV2: p = 0.83).
Recorded NU cell population characteristics. A, Recorded cell locations. Locations are expressed in anteroposterior (AP) and dorsoventral (DV) coordinates relative to the abducens nuclei (posterior/ventral negative) and in mediolateral (ML) coordinates relative to the midline (right positive). Cells are color coded according to classification type as preferentially translation coding (blue filled; N = 59), tilt coding (green; N = 19), GIA coding (orange; N = 2), composite (gray; N = 7), or unclassified (black open; N = 8). Cells with responses to translation along the vertical (0°, 90°) axis that were larger than their horizontal-plane responses to both tilt and translation were identified as “vertical” translation cells and outlined in red (N = 12). Circles and squares denote identified (N = 72) and putative (N = 23) Purkinje cells, respectively. B, Spontaneous firing properties. Scatterplot of mCV2 versus mFR calculated for all recorded cells based on their spontaneous firing activity in the absence of a motion stimulus. Colors and symbols correspond to the classifications in A. Histograms in A and B illustrate marginal distributions. Bars above each histogram indicate median values. Asterisks denote significant differences (* p < 0.05; **p < 0.01; ***p < 0.001). C, Comparison of cell horizontal-plane response gains for translation versus tilt. Plotted gains for translation and tilt correspond to estimates in the cell's maximum sensitivity direction for each stimulus in the horizontal plane. The histogram at the top right shows the distribution of tilt/translation gain ratios. Bars above the plot indicate mean values. The bottom right inset shows gain ratios for T − T, tilt, and T + T motion relative to translation for all cells (N = 65) recorded across all four motion stimuli (i.e., translation, tilt, T − T, and T + T). Colors and symbols correspond to the classifications in A. D, Distribution of PDs for translation for all translation-sensitive NU neurons whose tuning was characterized in 3D (i.e., including translation-coding, GIA-coding, composite, and unclassified cells; N = 73). Each data point in the scatterplot indicates the preferred azimuth (abscissa) and elevation (ordinate) with elevation angle spacing scaled according to Lambert's equal area projection of the spherical stimulus space. Histograms along the top and right sides of the plot show marginal distributions. Colors and symbols correspond to the classifications in A. The preferred horizontal-plane (azimuth) tilt directions for tilt-selective neurons (green symbols along 0° elevation; N = 19) and translation-sensitive neurons whose tuning was only characterized in 2D (diamonds along 0° elevation; N = 3) are also shown.
To characterize Purkinje cell SS responses to motion stimuli, we recorded neural activity as monkeys were sinusoidally translated along 13 directions spanning 3D space (Fig. 1C, blue and green lines). Most cells (86/95) were also characterized during rotations about the three cardinal (x,y,z) axes (Fig. 1C, orange arrows), and 73% (69/95) were further characterized during combined tilt/translation stimuli (“T + T” and “T − T” stimuli; see Materials and Methods) across horizontal-plane directions (Fig. 1C, green arrows). Based on these responses, cells were classified either as responding similarly to tilt and translation (i.e., like otolith afferents) such that they encoded net GIA or as preferentially encoding either translation or tilt. Cells that were neither GIA encoding nor better fit by either translation or tilt models were classified as “composite.” Comparison of the horizontal-plane sensitivities of our recorded cells to tilt versus translation (Fig. 2C) revealed that a majority of classified cells exhibited substantially larger responses to translation as compared with tilt with 68% of cells (59/87) being classified as preferentially translation encoding (Fig. 2C, filled blue symbols; mean tilt/translation gain ratio of 0.27), while 22% (19/87) were classified as tilt-encoding (Fig. 2C, filled green symbols; mean tilt/translation gain ratio of 4.2). Translation versus tilt-encoding neurons also reflected distinct patterns of response gain ratios for T − T, tilt, and T + T stimuli relative to translation (Fig. 2C, right bottom inset) with cells classified as translation coding (blue) exhibiting “V-shaped” gain ratio profiles similar to those that would be ideally predicted (i.e., T − T/translation = 1; tilt/translation = 0; and T + T/translation = 1). In contrast, cells classified as tilt coding (green) typically reflected much higher gain ratios across stimuli (note logarithmic y-axis scale) consistent with substantially larger sensitivities to tilt than translation. Notably, only two cells were classified based on their horizontal-plane responses as GIA encoding (Fig. 2C, orange circles), and both had substantially larger sensitivities to vertical-axis translation than to horizontal-plane tilt and translation stimuli. The remaining cells were characterized as composite (8%, 7/87; Fig. 2C, filled gray symbols). Thus, in agreement with previous studies (Yakusheva et al., 2007; Laurens et al., 2013; Laurens and Angelaki, 2020), most Purkinje cells in the NU reflected a solution to the tilt/translation ambiguity such that they preferentially encoded either translation or tilt.
Interestingly, translation- versus tilt-encoding cells also exhibited differences in their spontaneous firing properties and recording locations. In particular, as shown in Figure 2B, whereas translation-coding cells (blue) exhibited spontaneous firing activity that spanned the range of mFR and mCV2 values observed across the NU population, tilt cells (green) tended to reflect below average values of these measures such that median mFR and mCV2 values for tilt cells (median mFR = 31.0 spikes/s; mCV2 = 0.35) were significantly lower than those for translation-coding cells (median mFR = 46.2 spikes/s; mCV2 = 0.45; Wilcoxon rank-sum test, p = 0.0017 for mFR, p = 0.00025 for mCV2). Thus, while there was substantial overlap in their firing properties, on average tilt cells had lower and more regular firing rates than translation-coding cells with 53% of tilt cells, but only 14% of translation cells, reflecting both mCV2 and mFR values that were lower than the median NU population values. Conversely, 30% of translation cells and 0% of tilt cells had both mCV and mFR values that were higher than median NU values.
Translation- versus tilt-coding cells also differed in terms of recording locations. Translation-coding cells were broadly distributed across mediolateral (ML) and dorsoventral (DV) recording extents and just short of the full anteroposterior (AP) extent (from 5.9 to 12.8 mm posterior to the abducens; Fig. 2A, blue). However, tilt cells were located predominantly anteriorly (from 4.8 to 10.4 mm posterior to the abducens; Fig. 2A, green) and ventrally such that median AP and DV values for tilt cell location (median AP = −6.4 mm; median DV = −0.69 mm) corresponded to locations significantly more rostral and ventral than those for translation cells (median AP = −9.6 mm; median DV = 0.42 mm; Wilcoxon rank-sum test, p = 0.000023 for AP, p = 0.042 for DV). Most (74%) tilt cells were located within 8.5 mm posterior to the abducens, suggesting that they are likely to be found mainly in the nodulus (lobule X), in keeping with the observations of Laurens et al. (2013). Among translation-sensitive neurons, we also found a significant tendency for more caudal cells to have larger translation gains (r = −0.275; p = 0.035), suggesting a higher sensitivity to translation within the ventral uvula (lobule IXc,d).
The spatial tuning properties of all translation-sensitive neurons (i.e., all neurons except those classified as tilt encoding) were visualized by plotting their responses as a function of translation direction in azimuth and elevation to construct 3D tuning functions (Fig. 3A). Precise estimates of their PD for translation were computed by fitting neural responses with a 3D STC model (see Materials and Methods; Fig. 3D). As illustrated in Figure 2D, translation PDs (Fig. 2D, filled blue symbols) spanned 3D space when the head was upright and facing forward. PDs were uniformly distributed across azimuth directions but were largely concentrated in elevation within ±45° of the horizontal plane (Rao's spacing test, azimuth p = 0.5, elevation p = 0.001). Likewise, the tilt PDs of all tilt-sensitive neurons (Fig. 2D, filled green symbols), estimated using a 2D STC model, were uniformly distributed in the horizontal plane (Rao's spacing test, p = 0.5).
Example NU Purkinje cell with head-centered tuning for translation. A–C, Contour plots illustrating the cell's 3D response tuning for translation (0.5 Hz, ±9 cm, ±0.09 G) with the head upright (A) as well as after vertical-plane head reorientation 45° toward nose-down (B) and after horizontal-plane reorientation 42° to the left (C). Azimuth and elevation are expressed in body-/world-centered coordinates. Star: PD; pink circle: predicted PD for head-centered tuning; blue square: predicted PD for body-centered tuning. D, The cell's preferred translation direction (star) for each head orientation was estimated by fitting a 3D STC model to cell response gain and phase data (black circles) across stimulus directions (here illustrated for the upright orientation). E, IFRs (top) and STC model fit to gains and phases across elevations (bottom) for an azimuth angle of 45° (i.e., along dashed white line in B) with the head upright (blue lines and symbols) and after reorientation toward nose-down (red lines and symbols). F, IFRs (top) and STC model fit to gains and phases across azimuth angles (bottom) for 0° elevation (i.e., along dashed white line in C) with the head upright and forward (blue lines and symbols) and after reorientation to the left (green lines and symbols). Dashed black curves in E and F show the predictions for head-centered tuning. Dotted black lines: zero firing rate/stimulus amplitude.
Reference frames for encoding otolith signals during translation
To investigate the reference frames in which NU Purkinje cells encode otolith signals during translation, head- and body-centered reference frames were dissociated by comparing spatial tuning with the head upright to that after head reorientation relative to the body in vertical and/or horizontal planes (Fig. 1D). Because translation directions were defined in a coordinate frame that remained fixed to the body/world, the spatial tuning of a neuron encoding translation in body-centered coordinates should be invariant to changes in head-re-body position (Fig. 1D, blue squares). In contrast, cells encoding translation in head-centered coordinates (i.e., like vestibular afferents) should exhibit systematic shifts in preferred tuning with changes in head orientation (Fig. 1D, pink circles).
To quantify spatial tuning shifts across the neural population, we computed DIs for each cell and plane of head reorientation that expressed the extent of the cell's tuning shift as a fraction of that predicted for head-centered tuning. In the majority of cases (N = 41/49 head reorientations), PD shifts were quantified fully in 3D, taking into account the extent of shift in both azimuth and elevation along the “ideal trajectory” for a transformation between head- and body-centered coordinates (i.e., the DI; Fig. 1H, green trace). In addition, we quantified the angular displacement orthogonal to this trajectory (Fig. 1H, angular deviation error, ε; see Materials and Methods). A DI of 1 (and ε of 0) indicates a tuning shift equivalent to that predicted for head-centered tuning, whereas a DI of 0 indicates no shift, consistent with body-/world-centered coding.
Figure 3 illustrates a representative NU Purkinje cell. With the head in the upright orientation, the PD of the cell was 58.8° in azimuth and 20.9° in elevation (Fig. 3A, white star). However, after vertical-plane head-re-body reorientation by 45° toward nose-down, the cell's PD shifted by −23.5° in elevation and −10.7° in azimuth. This is close to the predictions for head-centered encoding of translation as illustrated in the contour plot of Figure 3B (star closer to pink circle than blue square) and STC model fits to the data across elevations in the 45° azimuth plane (Fig. 3E, bottom; red curve close to black dashed curve). Similarly, after head reorientation in the horizontal plane by 42° to the left, the cell's PD shifted by 45.1° in the same direction as the head (Fig. 3C,F). Shifts in both planes were consistent with encoding of translation in a mainly head-centered reference frame as reflected by DIs close to 1 (DIvert = 0.90; DIhor = 1.07) and small ε values (εvert = 5°; εhor = 4°).
Similar to the example cell of Figure 3, NU cells generally exhibited tuning properties that were more consistent with head-centered coding. This is shown in Figure 4, which summarizes the distributions of DIs (Fig. 4A) and ε values (Fig. 4C, top, green) for all NU cells tested across head reorientations in the vertical and/or horizontal planes. Also shown for comparison are the DI and ε distributions for rFN and VN cells from the prior study of Martin et al. (2018) (Fig. 4B and C, bottom, red: rFN; blue: VN). DI distributions for NU cells reflected median DI values that were close to 1 for reorientation in both planes (Fig. 4A; DIvert = 0.79; DIhor = 0.94), while mean absolute ε values were close to 0 (Fig. 4C, top; mean ε = 4.7° across both planes). In line with this, 87% (20/23) of DI values for horizontal-plane reorientation were statistically indistinguishable from 1, and while this percentage was slightly lower for vertical-plane reorientation (62%, 16/26), there was no significant difference in the DI distributions for reorientation in vertical versus horizontal planes (Wilcoxon rank-sum test, p = 0.11). For the subset of cells recorded across head reorientations in both planes (N = 17), no correlation was found between their horizontal- and vertical-plane DI values (r = −0.32, p = 0.22). Notably, DI values for NU cells closely resembled those previously reported for rostral VN cells, which were found to be predominantly head-centered (Martin et al., 2018; Fig. 4B, bottom, blue). No significant difference was found in the DI distributions of the two populations (Wilcoxon rank-sum test, p = 0.94). In contrast, the DI distribution of rFN cells was substantially more broadly distributed between body- and head-centered reference frames (Fig. 4B, top, red) with a median DI value (0.61) that was significantly lower than that of NU cells (Wilcoxon rank-sum test, p = 0.000001). NU cell translation responses thus reflected a coding of otolith signals that was significantly more head-centered than that of rFN neurons.
Distribution of DI and ε values for the spatial tuning of otolith signals during translation across changes in head-re-body orientation. DI values of 0 and 1 indicate tuning shifts consistent with body- and head-centered encoding of otolith signals, respectively. A, DI distribution for NU cells for vertical-plane (top histogram; N = 26) and horizontal-plane (bottom histogram; N = 23) head reorientations. B, Combined vertical- and horizontal-plane DI distributions for rFN cells (top histogram, red; vertical, N = 47; horizontal, N = 27) and VN cells (bottom histogram, blue; vertical, N = 16; horizontal, N = 8) replotted from the study of Martin et al. (2018). DIs in A and B are classified based on bootstrapped DI 95% CIs as head-centered (dark colors), body-centered (pale colors), or intermediate (hatched). Cells for which bootstrapped DIs included both 0 and 1 were labeled as unclassified (black). Vertical bars above each plot indicate the medians of the populations. C, Distributions of absolute ε values across both vertical- and horizontal-plane head reorientations. The top histogram shows the ε value distribution for NU cells (green), while the bottom histogram illustrates those for rFN (red) and VN (blue) cells replotted from the study of Martin et al. (2018). Dark colors indicate a significant difference from zero (N = 6 of 41 cases for NU; N = 16 of 62 cases for rFN; N = 7 of 20 cases for VN). Vertical bars above the plot indicate the means of each distribution.
This distinction in tuning properties across brainstem–cerebellar regions was further emphasized when responses were compared using a model-fitting analysis. Specifically, the DI analysis provided a model-independent characterization of tuning shifts. CIs on DI values obtained through bootstrap analyses (see Materials and Methods) provided an indication of whether those shifts could be considered statistically different from either head- or body-centered coding (i.e., DI of 1 or 0). However, a limitation of this approach for classifying cells is that the size of the CIs on our DI values was influenced by the quality of our STC fits in each head orientation. Consequently, a cell with a DI close to but slightly <1 (e.g., 0.8) could be classified as intermediate (i.e., DI statistically different from both 1 and 0) if the STC function provided an excellent fit (and very narrow DI CIs), while a second cell with the same DI but a poorer STC function fit would be more likely to be classified as head-centered (i.e., DI not statistically different from 1). Furthermore, because the DI analysis considered tuning shifts in only one plane of head reorientation at a time, it thus provided little insight as to how a given cell should be classified when considered fully in 3D. Thus, to address these issues, we performed a second model-fitting analysis that provided another means of classifying cell spatial tuning properties. This analysis assessed whether the tuning of each cell was best explained by a body- versus a head-centered model by fitting neural responses with each of these models across multiple head orientations (see Materials and Methods).
For comparison with the DI results, we first fit each model to the data across two head orientations in a single plane (i.e., across upright and ear-/nose-down orientations or across upright and left orientations). The goodness of fit of each model was quantified using a partial correlation analysis. To facilitate interpretation and visualization of the results, partial correlation coefficients (normalized using Fisher's r-to-Z transform) for fits of the head-centered model were plotted versus those for the body-centered model (Fig. 5A). Cells in the upper-left region of the plot were significantly better fit by the head-centered model, whereas those in the lower-right region were significantly better fit by a body-centered model. Cells falling in the central diagonal region were not better fit by one model as compared with the other and were classified as “intermediate.”
Correlation of otolith spatial tuning with head-centered and body-centered models. A, B, Scatterplots of head- versus body-centered model partial correlation coefficients (Z-transformed) when translation response gains and phases for NU cells (green) were fit with each model across either (A) two head orientations (circles: upright and after vertical-plane reorientation, N = 26; squares: upright and after horizontal-plane reorientation, N = 23) or (B) three head orientations (upright and after vertical and horizontal-plane reorientations, N = 17). Corresponding results for model fits to rFN (red; N = 25) and VN (blue; N = 7) cells from the study of Martin et al. (2018) are shown superimposed in B for comparison. Significance regions are based on the difference between head- and body-centered model fit Z-scores corresponding to p < 0.05 (top left: head-centered; bottom right: body-centered; middle diagonal region: not significantly better correlated with either model and classified as “intermediate”). Gray lines in A link data points associated with the same cell for head reorientation in different planes.
Using this approach, we found that all (100%; 23/23) NU neurons were better fit by a head-centered model for horizontal-plane head reorientation (Fig. 5A, open green squares). Similarly, for vertical-plane reorientation, a majority of cells (85%; 22/26) were classified as head-centered, while the remaining 15% (4/26) were classified as intermediate (Fig. 5A, filled green circles). The predominance of head-centered translation coding was further emphasized when the model-fitting analysis was extended across all three head orientations for the subset of cells (N = 17) characterized for reorientations in both vertical and horizontal planes. The results of this analysis are shown in Figure 5B, superimposed on the results of a similar analysis previously reported for rFN and rostral VN cells (Martin et al., 2018). All NU cells characterized fully in 3D (Fig. 5B; green circles) were classified as head-centered. In marked contrast, rFN cells were broadly distributed across categories with 52% of cells classified as either intermediate or body-centered. Consequently, when examined fully in 3D, NU cells could not account for the spatial tuning properties observed across the rFN population.
Importantly, although NU spatial tuning properties were generally inconsistent with transforming otolith signals toward body-centered coordinates, this does not necessarily rule out a role for these cells in the required transformations. In particular, theoretical studies have shown that cells at intermediate stages of neural networks involved in computing reference frame transformations often reflect posture-dependent changes in response gain (i.e., “gain fields”; Zipser and Andersen, 1988; Salinas and Abbott, 1995, 1996; Pouget and Sejnowski, 1997; Xing and Andersen, 2000; Deneve et al., 2001; Blohm et al., 2009). Thus, as a next step, we also examined how cell response gains and phases in the cell's PD changed across head orientations (Fig. 6A).
Dependence of translation tuning parameters on head orientation. Tuning parameters after head reorientation relative to the body in the vertical (circles) and horizontal (squares) planes are plotted versus the corresponding values with the head upright and straight forward. A, Gain in the maximum response direction. B, Phase in the maximum response direction. C, STC ratio. Filled symbols indicate significant differences after head reorientation as compared with upright/forward. Dashed line: unity slope.
We found that many cells exhibited changes in response gain that reached significance in 44% of cells (bootstrap analysis; 95% CIs on changes did not include 0). However, these changes were typically very small (average 13% or 2.9 ± 2.4 spikes/s change from upright corresponding to a 0.32% change per degree of change in head angle). Furthermore, while comparable in size to the gain changes previously reported in the rFN and VN (0.36%/° in rFN and 0.24%/° in VN; Martin et al., 2018), they were substantially smaller than the posture-dependent gain fields observed in cortical areas that have been implicated in reference frame transformations (e.g., ≈1%/° eye position in LIP and 1–3%/° in area 7a: Andersen et al., 1985, 1990; 1.7%/° head/body-re-world position in area 7a: Snyder et al., 1998; 2%/° hand position and 3.4%/° eye position in PRR: Chang et al., 2009). No correlation was found between DI and the extent of gain change for reorientation in either horizontal or vertical planes (horizontal: r = 0.12, p = 0.58; vertical: r = −0.02, p = 0.94). Other tuning properties varied little across head orientations, with a minority of cells showing significant changes in response phase (6.25%; Fig. 6B) or in the ratio of minimum to maximum response gain (STC ratio; 18.8%; Fig. 6C). Consequently, NU cells not only exhibited spatial tuning consistent with head-centered encoding of translation but showed little evidence for head-orientation-dependent changes in activity that might be expected at intermediate stages of a reference frame transformation.
Spatial transformation of canal signals
The above results provide evidence that, like otolith afferents, NU cells encode otolith signals predominantly in a head-centered reference frame. However, unlike otolith afferents, which respond similarly to tilts and translations, most NU cells preferentially encode either translation or tilt (Fig. 2C). Previous studies have shown that NU Purkinje cells reflect a solution to the tilt/translation ambiguity obtained by combining otolith signals with canal signals that have been spatially transformed into estimates of tilt relative to gravity (Yakusheva et al., 2007; Laurens et al., 2013). That is, in agreement with theoretical predictions (Green and Angelaki, 2004, 2007), canal signals in the NU are not head-centered but instead have been transformed into an estimate of the earth-horizontal component of rotation. However, whether such canal-derived tilt estimates are encoded in head- versus body-centered coordinates remains unknown. Importantly, to reliably estimate translation, canal-derived tilt estimates must be appropriately matched to otolith signals across horizontal-plane changes in head orientation with respect to the body.
To confirm that this was indeed the case for NU translation-selective neurons, as well as to investigate the reference frames in which tilt-selective neurons encode motion, we characterized the spatial tuning of canal signals for a subset of recorded NU cells (30/95) across changes in body and/or head orientation. Cells were examined not only during translations but also during tilts and additive/subtractive combinations of tilt and translation stimuli (“T − T” and “T + T”; see Materials and Methods; Fig. 1E). Among these, the T − T stimulus is of particular relevance because it produces a net GIA of zero along the motion axis and thus no dynamic activation of otolith afferents tuned for that axis (Angelaki et al., 2004). This stimulus thus provides a means of isolating semicircular canal contributions to the cell's response. To confirm that, as previously reported (Yakusheva et al., 2007; Laurens et al., 2013), the canal signals carried by NU cells had been spatially transformed into true 3D estimates of tilt (i.e., as opposed to reflecting head-centered rotation signals), cell responses were characterized for earth-vertical-axis rotation (EVAR) and for combinations of tilt and translation stimuli both with the head/body upright and after the whole body was statically reoriented by 45° relative to gravity. Importantly, we compared cell responses to tilt and translation stimuli along the axis closest to the cell's PD for T − T with the body upright to those along the same axis after the body was statically reoriented along a perpendicular direction (e.g., body reorientation along the y-axis for a T − T PD close to the x-axis; Fig. 1Fi,ii). Consequently, the dynamic linear acceleration stimulus to the otoliths was similar across body orientations. In contrast, tilts stimulated different sets of canals in the different body orientations (i.e., mainly vertical canals with the body upright but a combination of vertical and horizontal canals after whole-body reorientation). Despite the different patterns of canal activation, cells carrying canal signals that had been transformed into true 3D tilt estimates should respond in the same way to tilt and to combined tilt/translation stimuli across body orientations while remaining unresponsive to EVAR. Furthermore, cells encoding such canal-derived tilt estimates in head-centered coordinates should reflect spatial tuning for the T − T stimulus (i.e., which isolates canal signals during earth-horizontal-axis rotation) that shifts with the head when it is reoriented relative to the body in the horizontal plane (Fig. 1Fiii).
Figure 7 shows an example translation-selective NU Purkinje cell whose responses to translation, tilt, and combined tilt/translation stimuli were characterized when upright as well as after whole-body reorientation relative to gravity and head-re-body reorientation in the horizontal plane. In the upright orientation, this cell responded robustly to translation but exhibited little response to tilt (Fig. 7Ai). When examined across horizontal-plane directions, the cell's translation response was largest for motions close to the 0° azimuth axis (Fig. 7C, left, blue trace). Consistent with this cell's selectivity for translation, responses during T + T and T − T stimuli were similar to those during translation (Fig. 7Ai). Furthermore, the spatial tuning and temporal properties of T − T responses (Fig. 7C, right, blue trace) were closely aligned with those during translation, illustrating that the earth-horizontal canal and otolith components of the cell's response were matched in the appropriate fashion to distinguish tilts and translations. No response was observed during rotations about an earth-vertical axis (Fig. 7Bi).
Example translation-encoding NU Purkinje cell reflecting a canal-derived tilt signal component encoded in head-centered coordinates. A, IFR during translation (0.5 Hz, ±9 cm, ±0.09 G), tilt (0.5 Hz, ±5.19°, ±0.09 G), T + T (±0.18 G), and T − T (0 G) stimuli with the head upright (i), after whole-body reorientation by 45° toward ear-down (ii), and after head-re-body reorientation in the horizontal plane by 45° to the left (iii). Illustrated responses are for tilt and translation stimuli applied along the head x-axis, which is aligned with the 0° azimuth direction in body coordinates in i and ii and the 45° azimuth direction in body coordinates after the head is reoriented relative to the body in iii. Black traces represent sinusoidal fits to IFRs. The stimulus traces (bottom) show tilt angular position (green), translational acceleration (blue), and net GIA (red). B, IFR responses during EVAR (0.5 Hz, ±31.4°/s, ±10°) with the head upright (i) and after whole-body reorientation by 45° toward ear-down (ii). The stimulus traces (bottom) show earth-vertical angular position (orange). Dotted black lines in A and B: zero firing rate/stimulus amplitude. C, STC model fits to response gains and phases across horizontal-plane azimuth angles for translation (left) and T − T (right) stimuli with the head/body upright and forward (blue lines and symbols) and after head-re-body reorientation by 45° to the left (red lines and symbols). Gains and phases are expressed relative to translational acceleration. Dashed black curves in C indicate the predictions for head-centered tuning.
Similar observations were made after whole-body reorientation relative to gravity by 45° toward left-ear-down (i.e., along the 90° azimuth or y-axis). The cell remained selectively responsive to translation (Fig. 7Aii), exhibiting responses to tilts and translations along the 0° azimuth direction (i.e., x-axis) that were similar to those in the upright orientation. Furthermore, it responded robustly to T − T motion but remained unresponsive to EVAR (Fig. 7Bii), even though this stimulus now activated the vertical canals—a canal stimulus to which the cell had responded robustly during upright T − T motion (Fig. 7Ai, fourth column). These observations confirm that the cell's response did not simply reflect head-centered canal signals but instead canal signals that had been spatially transformed into estimates of the earth-horizontal component of rotation (i.e., tilt), as required to resolve the tilt/translation ambiguity in 3D. Most importantly, when the head was reoriented relative to the body by 45° in the horizontal plane (Fig. 7Aiii), not only did the cell's PDs for translation shift with the head by 42° (DI of 0.93) toward the prediction for head-centered coding (Fig. 7C, left, red trace closely aligned with black dashed trace) but the cell's PD for T − T shifted to a similar extent (43°; DI of 0.96; Fig. 7C, right). Neither DI was statistically different from 1 (bootstrap test; 95% CIs included 1). Consequently, this cell encoded both otolith signals and canal-derived tilt signals in a head-centered reference frame.
Similar conclusions were reached for tilt-selective neurons as illustrated for the example Purkinje cell in Figure 8. In contrast to the translation-encoding neuron of Figure 7, this cell responded robustly to all stimuli involving tilt but exhibited little response to pure translation (Fig. 8Ai). Like the cell of Figure 7, however, this tilt-selective cell exhibited little response to EVAR both upright and after whole-body reorientation (Fig. 8B). Furthermore, its responses to tilt remained consistent after whole-body reorientation (Fig. 8Aii), revealing that it did not simply encode head-centered vertical canal signals but instead a combination of vertical and horizontal canal-derived signals that had been spatially transformed into an estimate of reorientation relative to gravity. Most importantly, when the head was reoriented in the horizontal plane (Fig. 8Aiii), the cell's spatial tuning for tilt and T − T stimuli shifted with the head (Fig. 8C) consistent with the predictions for head-centered tilt coding (tilt DI: 0.99; T − T DI: 0.94).
Example tilt-encoding NU Purkinje cell. A, IFR during translation (0.5 Hz, ±9 cm, ±0.09 G), tilt (0.5 Hz, ±5.19°, ±0.09 G), T + T (±0.18 G), and T − T (0 G) stimuli with the head upright (i), after whole-body reorientation by 45° along the 135° azimuth direction (ii), and after head-re-body reorientation in the horizontal plane by 45° to the left (iii). Illustrated responses are for tilt and translation stimuli applied along the head 45° azimuth axis, which is aligned with the body 45° azimuth direction in i and ii and the 90° body azimuth direction after the head is reoriented relative to the body in iii. Black traces represent sinusoidal fits to IFRs. The stimulus traces (bottom) show tilt angular position (green), translational acceleration (blue), and net GIA (red). B, IFR responses during EVAR (0.5 Hz, ±31.4°/s, ±10°) with the head upright (i) and after whole-body reorientation by 45° along the 135° azimuth direction (ii). The stimulus traces (bottom) show angular position (orange). Dotted black lines in A and B: zero firing rate/stimulus amplitude. C, STC model fits to response gains and phases across horizontal-plane azimuth angles for tilt (left) and T − T (right) stimuli with the head/body upright and forward (blue lines and symbols) and after head-re-body reorientation by 45° to the left (red lines and symbols). Gains and phases are expressed relative to the acceleration due to tilt. Dashed black curves in C indicate the predictions for head-centered tuning.
Figure 9 summarizes the responses observed for the subset of NU cells examined for different combinations of tilt and translation motions across changes in whole-body orientation (N = 22). As shown in Figure 9A, response gains for the different motion stimuli were similar across whole-body orientations, reflecting population regression slopes across stimuli that were close to and not statistically different from one for otolith and canal response components considered individually (translation slope: 0.96, CI: [0.88,1.05]; T − T slope: 0.89, CI: [0.72,1.05]; all stimuli slope: 0.91, CI: [0.86,0.97]). Furthermore, for translation-sensitive neurons, otolith and canal-derived tilt signals remained appropriately amplitude matched (i.e., as required to estimate translation) as reflected in ratios of their response gains during T − T as compared with translation (T − T/translation) that were distributed close to 1 both upright and after whole-body reorientation (mean upright: 0.89; body reoriented: 0.94).
NU Purkinje cells reflect the computations to estimate tilt and translation across substantial changes in whole-body orientation. A, Response gains after whole-body reorientation relative to the gravity for translation (blue), tilt (black), T + T (green), and T − T (red) stimuli plotted versus the corresponding gains with the whole-body upright (N = 25 reorientations across 22 cells). Response gains in both body orientations are for motions along the axis (0, 45, 90, 135°) closest to the cell's upright horizontal-plane PD for the T − T stimulus. The whole-body was reoriented by 45° along the axis perpendicular to this PD direction (Fig. 1Fi,ii). The top inset shows the distribution of T − T/translation gain ratios with the head upright (gray) as compared with after body reorientation (red) for all translation-sensitive cells (i.e., all except tilt cells; N = 11 cells and 14 reorientations). Vertical bars above the plot indicate distribution means. B, Cell response gain for canal stimulation during EVAR plotted versus canal response gain for earth-horizontal-axis rotation during T − T motion with the head upright (gray; N = 20) and after whole-body reorientation (red; N = 22 reorientations across 20 cells). The T − T motion direction and body reorientation axis for each cell were the same as in A. Top inset shows the distribution of EVAR/T − T canal gain ratios with the head upright (gray) as compared with after body reorientation (red). Vertical bars above the plot indicate distribution means. Dark gray/red: translation cells; pale gray/red: tilt cells.
More direct evidence that recorded NU cells carried a canal-derived tilt estimate was obtained by comparing their responses to canal stimulation during EVAR to those during earth-horizontal-axis rotation using the T − T stimulus (Fig. 9B). Cells reflecting such a tilt estimate should respond during T − T motion but should not respond to EVAR. Consistent with this, in the upright orientation, NU cells exhibited negligible responses to EVAR, which stimulated mainly the horizontal canals, but substantial responses to T − T motion, which stimulated mainly the vertical canals (Fig. 9B, gray circles). This was reflected in a mean EVAR/T − T ratio of 0.11 (Fig. 9B, inset, gray). Similarly, after whole-body reorientation, cells continued to reflect negligible responses to EVAR even though in the new body orientation EVAR now activated both vertical and horizontal canals (Fig. 9B, red circles). Importantly, after whole-body reorientation by 45°, both EVAR and T − T motion activated the vertical (and horizontal) canals to similar extents. Thus, if the responses to T − T motion observed when upright were due to head-centered vertical canal signals, after whole-body reorientation responses to EVAR and T − T motion should have been similar in amplitude (i.e., EVAR/T − T ratio close to 1). In contrast, EVAR/T − T ratios after reorientation remained close to zero (mean EVAR/T − T of 0.20) consistent with the transformation of canal signals on these cells into true estimates of dynamic tilt.
Finally, to investigate whether NU cells encoded canal-derived tilt signals in head- versus body-centered coordinates, their spatial tuning in the body upright orientation with the head facing forward was compared with that after head reorientation to the left. As illustrated in Figure 10A, DIs for responses to T − T motion (i.e., canal-derived estimates of tilt) were narrowly distributed about 1 consistent with head-centered coding (median DI of 1.01 not different from 1; Wilcoxon signed-rank test, p = 0.96). Furthermore, model fits across horizontal-plane head orientations revealed that cell responses to T − T motion were significantly better correlated with a head-centered as compared with a body-centered model (Fig. 10B). Consequently, like otolith signals, canal-derived estimates of tilt relative to gravity were encoded in head-centered coordinates.
Head-centered coding of canal-derived tilt signals. A, Distribution of DI values for the canal-derived tilt component of NU cell responses (isolated during T − T motion) across changes in head orientation in the horizontal plane (N = 17, including 11 translation and 6 tilt cells). DIs were classified based on bootstrapped DI 95% CIs as head-centered (dark colors), body-centered (pale colors), or intermediate (hatched). The vertical bar above the plot indicates the population median. B, Correlation of NU canal-derived tilt signals (i.e., during T − T motion) with head- and body-centered models. The plot shows partial correlation coefficients (Z-transformed) for head-centered versus body-centered model fits across two head-re-body orientations (upright and after horizontal-plane reorientation). Significance regions are based on the difference between head- and body-centered model fit Z-scores corresponding to p < 0.05 (top left: head-centered; bottom right: body-centered; middle diagonal region: not significantly better correlated with either model and classified as “intermediate”). Dark green: translation cells; pale green: tilt cells.
Discussion
Activities such as postural control (Karmali et al., 2021; Mildren and Cullen, 2023), navigation (Yoder and Taube, 2014), spatial perception (Clemens et al., 2011; Gu, 2018), and voluntary movement (Moreau-Debord et al., 2014; Blouin et al., 2015) rely on estimates of our body's motion and orientation in space. Vestibular signals are essential for such estimates, but the motions associated with each sensory signal must be correctly interpreted and transformed into body-centered coordinates.
Here, we examined for the first time whether the NU of the posterior vermis—regions implicated in resolving the otolith tilt/translation ambiguity—reflect body-centered motion coding. Unlike neurons downstream in the rFN, many of which reflect transformation of vestibular signals toward body-centered coordinates (Kleine et al., 2004; Shaikh et al., 2004; Martin et al., 2018), NU cells encoded head-centered otolith signals. Furthermore, consistent with computations to resolve the tilt/translation ambiguity (Merfeld et al., 1993; Green and Angelaki, 2004, 2007; Laurens and Angelaki, 2017), canal signals in the NU had been spatially transformed into world-/gravity-referenced rotation estimates, signaling dynamic tilt (Yakusheva et al., 2007; Laurens et al., 2013). However, these tilt estimates shifted with head-re-body position in the horizontal plane indicating encoding in head-centered coordinates. These results thus imply that body-centered estimates of motion and orientation are computed elsewhere, either by further transformation of NU outputs or via parallel computations in other regions.
Estimates of translation and tilt in the NU
Compatible with previous investigations (Yakusheva et al., 2007; Laurens et al., 2013), most Purkinje cells in the primate NU could be categorized as translation or tilt encoding, with only a minority (10%) not better correlated with either motion or the net GIA. They also exhibited little response to earth-vertical-axis rotation, regardless of body-re-gravity orientation, but responded robustly to canal stimulation during earth-horizontal-axis rotation from upright (i.e., T − T motion; Yakusheva et al., 2007). Here, we further show that canal-derived responses to earth-horizontal-axis rotation remain consistent across substantial changes in body-re-gravity orientation, confirming that both vertical and horizontal canal signals are combined and spatially transformed into estimates of tilt with respect to gravity.
Laurens et al. (2013) first reported tilt-encoding cells in the NU, providing evidence for the 3D computations to estimate reorientation relative to gravity by demonstrating similar responses to sinusoidal tilts from upright and to tilt produced by constant-velocity yaw rotation about an axis tilted 10° from upright. The stimuli used in the current experiments extend these findings by explicitly isolating the canal signal contributions to these computations (i.e., using the T − T stimulus) and confirming not only that they have been spatially transformed into tilt estimates but also that canal and otolith signals remain appropriately matched to resolve the tilt/translation ambiguity over a broad range of body orientations. Thus, our observations complement previous evidence that NU Purkinje cells reflect the output of the 3D computations for tilt/translation discrimination (Yakusheva et al., 2007; Laurens et al., 2013).
Most importantly, however, we show that translation and tilt estimates in the NU are encoded in head-centered coordinates. This emphasizes a critical distinction in the reference frames associated with the motion representations NU cells encode (i.e., translation and tilt) versus those of the sensory signals (i.e., otolith and canal) used to compute them. Specifically, resolving the tilt/translation ambiguity requires transforming canal signals into a specific world-/gravity-referenced rotation signal—the earth-horizontal component of rotation (i.e., dynamic tilt). However, the tilt estimates resulting from those canal transformations are head-centered—their tuning remains fixed to a particular head axis across changes in static head-re-body orientation. Thus, NU cells encode tilt signals relevant for estimating head orientation with respect to gravity.
Distinct pathways for computing head- versus body-centered motion estimates?
If translation and tilt estimates in the NU are head-centered, then where are body-centered estimates computed? One possibility is the rFN, where many neurons reflect a vestibular transformation toward body-centered coordinates (Kleine et al., 2004; Shaikh et al., 2004; Martin et al., 2018). However, there is evidence to suggest that at least part of the transformation of rotation signals occurs upstream in the AV (Manzoni et al., 1998; Manzoni et al., 1999). Many AV cells also combine dynamic neck proprioceptive and vestibular signals to encode representations intermediate between head and body rotation (Zobeiri and Cullen, 2022). While AV cells have not yet been characterized during translational motion, a similar role for the AV in the head-to-body transformation of translation estimates is compatible with our recent suggestion that the required computations largely occur upstream in the cerebellar cortex (Martin et al., 2018). Here, we show that they do not occur in the NU, suggesting that they instead occur either in the AV or in a distributed AV–rFN circuit. But if the computations take place largely upstream in the AV, how then do rFN cells also inherit at least a partial solution to the tilt/translation ambiguity?
It has been suggested that tilt and translation estimates are conveyed to the rFN via direct projections from the NU (Angelaki et al., 2010). However, while the most rostral portions of the FN implicated in body postural control and locomotion receive abundant AV projections (Haines, 1976; Armstrong and Schild, 1978; Fujita et al., 2020), the NU projects primarily to more caudal and/or ventral FN regions (Haines, 1977; Armstrong and Schild, 1978; Dietrichs, 1983; Wylie et al., 1994) targeting populations that, at least in rodents, appear largely (Fujita et al., 2020), although not necessarily completely (Gruver et al., 2024) distinct from those receiving AV projections. Consequently, while most translation-responsive neurons in Martin et al. (2018) likely received projections from the AV, it remains unclear to what extent the cells described in that study or others of the primate rFN (Zhou et al., 2001; Kleine et al., 2004; Shaikh et al., 2004; Mackrous et al., 2019) received direct NU projections. Alternatively, therefore, the rFN may inherit a solution to the tilt/translation ambiguity from the NU only indirectly via brainstem circuits and the AV (Ruggiero et al., 1977; Kotchabhakdi and Walberg, 1978; Lee et al., 2014), where translation and tilt estimates are integrated with proprioceptive signals and further transformed.
Another intriguing possibility, however, is that a solution to the tilt/translation ambiguity is independently computed in the AV itself. Indeed, vestibular processing through at least partially distinct cerebellar cortical pathways may also explain other distinctions in NU versus rFN motion representations. Whereas most NU cells can be classified as predominantly tilt or translation coding, rFN properties are more broadly distributed with many cells responding substantially but unequally to both motions (Angelaki et al., 2004; Green et al., 2005) and/or to earth-vertical-axis rotation (Siebold et al., 1997; Zhou et al., 2001; Shaikh et al., 2005a). These more complex properties may reflect body motion representations for different behaviors (e.g., trunk postural control, reaching, and locomotion), where estimates of pure translation or tilt about head-centered axes are less relevant. In principle, such representations could arise by combining tilt and translation estimates computed in the NU, and conveyed either directly or indirectly via the vestibular nuclei to the rFN, with other more afferent-like vestibular signals. Alternatively, they might reflect vestibular processing through different cerebellar pathways (e.g., the AV). Future work examining evidence for a 3D solution to the tilt/translation ambiguity and vestibular reference frames in the AV versus rFN will help distinguish these possibilities.
Collectively, these observations and our current findings lead us to hypothesize that there exist largely distinct cerebellar pathways/modules for computing head- versus body-centered motion representations, each reflecting at least a partial solution to the tilt/translation ambiguity and subserving distinct functional roles. In particular, head-centered NU translation and tilt estimates may play a primary role in stabilizing the head and gaze in space, forming a stable earth-horizontal platform for integrating visual and vestibular cues that serves as a reference for perception of motion and orientation relative to the external world—essential for both motor (e.g., postural control; Massion, 1994) and more cognitive functions (e.g., navigation; Yoder and Taube, 2014; Laurens et al., 2016). Such a role is consistent with NU projections to brainstem nuclei, which mediate vestibulocollic reflexes and eye movement control (Barmack, 2003; Meng et al., 2014) and with deficits after NU lesions (Dow, 1938; Angelaki and Hess, 1995; Wearne et al., 1998; Tarnutzer et al., 2015).
In contrast, pathways through the AV and rFN may play a more direct role in maintaining body postural equilibrium (Massion, 1994; Horak and Macpherson, 1996) and in estimating body motion for heading perception (Gu, 2018), path integration (Rochefort et al., 2013), and goal-directed action (Medendorp and Selen, 2017; Martin et al., 2021). This is consistent with rFN projections to brainstem regions involved in postural control and locomotion (Batton et al., 1977; Homma et al., 1995; Fujita et al., 2020) and to thalamic nuclei projecting to parietal areas that encode body-centered motion (Akbarian et al., 1992; Meng et al., 2007; Chen et al., 2013). Future work further exploring the nature of motion representations within different cerebellar pathways and their downstream targets will be important to elucidate their functional contributions to a broad range of behaviors.
Footnotes
This work was supported by an operating grant from the Canadian Institutes of Health Research (CIHR; PJT-153257), an infrastructure grant from the Canadian Foundation for Innovation (CFI), and a CIHR PhD fellowship to C.Z.M. and CIHR MSc and FRQS PhD fellowships to F.B. We thank P. Cisek for comments on the manuscript and M. Latourelle for excellent technical assistance.
↵*F.B. and C.Z.M. contributed equally to this work.
The authors declare no competing financial interests.
- Correspondence should be addressed to Andrea M. Green at andrea.green{at}umontreal.ca.
