Ground-truth encoding of self-motion in the primate cerebellar nodulus and uvula

Domain: chemistry
Published: 2026-02-25
Editorial outcome: minor_revision

Abstract
Accurate internal estimates of self-motion and orientation relative to gravity are fundamental for stabilizing gaze, controlling posture, and navigating through dynamic environments. Prevailing theories propose that the cerebellar nodulus and uvula (NU) employ internal models to suppress sensory input arising from predictable, self-generated motion. However, this assumption has never been directly tested. Here, we recorded NU Purkinje cell activity in rhesus monkeys during active and passive head movements. We found neurons responsive to passive translations remained equally sensitive to self-generated movements, encoding net head motion in space irrespective of its source. Furthermore, external perturbation did not influence these ground-truth encoding. When active head motion was blocked, Purkinje cell activity remained unchanged – demonstrating a lack of efference copy integration. During active tilts, NU neurons encoded both dynamic motion and static orientation relative to gravity. These findings challenge the internal model hypothesis and establish the NU as a ground-truth, context-invariant estimator of self-motion, supporting stable behavior in dynamic environments.

Introduction
To successfully navigate the world, the brain must maintain accurate estimates of self-motion and spatial orientation relative to gravity to stabilize gaze and posture. These estimates are computed by integrating multimodal sensory information – including vestibular (i.e., semicircular canal and otolith), visual, somatosensory, and motor-related signals1–4. During everyday behaviors, much of this sensory feedback arises from active exploration, where distinguishing between inputs generated by our own actions and those that are externally driven or unexpected is essential for perceptual stability and accurate motor control (reviewed in Brooks and Cullen5). Recent evidence suggests cerebellar circuits in the anterior vermis use efference copies of motor commands to build forward internal models that predict the sensory consequences of behavior6. This computation underlies the suppression of expected reafferent signals downstream in the cerebellar output nuclei7–10, resulting in selective encoding of sensory prediction errors generated by unexpected perturbations and motor errors – a framework often assumed to apply across the cerebellum.

However, beyond signaling unexpected events to drive reflex responses for balance, the brain must also maintain a stable, context-invariant estimate of self-orientation and motion to support functions such as spatial awareness, arousal, and autonomic regulation. How the brain meets these competing demands – and where such a veridical “ground-truth” representation is computed – remains unknown.

One candidate for generating such a context-invariant estimate is the nodulus and uvula (NU) – lobules X and IX of the posterior cerebellar vermis – which integrate inputs from the semicircular canals and otolith organs to encode self-motion in a gravity-centered reference frame11,12. The NU is commonly assumed to filter out self-generated motion via internal forward models, selectively encoding externally generated perturbations12. However, several anatomical and physiological features suggest an alternative role. Notably, the NU receives robust monosynaptic input from vestibular afferents that encode head motion with high fidelity regardless of behavioral context13–16. These afferents maintain consistent tuning during both passive and active movements, including voluntary head turns and natural locomotion, raising the possibility that the NU functions as an inertial “ground-truth” estimator rather than a predictive filter. Moreover, NU Purkinje cells project to regions of the fastigial nucleus implicated in spatial awareness, arousal, and autonomic control – systems that require a veridical, context-independent representation of motion and orientation17–20. Collectively, this anatomical and functional evidence positions the NU as a strong candidate for providing veridical self-motion estimates essential for both motor and non-motor functions.

Here, we directly tested whether and how NU Purkinje cells – the output neurons of the cerebellar cortex – encode actively generated head movements. We found that neurons sensitive to passive translations maintained their sensitivity during comparable active translations. Furthermore, when active and passive motion were combined, NU Purkinje cells encoded the total head movement in space without distinguishing the source. During perturbations in which neck motor commands were issued but head motion was prevented, Purkinje cell activity remained unchanged, indicating no integration of efference copy signals. For active head tilts, which require integrating otolith and semicircular canal input to determine the motion and sustained head position relative to gravity, Purkinje cells faithfully encoded both the dynamic motion and static tilt. Taken together, our findings overturn the prevailing view that the NU primarily implements predictive suppression of reafference, demonstrating instead that it provides a robust, context-independent code for self-motion and spatial orientation. This veridical encoding, unique within the vestibular cerebellar vermis, positions the NU as an essential hub for both motor and non-motor functions – serving as a stable, gravity-centered ground truth against which internal predictions can be evaluated during voluntary movement.

Results
We recorded high-density extracellular neural activity from Purkinje cells in the NU of two alert rhesus monkeys. Purkinje cells included in this study were sensitive to passive vestibular stimulation and insensitive to eye movement. We first applied anterior or posterior directed passive whole-body translations to assess each Purkinje cell’s sensitivity to vestibular stimulation (Fig. 1A, first column; passive whole-body condition, and Supplementary Fig. 1). Using the same motion profile, we then assess sensitivity to neck proprioceptive stimulation by translating their body while their head was held stationary in space (Fig. 1A, second column; passive body under head condition). In our population, we found that the majority (95.5%, N=74) of Purkinje cells that were sensitive to vestibular stimulation were also sensitive to neck proprioceptive stimulation. Responses of an example Purkinje cell to passive vestibular and proprioceptive stimulation can be seen in Supplementary Fig. 2A, and the distribution of responses across the population are shown in Supplementary Fig. 2B. Overall, NU Purkinje cell responses to vestibular and neck proprioceptive stimulation were comparable to previous recent findings21.

NU Purkinje cells provide ground truth signals about self-motion translations

Vestibular feedback received by the brain during daily life often results from our own voluntary movements. However, prior neurophysiological studies of primate NU Purkinje cells have focused exclusively on how these neurons encode vestibular signals elicited by passively applied, externally generated motion. Accordingly, we next recorded the responses of NU Purkinje cells during actively generated head movements and compared them to responses evoked by experimentally applied passive head movements matched in kinematics. To directly compare sensory encoding across conditions, we recorded NU Purkinje cell activity while monkeys actively translated their heads relative to their bodies for a reward along the anteroposterior axis (Fig. 1A, fourth column; active head on body condition). We then applied passive head-on-body translations with matched kinematics to generate comparable vestibular and neck proprioceptive stimulation in the absence of self-generated motion (Fig. 1A, third column; passive head on body condition).

The results for two example Purkinje cells – one whose firing was more in phase with head velocity (Cell 1) and another aligned with head acceleration (Cell 2) – are shown in Fig. 1B. Both cells exhibited consistent and robust modulation across repeated trials of passive head translation (Fig. 1B, left panel). To characterize their temporal response dynamics, we applied a least-squares dynamic linear regression model incorporating three kinematic terms (head velocity, acceleration, and jerk) to fit firing rates during passive head movements (solid blue line superimposed on the gray mean firing rate). With this model, the average variances accounted for (VAF) were comparable in the passive and active condition (0.43 ± 0.18 and 0.41 ± 0.17, respectively (p=0.5). We then used this passive condition–derived model to predict how each Purkinje cell would respond during active head movements, assuming its kinematic sensitivity remained unchanged (dashed blue line). As shown in the right panels of Fig. 1B, both example cells exhibited robust modulation during active head on body translations, evident in both the mean firing rate (gray shaded region) and trial-by-trial responses. Importantly, for each neuron, the passive condition–derived model prediction during active motion closely matched the prediction generated from passive responses (solid red line), indicating that both cells maintained similarly strong modulation during active and passive head translations.

The observations from these two example Purkinje cells were representative of the broader population and are summarized in Fig. 1C for the subset of cells that remained well-isolated across both active and passive head-on-body translation conditions (N=95). Across the population, NU Purkinje cells exhibited comparable firing rate sensitivities to motion in both active and passive conditions, as illustrated by the overlapping distributions of response gains (Fig. 1C, histograms). The mean sensitivity (dotted vertical lines) did not differ significantly between active and passive conditions (preferred: active 19.8 ± 14.9 vs. passive 19.8 ± 13.0 sp/s/m/s², p=0.6021), indicating that, for most cells, self-generated motion did not suppress or enhance encoding of head kinematics. This pattern held true for responses in both the preferred (Fig. 1C) and non-preferred (Supplementary Fig. 3A) directions of movement (non-preferred: active 21.2 ± 19.5 vs. passive 22.2 ± 19.2 sp/s/m/s², p=0.6847). These results suggest that, at the population level, NU Purkinje cells maintain consistent encoding of self-motion regardless of whether movements are externally applied or actively generated.

While the above analysis emphasized the similarity in average sensitivity across the population (Fig. 1C), an equally important feature of NU Purkinje cell responses is their marked heterogeneity in temporal tuning. Importantly, this diversity is preserved during self-generated motion. As shown in the heatplots of Fig. 2A, individual neurons exhibit a wide range of firing phases, collectively tiling the full cycle of self-motion. This richness in response dynamics, evident under passive conditions, remains intact during active head-on-body translations. Moreover, the sensitivity and phase of individual neurons were strongly correlated between active and passive conditions in both the preferred (Fig. 2B; sensitivity R²=0.7728, phase R²=0.8646, p-values<0.0001) and non-preferred (Supplementary Fig. 3B; sensitivity R²=0.4439, phase R²=0.8722, p-values<0.0001) directions. Neurons with positive sensitivities preferred posterior motion, while those with negative sensitivities preferred anterior motion (Fig. 2B), and the magnitudes of these sensitivities clustered symmetrically across the two directions. Correspondingly, phases tended to cluster around a similar phase lead or lag relative to acceleration. Polar plots illustrate that neurons maintain their tuning characteristics across contexts. Although mean sensitivities did not differ, the preserved heterogeneity in temporal dynamics underscores the stability and richness of population coding in the NU during both externally applied and self-generated motion.

To further probe the diversity of temporal tuning across movement contexts, we next classified individual Purkinje cell responses based on their firing rate dynamics during active and passive head-on-body motion. Using a model-based decomposition of each neuron’s response (see Methods), we categorized tuning profiles as linear, rectifying, v-shaped, or other (example cells shown in Supplementary Fig. 4A), and found a comparable distribution of response types across conditions (Supplementary Fig. 4B). Unlike vestibular afferents and nuclei neurons that encode motion linearly, Purkinje cells can exhibit heterogeneous and nonlinear tuning – a feature also reported in other regions of the vestibular vermis4,22,23. We then examined the specific temporal features driving each neuron’s sensitivity – defined here as the depth of modulation – and found that response dynamics remained consistent across active and passive conditions. During passive head translations, 48% of NU Purkinje cells exhibited modulation most strongly aligned with linear acceleration, while 41% were velocity-aligned and 11% with jerk (Supplementary Fig. 4C, left panel). This heterogeneity persisted during active motion, with similar proportions of neurons aligned to acceleration (44%), velocity (44%), and jerk (13%) (Supplementary Fig. 4C, right panel). The persistence of this heterogeneity across movement contexts is also supported by the consistency in the phase as well as sensitivity of the response between active and passive conditions (Fig. 2B). These results reinforce the conclusion that the rich diversity in NU Purkinje cell response dynamics is not context-dependent, but rather reflects a stable and robust feature of cerebellar encoding across both self-generated and externally applied movements.

NU Purkinje cells encode total self-motion in space when active and passive motion are experienced concurrently

So far, we have shown that NU Purkinje cells encode self-generated movement with similar fidelity as passively imposed movements. These results indicate that NU Purkinje cells provide a context-independent, ground truth representation of self-motion in space, whether movements are actively generated or passively applied. We next asked whether this ground truth representation of self-motion in space is preserved when active and passive movements occur simultaneously. To test this, we applied passive whole-body anteroposterior translations while monkeys concurrently generated active head-on-body movements. Figure 3A illustrates the response of an example Purkinje cell during combined active and passive motion. The top traces show active head motion (red), passive whole-body translation (blue), and the resulting total head motion in space (purple), which is the sum of the two. The lower panel illustrates the neuron’s firing rate (gray shaded region), with two model predictions overlaid: the blue dashed line reflects the prediction based on passive motion alone, while the solid purple line reflects the prediction based on total motion. Strikingly, the total-motion model well predicted the neuron’s firing rate, whereas the passive-motion-based prediction failed to account for the response. Thus, this finding confirms that the neuron continues to encode an accurate, context-independent representation of self-motion in space, even when active and passive movements occur simultaneously.

The example in Fig. 3A illustrates that a single NU Purkinje cell integrates both active and passive components to represent total self-motion. To extend this observation across our population of NU Purkinje cells, we next conducted a quantitative model-based analysis. For each neuron, we first estimated sensitivity to the passive component of motion generated by the applied passive whole-body translations. We then fit the residual firing rate – i.e., the portion not explained by passive motion – with the active component of head motion (see Methods). Across the 52 Purkinje cells tested, sensitivities to the active and passive components were statistically indistinguishable (p=0.5038). Furthermore, response phases to passive and active components were well aligned across neurons (R²=0.5433, p<0.0001; Fig. 3B, right panel). Thus, taken together, these results establish that NU Purkinje cells provide a veridical representation of self-motion in space regardless of whether it occurs passively, is generated actively, or involves both in combination.

Motor command signals do not influence NU Purkinje cell activity

Our findings thus far demonstrate that NU Purkinje cells reliably encode self-motion in space by integrating vestibular and proprioceptive input, regardless of whether movement is actively generated, passively imposed, or experienced concurrently. This context-independent encoding suggests that these neurons are not influenced by motor command signals. To directly test this, we implemented a motor-only condition in which the monkey attempted to initiate voluntary head movements, but actual motion was prevented. As a result, motor commands were issued to the neck musculature, but there was no head displacement in space (i.e., no vestibular input) and no head movement relative to the body (i.e., minimal proprioceptive feedback from neck receptors).

To confirm the presence of motor output, we recorded isometric force generation using a transducer mounted on the sled, capturing the onset of intended movement. Example responses from three Purkinje cells (the same cells shown in Fig. 1 plus an additional cell) are presented in Fig. 4A. In contrast to the robust modulation observed during both active and passive head motion, neither cell showed detectable modulation in activity when only motor commands were present. This result generalized across the population: in the 60 NU Purkinje cells tested, sensitivity during attempted head motion was significantly lower than during either active or passive movement (p<0.0001; Fig. 4A, bar graph). Furthermore, we assessed whether the baseline firing rates changed after motor commands were sent and found they remained stable between the 50 ms before and after the onset of intended movement (p=0.8090; Fig. 4B), consistent with the absence of efference-copy signals influencing NU Purkinje cell output.

Together, these findings demonstrate that NU Purkinje cell activity reflects only sensory input and is not influenced by motor commands. This sensory-specific tuning, coupled with the indistinguishable responses observed during active and passive motion, provides compelling evidence that NU Purkinje cells encode a context-independent, ground truth representation of self-motion in space. Notably, this pattern diverges from prior work in the anterior vermis, where Purkinje cells have been shown to respond to motor-related signals in the absence of actual movement. The functional implications of this regional distinction will be explored further in the Discussion.

NU Purkinje cells encode active changes in head orientation relative to gravity

The NU receives direct input from both the otolith organs and semicircular canals and is a key site for integrating these signals. This integration is necessary because, as stated by Einstein’s equivalence principle, the effects of gravity and linear acceleration are physically indistinguishable. The otoliths encode net linear acceleration and cannot, on their own, differentiate between head tilt relative to gravity and actual translation. Resolving this ambiguity requires combining otolith signals with rotational input from the semicircular canals. This computation has been demonstrated in the NU, with its output observed in Purkinje cell activity during passive motion24, reviewed in Cullen11. During head tilt, both the semicircular canals and otoliths are activated by angular rotation and by the change in head orientation relative to gravity, respectively, whereas linear translation stimulates only the otoliths. Importantly, recent work has shown that neurons in the fastigial nucleus, the downstream target of Purkinje cells in the vermis, can distinguish between active and passive tilts, consistent with the operation of an internal model that accounts for the gravitational component of otolith signals25. We therefore asked whether NU Purkinje cells, which provide input to this pathway, also differentiate active from passive tilts, or whether, as observed for translations, their encoding remains invariant across behavioral context.

To test whether NU Purkinje cells differentiate between active and passive head tilts, we first identified neurons that responded to passively applied head-on-body pitch rotations. We then recorded from the same neurons while the monkey performed active upward and downward head pitch movements for a reward. Figure 5A shows an example neuron’s simple spike modulation during the dynamic phase of head reorientation relative to gravity in both conditions. This neuron exhibited highly similar firing patterns during active and passive tilt. This similarity in response was robust across the population (N=47), with nearly identical distributions of sensitivity to active and passive head tilts (Fig. 5B, histograms).

Furthermore, as shown in Fig. 5C, individual neurons displayed a broad range of firing phases during passive tilt (left), and this diversity was preserved during active tilt (right), collectively tiling the full cycle of head motion. Importantly, each individual Purkinje cell maintained its tuning across conditions: sensitivity and phase were strongly correlated between active and passive tilts (Fig. 5D; sensitivity R²=0.7399, phase R²=0.7627), with no significant difference in sensitivity (p=0.9595; bar graph inset). Comparable results were also observed in the non-preferred direction (sensitivity R²=0.7839, phase R²=0.8357; p=0.0775; Supplementary Fig. 5). Thus, these findings reveal that, even in the context of gravitationally complex tilt movements, NU Purkinje cells preserve both the structure and fidelity of their responses across behavioral conditions – supporting context-invariant encoding of self-motion.

Finally, the analyses above focused on dynamic tilts, where Purkinje cell responses tracked changes in head orientation relative to gravity. Accordingly, we next asked whether NU neurons similarly encode static head position in a context-independent manner. Previous work has shown that gravity-related modulation in fastigial nucleus neurons is suppressed when the head is actively, rather than passively, brought into a fixed position25. To directly test whether this is also the case for NU Purkinje cells, we analyzed a subset of neurons (N=38) recorded while the head was held motionless in an upward or downward pitch position that had been reached either by passively tilting the head or through the animal’s own voluntary movement. Overall, across our population, we found that the distribution of responses was comparable across both active and passive conditions (Fig. 6A). Furthermore and importantly, each individual Purkinje cell maintained its firing activity across conditions (Fig. 6B) (upward: R²=0.8269; downward: R²=0.6598; Fig. 6B), with no significant difference in sensitivity (upward: passive 42.4 ± 18.0 sp/s, active 44.4 ± 19.6 sp/s, p=0.1399; downward: passive 44.6 ± 19.1 sp/s, active 47.2 ± 20.7 sp/s, p=0.2098; bar graph inset).

Thus, in clear contrast to the fastigial nucleus, NU Purkinje cells maintain consistent encoding of orientation relative to gravity, regardless of whether it is achieved actively or passively – mirroring the context-independent encoding observed during dynamic translations and tilts. Together, these findings demonstrate that NU Purkinje cells provide a stable, movement-invariant representation of orientation relative to gravity across both static and dynamic conditions.

Methods
Experimental model and participant information
All experimental procedures performed in this study received full approval from the Johns Hopkins University Animal Care and Use Committee and adhered to the guidelines outlined by the United States National Institutes of Health (Protocol PR22M342). Neural recordings from the cerebellum were performed on one female and one male rhesus macaque (Macaca mulatta), weighing 8 and 11 kg. A total of 32 recording sessions were performed on separate days. These animals were maintained in a controlled environment with a 12-hour light/dark cycle throughout the duration of the study. Both rhesus monkeys exhibited overall good health, and did not require any medication during the course of this experiment, and had previously participated in other research studies within our laboratory.

Surgical procedures
Each rhesus monkey underwent aseptic surgical preparations to allow for chronic extracellular recording following previously established protocols63. Each animal received pre-anesthetic medications, including ketamine hydrochloride (15 mg/kg i.m.), buprenorphine (0.01 mg/kg i.m.), and diazepam (1 mg/kg i.m.), to ensure analgesia and muscle relaxation. To minimize swelling and prevent infection, loading doses of dexamethasone (1 mg/kg i.m.) and cefazolin (50 mg/kg i.v.) were administered. To stabilize heart rate and minimize salivation, anticholinergic glycopyrrolate (0.005 mg/kg i.m.) was also administered before surgery, and subsequently injected every 2.5–3 h during the surgical procedure. Anesthesia was maintained during surgery using isoflurane gas (0.8–1.5%), combined with a minimum of 3 l/min of 100% oxygen, adjusted to achieve the desired level of anesthesia. Vital signs, including heart rate, blood pressure, respiration, and body temperature, were monitored continuously throughout the surgical procedure.

Animals were implanted with a custom-made medical-grade titanium head post for head fixation and recording chambers that allowed targeting of the nodulus and uvula in the posterior cerebellar vermis. In the first rhesus monkey, stereotaxic targeting procedures were used to position the recording chambers, and targeting was examined post-implantation using a CT scan with guide tubes placed in the brain. In the second rhesus monkey, recording chambers were positioned based on the co-registration of a CT and MRI scan and by using Brainsight (Brainsight 2 Vet, Rogue Research, Montreal, Canada). A second CT scan was performed post-implantation and co-registered to the MRI to examine placement of the recording chambers and targeting of neural structures. Titanium screws and Simplex P bone cement (Stryker Orthopedics, Mahwah, NJ) were used to chronically secure the implant to the skull. Within the recording chamber, a craniotomy was carefully performed to provide access to the brain. Post-surgery, medications including dexamethasone (0.5 mg/kg i.m. for 4 days), anafen (2 mg/kg on the first day, 1 mg/kg on subsequent days), and buprenorphine (0.01 mg/kg i.m. every 12 h for 2–5 days, depending on the animal’s pain level) were delivered. To prevent infection, Cefazolin (25 mg/kg) was injected twice daily for 10 days. Before beginning experimental procedures, the animals were allowed to recover for a 2 week period post-surgery.

Experimental procedures
The monkey was head-fixed using a head post attached to a near-frictionless linear head sled that could enable translations of the head relative to the body in both the mediolateral and anteroposterior directions. The monkey was seated in a primate chair that was secured on top of a linear sled that could provide anteroposterior or mediolateral whole-body translations. Recordings were performed using acute electrode insertions on each session to record from a unique neural population. The electrode was inserted using a custom microdrive and a sterile guide tube that penetrated the tentorium. Electrodes were removed at the end of every session. During each recording, Purkinje cells were identified physiologically and by laminar context: as the electrode advanced from the molecular layer into the Purkinje cell layer, we observed complex spike-dominant activity in the dendritic region followed by simple spike activity at somatic depths, often still accompanied by identifiable complex spikes. The firing pattern of these simple spikes was tonic and irregular, consistent with Purkinje cell physiology. We first searched for and isolated neurons that showed modulation in response to vestibular stimulation and subsequently tested experimental conditions on these neurons. To test sensitivities to vestibular and proprioceptive stimulation, we applied passive vestibular stimulation by translating the whole body on the linear sled. We then held the head stationary relative to earth and applied passive proprioceptive stimuli by translating the body underneath a stationary head. We applied combined vestibular and proprioceptive stimulation by translating the head on an earth-stationary body. Finally, we allowed the monkey to make active voluntary translations in the anterior and posterior directions for a reward.

Combined active and passive motion was also examined by translating the whole body in the anterior and posterior direction at the same time that the monkey made an active head translation. Finally, in some trials, we unexpectedly locked the head sled such that motor commands were sent, but no head motion (and thus no sensory stimulation) occurred. In these trials, we recorded the force applied to the locked head sled by the monkey to determine when the onset of the intended head movement occurred. Similarly, to examine encoding of changes in head orientation relative to gravity, we first applied passive pitch and roll motion of the head on the body by releasing rotational and translation joints in the head post. Finally, we allowed the monkey to make active head pitch movements upwards and downwards for a reward.

Data acquisition
We recorded 3D linear acceleration and 3D angular velocity of the head from an inertial measurement unit (IMU) mounted on the head post, linear motion of the primate chair using a 3D accelerometer, and the force applied to the head post using a load cell transducer (Omegadyne). Analogue signals were sampled at 1 kHz (Blackrock Microsystems). Neural activity was recorded from high-density (128 ch) silicon read-write electrodes from the NU (IMEC). The 128 channels were arranged in a zig-zag pattern and spanned a 1.6 mm recording area. Neural signals were amplified, band pass filtered (0.1 Hz – 7.5 kHz) and digitized by four 32-channel RHS stim/recording head stages (Intan technologies) and streamed by an RHS stim/recording controller (Intan technologies, v3.4.0) at 30 kHz. Kilosort v2.5 was used to spike sort, and neural data were further curated in Phy2. Only isolated single units that showed significant modulation during passive vestibular stimulation (p<0.05) and were present across a set of paradigms were included in further analyses.

Quantification and analysis
Kinematic signals were low-pass filtered at 10 Hz, and linear velocity and jerk were calculated by integrating and differentiating the recorded acceleration signal, respectively, using MATLAB v9.8 (MathWorks). Similarly, angular position and acceleration signals were calculated by integrating and differentiating the recorded angular velocity signal from the IMU, respectively. Each trial of motion was extracted by segmenting the data at the onset and offset of movement. Firing rate was calculated using a kaiser filter with a cutoff of 7 Hz64. Each Purkinje cell’s firing rate response to translational motion was estimated using linear regressions to find sensitivity to three kinematic terms (velocity, acceleration, and jerk).

f_r(t) = b + S_v X_dot(t) + S_a X_ddot(t) + S_j X_dddot(t) (1)

where f_r(t) is the estimated firing rate, b is a bias term representing background firing rate, S_v, S_a, and S_j are coefficients representing the velocity, acceleration, and jerk gains respectively and X_dot, X_ddot and X_dddot are head velocity, acceleration, and jerk, respectively. For head-on-body motion (active or passive) we used kinematic signals recorded from the head. For body-under-head motion, we used kinematic signals recorded from the primate chair. The same analysis was performed to examine Purkinje cell sensitivity to active and passive head tilts; however, we used angular head position, velocity, and acceleration terms. This least-squares regression was solved for non-negative and non-positive criterion to ensure sign consistency across estimated coefficients. For each model coefficient in the analysis, we computed 95% confidence intervals using a nonparametric bootstrapping approach (n=2000)65,66. All non-significant coefficients were set to zero. Similarly, we calculated a firing rate prediction for the active condition by substituting the gains computed for the passive condition into the equation above. During combined active and passive motion, we first used kinematic signals from the chair, representing the passively applied motion, in the regression analysis to calculate sensitivity coefficients and generate a firing rate prediction. We then subtracted the passive estimate from the observed firing rate and fit the residual firing rate with the active component of motion, calculated as total head motion minus the applied chair motion. Coefficients were used to estimate the sensitivity and phase of each Purkinje cell’s response using the following equations:

Sensitivity = sgn(S_j, S_a, S_v, i) * sqrt((2*pi*f)^2 * S_j^2 + (2*pi*f*S_v)^2 + (2*pi*f*S_a)^2) (2)

Phase = tan^-1((2*pi*f)^2 * S_j - S_v) / (2*pi*f*S_a) (3)

Where the sign terms were +1 or -1 for positive and negative coefficients, respectively, and the frequency (f) was 1 Hz to reflect the 500 ms half-cycle of motion that the stimulation consisted of. Similarly, sensitivities and phases for angular motion were also calculated, but instead using coefficients obtained for position, velocity, and acceleration.

We assessed the contribution of velocity, acceleration, and jerk to each Purkinje cell’s response by running linear regressions without the term of interest and calculating the decrease in the variance accounted for (VAF). Purkinje cell responses to passive and active head-on-body motion were classified as linear, rectifying, or v-shaped. Linear neurons increased their firing rate in response to motion applied in one direction and decreased their firing rate with motion in the opposite direction, with a similar magnitude of sensitivity (within 8 sp/s/m/s^2). Rectifying neurons primarily had responses only in one direction and minimal modulation in the other (below 8 sp/s/m/s^2). V-shaped neurons showed similar increases in both motion directions (within 8 sp/s/m/s^2). Remaining Purkinje cells that did not fit these three criteria were classified as other. We defined the preferred direction of the neuron as the direction of motion (e.g., anterior or posterior) that increased its firing rate, or had the larger increase in firing rate for v-shaped Purkinje cells.

Pairwise t-tests were used to compare absolute sensitivity to passive versus active head-on-body motion for both translations and the dynamic portion of head tilts. These comparisons were performed separately for the preferred and non-preferred movement directions. Pearson correlations were also used to assess the relationship between active versus passive sensitivity and phase, as well as between the passive versus the active component of combined motion for sensitivity and phase. During head pitch, we also extracted the static portion of head reorientations relative to gravity upwards and downwards for both passively applied movements and active movements. We examined the relationship between Purkinje cell firing rates during the static portion of the tilt between active and passive conditions Pearson correlations, and compared the firing rate between conditions using paired samples t-test (performed separately for upward and downward head pitch). Data are shown as mean ± SEM.

To examine Purkinje cell sensitivities to motor commands, we analyzed both the change in firing rate and the response to a theoretical head movement that would have occurred if the head was not restrained. Specifically, we compared Purkinje cell firing rates at the onset of movement (first 50 ms) relative to baseline (50 ms prior to the movement) using a paired samples t-test. We also superimposed the mean kinematics from the active head movements and calculated sensitivity to this theoretical motion, and compared this to passive and active head movement sensitivities.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The current study examined vestibular activity in the posterior part (NU) of the cerebellar vermis under active and passive self-motion condition. The main finding is that unlike many previously reported areas showing suppressed neural activity under active motion, NU activity remains, meaning not being suppressed by the motor command efference copy signal. This finding is important, because it provide a neural substrate that serves maintenance of monitoring self-motion perception from the vestibular signals during active motion. The experiments, including those controlled ones, are well performed, as always in their previous studies. The results are clear and persuasive. The paper is well written. I only have some minor comments for better presentations of their results.\n1. line 23-24: The statement sounds too strong. It can be softened to something like: \"Recent evidence suggest that cerebellar circuits in the anterior vermis may use efference copies...\"\n2. Vestibular and Proprioceptive, Supple 2B: show comparison of the two on a cell by cell basis, to see whether there is a correlation there; what about the preference? Are they consistent so that passive whole body rotation and neck proprioceptive response can be summed to enhance activity during passive head on body motion (their previous report)? Can show a similar scatter plot of comparison of preference between the two conditions.\n3. Linear, rectifying, v-shaped neurons, Supple 4: show some examples for each category. In addition, it is a bit surprising that the linear group does not dominate, instead, there are quite a high proportion of rectifying and v-shaped neurons. Isn't that linear should be expected based on vestibular coding (excitation and inhibition mechanism, e.g. in peripheral)?\n4. Line 313：The same work here also involves proprioceptive stimulation (head on body during active and passive motion). So this is the same to the rat study. I am not sure about why it says it is a key distinction?\n5. Data in many places are shown by pooling data from both animals. They need to be separated to indicate consistency across animals.\n6. The population results are highly relying on fitting functions. Thus the goodness of the fit needs to show they are good fittings.\n7. Figure 1C: why there are data missing in the middle around 0? Are there very few cells showing no modulation, or these cells are dropped out (with some criteria) in the presentation?\n8. Figure 3b lacks representative polar plots comparable to those presented in Figure 2b.", "reviewer_2": "Nature Communications, Manuscript ID: NCOMMS-25-63595-T\nTitle: Ground-truth encoding of self-motion in the primate cerebellar nodulus and uvula.\nAuthors: Mildren RL, Cullen KE\nGeneral comments\nThis paper addresses one of the critical issues of neuroscience: How does the cerebellar cortex contribute to the so-called “cerebellar internal model”? The authors chose the cerebellar nodules and uvula (NU) (older parts of the cerebellar cortex that receive converging vestibular and somatosensory inputs). They examined the activities of NU cells under various external and internal conditions. They made three important observations: 1) NU cells responsive to passive head translations remained equally sensitive to self-generated movements; 2) these NU cells demonstrated a lack of efference-copy integration; 3) NU cells encoded both dynamic motion and static orientation relative to gravity. These findings overturn the internal model hypothesis and establish the NU as a ground-truth, context-invariant estimator of self-motion, supporting stable behavior in dynamic environments.\nThe experimental design, data analyses, conclusions, and discussion all appear reasonable. I have only some concerns about the identification of Purkinje cells and the presentation of the data.\nSpecific comments\n1. Page 5, Results, line 64, “Purkinje cells”: I did not find an identification of PCs in either the Results or Methods sections. Conventionally, the identification of PCs depends on the non-simultaneous co-existence of simple spikes and complex spikes in the same unit. Of course, I understand your recording system may not allow its application for all neurons. Nevertheless, the authors should describe the identification of PCs in detail, as it is crucial for addressing the question raised in this study.\n2. If the recording electrodes were implanted chronically in the cerebellar cortex, how is it possible to distinguish neurons recorded from the same electrode on different recording sessions?\n3. The data presented on pages 6 and 7 are impressive and convincing.\n4. Page 7, lines 139-141, “Using a model-based decomposition of each neuron's response (see 140 Methods), we categorized tuning profiles as linear, rectifying, v-shaped, or other, and found a comparable distribution of response types across conditions (Extended Data Fig. 4A)”.: It is helpful to show an example of activity for each category of neurons.\n5. Page 7, lines 146-148, “This heterogeneity persisted during active motion, with similar proportions of neurons aligned to acceleration (44%), velocity (44%), and jerk (13%) (Extended Data Fig. 4B, right panel).”: Did you find the persistence of the heterogeneity for individual neurons, or did you see changes in tuning profiles between different movement contexts?\n6. Page 9, lines 204-205, “Furthermore, firing rates did not differ between the 50 ms before and after the onset of intended movement (p = 0.8090; Fig. 4B).”: The two panels in Fig. 4B are not consistent with each other. In the left panel, the firing rate of PCs shows significant variance for the baseline condition and the movement onset, while in the bar graph, the variance appears minimal.\n7. Page 17, line 471, “IMU”: What is IMU? I did not find its explanation in the manuscript.\n8. Page 26, Figure 1C: I recommend converting the upper and lower panels into a 2D plot to illustrate the relationship between PC sensitivities for the active and passive conditions.\n9. Page 28, Figure 2B: For both sensitivity and phase, PCs tend to make two clusters: one positive and the other negative. It is helpful to discuss its interpretations.\n10. Page 29, Figure 3A: Does the difference between the purple line (total motion estimate) and the blue-hatched line (passive motion estimate) represent an active motion estimate?\n11. Page 29, Figure 3B: The inset bar graph in the left panel: How did you calculate the mean sensitivities? There is a discrepancy between the significant variance in the 2-D plot and the small variance in the bar graph.\n12. Page 30, Figure 4A: The same two neurons are used in both Figs. 1 and 4. Are they truly representative of the whole population of PCs?\n13. Page 30, Figure 4A: There is no explanation about the bar graph in the Figure legend.\n14. Page 30, Figure 4B: It is helpful to show the 50 ms time window for Fig. 4B in Fig. 4A.\n15. Page 30, Figure 4B, the bar graph: It should demonstrate modulation from the baseline, rather than the raw firing rate.\n16. Page 34, Figure 7: It is helpful to show the references in the legend."}, "author_response": "We thank the reviewer for the positive feedback on our manuscript regarding our well performed experiments and persuasive results. As detailed below, we have addressed each of the reviewer’s comments.\n1. line 23-24: The statement sounds too strong. It can be softened to something like: \"Recent evidence suggest that cerebellar circuits in the anterior vermis may use efference copies...\"\nWe have revised this sentence to: “Recent evidence suggests cerebellar circuits in the anterior vermis use efference copies of motor commands to build forward internal models that predict the sensory consequences of behavior6.”\n2. Vestibular and Proprioceptive, Supple 2B: show comparison of the two on a cell by cell basis, to see whether there is a correlation there; what about the preference? Are they consistent so that passive whole body rotation and neck proprioceptive response can be summed to enhance activity during passive head on body motion (their previous report)? Can show a similar scatter plot of comparison of preference between the two conditions.\nWe have added histograms of sensitivities in the non-preferred direction (Supplementary Fig. 2B). We have also added scatter plots showing that combined stimulation enhances responses relative to vestibular stimulation alone (points falling above unity), as well as bar graphs comparing responses for vestibular, proprioceptive and combined conditions.\n3. Linear, rectifying, v-shaped neurons, Supple 4: show some examples for each category. In addition, it is a bit surprising that the linear group does not dominate, instead, there are quite a high proportion of rectifying and v-shaped neurons. Isn't that linear should be expected based on vestibular coding (excitation and inhibition mechanism, e.g. in peripheral)?\nWe appreciate the reviewer’s comment and have added representative examples of linear, rectifying, and v-shaped Purkinje cell response profiles to Supplementary Fig. 4A.\nRegarding the distribution of response types, while vestibular primary afferents and vestibular nuclei neurons typically display linear encoding, Purkinje cell simple-spike responses often do not. This nonlinearity likely emerges from multiple stages of processing within the cerebellar cortex. Vestibular and somatosensory afferents undergo substantial transformation as they pass through the granule-cell layer, where convergence of multiple inputs onto individual granule cells can introduce nonlinearities. In addition, mossy fiber and parallel fiber synapses exhibit a range of short-term plasticity properties, including synaptic depression and facilitation, which further shape Purkinje cell responses (Chabrol et al., 2015).\nIn this context, we have revised the Results (Lines 147–149) to note that nonlinear tuning patterns have been documented previously in other regions of the vestibular cerebellum, including the anterior vermis (Zobeiri & Cullen, 2022, 2024, Mildren and Cullen 2025), and in Purkinje cell responses during locomotion (Sauerbrei et al., 2015). Thus, while linear encoding is common in earlier stages of vestibular processing, nonlinear response profiles in Purkinje cells are well established and expected.\n4. Line 313：The same work here also involves proprioceptive stimulation (head on body during active and passive motion). So this is the same to the rat study. I am not sure about why it says it is a key distinction?\nWe appreciate the reviewer’s comment and have revised Lines 323–332 to explicitly state that the rat study conflated two variables: active movement and proprioceptive input. Their passive condition consisted of whole-body rotation, which drives vestibular afferents but generates little or no proprioceptive input from the neck or body, whereas their active condition involved freely generated head movements that necessarily engage both vestibular and proprioceptive pathways. Thus, differences attributed to efference-copy mechanisms could instead reflect altered somatosensory input, given that NU Purkinje cells integrate proprioceptive cues.\nIn contrast, our study directly compares active head-on-body motion to passively applied head-on-body motion, isolating the effect of motor command while holding neck-proprioceptive input constant. This distinction is important, and we have revised the text to more explicitly emphasize it.\n5. Data in many places are shown by pooling data from both animals. They need to be separated to indicate consistency across animals.\nTo demonstrate consistency across animals, we now include separate data for each monkey in Supplementary Fig. 3C. These panels clearly show that the key active–passive comparisons hold in both subjects.\n6. The population results are highly relying on fitting functions. Thus the goodness of the fit needs to show they are good fittings.\nWe have examined the goodness of fit using variance accounted for (VAF) and included this information in the results (lines 99-101). We found the fits are robust and the average VAFs were comparable in the passive and active conditions (0.43 ± 0.18 and 0.41 ± 0.17, respectively (p = 0.5).\n7. Figure 1C: why there are data missing in the middle around 0? Are there very few cells showing no modulation, or these cells are dropped out (with some criteria) in the presentation?\nWe thank the reviewer for highlighting this point. We have expanded the Methods (Lines 478–479 and 507–508) to explain that we deliberately included only vestibular-sensitive neurons in our sample. Neurons with negligible vestibular modulation were excluded during both recording and post-processing. Therefore, the distribution naturally contains fewer points near zero.\n8. Figure 3b lacks representative polar plots comparable to those presented in Figure 2b.\nWe have added polar plots to Figure 3B, consistent with the presentation format in previous figures.\nWe thank the reviewer for their thoughtful comments and address each point below.\nSpecific comments\n1. Page 5, Results, line 64, “Purkinje cells”: I did not find an identification of PCs in either the Results or Methods sections. Conventionally, the identification of PCs depends on the non-simultaneous co-existence of simple spikes and complex spikes in the same unit. Of course, I understand your recording system may not allow its application for all neurons. Nevertheless, the authors should describe the identification of PCs in detail, as it is crucial for addressing the question raised in this study.\nWe have revised the manuscript to provide a clearer description of the identification criteria. Specifically, we have now expanded the Methods (Lines 473-477) to explain that advancing the electrode from the molecular layer into the Purkinje cell layer produced initially complex spike activity in the dendritic region, followed by simple spike activity (sometimes with identifiable complex spikes as well) at the Purkinje cell layer. These recordings had a depth consistent with the PC layer (preceded by complex spike activity, and above clearly discernible nuclei neuron activity), as well as typical tonic, irregular simple spike firing typical of Purkinje cells.\n2. If the recording electrodes were implanted chronically in the cerebellar cortex, how is it possible to distinguish neurons recorded from the same electrode on different recording sessions?\nWe clarified in the Methods (Lines 470–473) that the electrodes were acutely inserted during each recording session, withdrawn afterward, and reinserted at new sites for subsequent sessions. Thus, each session sampled unique neural populations.\n3. The data presented on pages 6 and 7 are impressive and convincing.\nWe thank the reviewer for this encouraging feedback!\n4. Page 7, lines 139-141, “Using a model-based decomposition of each neuron's response (see 140 Methods), we categorized tuning profiles as linear, rectifying, v-shaped, or other, and found a comparable distribution of response types across conditions (Extended Data Fig. 4A)”.: It is helpful to show an example of activity for each category of neurons.\nWe have added examples of a linear, rectifying, and v-shaped neurons to Supplementary Fig. 4A.\n5. Page 7, lines 146-148, “This heterogeneity persisted during active motion, with similar proportions of neurons aligned to acceleration (44%), velocity (44%), and jerk (13%) (Extended Data Fig. 4B, right panel).”: Did you find the persistence of the heterogeneity for individual neurons, or did you see changes in tuning profiles between different movement contexts?\nWe observed a persistence of this heterogeneity across movement contexts for individual neurons. This finding is also supported by the consistency in the phase as well as sensitivity of the response between active and passive conditions in Fig 2B. We have clarified this point in the text (lines 156-158).\n6. Page 9, lines 204-205, “Furthermore, firing rates did not differ between the 50 ms before and after the onset of intended movement (p = 0.8090; Fig. 4B).”: The two panels in Fig. 4B are not consistent with each other. In the left panel, the firing rate of PCs shows significant variance for the baseline condition and the movement onset, while in the bar graph, the variance appears minimal.\nThe left panel displays per-neuron values (where there is substantial between-cell variability as the reviewer noted). In contrast, the bar plot summarizes the population mean ±SEM across neurons. With a larger sample, SEM is small even when between-cell variance is wide, which is why the bar appears tighter. Our paired comparison of the 50-ms pre- vs post-onset windows showed no systematic shift in firing rate (p = 0.809), consistent with the bar plot. To improve clarity, we have added mean ±standard error in the figure captions.\n7. Page 17, line 471, “IMU”: What is IMU? I did not find its explanation in the manuscript.\nWe have defined the acronym for IMU (Inertial measurement unit) where it is first mentioned.\n8. Page 26, Figure 1C: I recommend converting the upper and lower panels into a 2D plot to illustrate the relationship between PC sensitivities for the active and passive conditions.\nWe thank the reviewer for this suggestion and examined it by constructing a version of the histogram that illustrates the relationship between PC sensitivities in active and passive conditions (see plot). However, we found that it did not provide additional insight into our findings given that the relationship between active and passive sensitivities is already shown directly and explicitly in the neuron-by-neuron scatter plots in Fig. 2B. These plots display the same values the reviewer is asking to visualize and do so more clearly than a multidimensional histogram. As the additional plot would therefore be redundant, we have elected not to include it in the manuscript.\n9. Page 28, Figure 2B: For both sensitivity and phase, PCs tend to make two clusters: one positive and the other negative. It is helpful to discuss its interpretations.\nWe have revised the text to explain that neurons with positive sensitivities prefer motion in the posterior direction, whereas those with negative sensitivities prefer anterior motion, and sensitivities tend to cluster around a similar absolute value regardless of whether posterior or anterior motion is preferred. Correspondingly, phases tended to cluster around a similar lead or lag relative to acceleration. These specific additions are now included in the revised Results section (Lines 133–137).\n10. Page 29, Figure 3A: Does the difference between the purple line (total motion estimate) and the blue-hatched line (passive motion estimate) represent an active motion estimate?\nWe have revised the Methods (lines 535-536) to more clearly explain that the active component represents the residual after subtracting the passive predicted firing rate from the observed rate. Thus, the difference between the firing rate (which is similar to the total motion estimate) and passive estimate should roughly match with the active estimate.\n11. Page 29, Figure 3B: The inset bar graph in the left panel: How did you calculate the mean sensitivities? There is a discrepancy between the significant variance in the 2-D plot and the small variance in the bar graph.\nWe now specify in the Methods that sensitivities are expressed as absolute values (to combine positive and negative frequencies) and that error bars represent mean ± SEM (see also response to comment 6 above).\n12. Page 30, Figure 4A: The same two neurons are used in both Figs. 1 and 4. Are they truly representative of the whole population of PCs?\nWe appreciate this comment and agree it is important to demonstrate that the example neurons are representative. We intentionally illustrate the responses of the same cells across figures to avoid the risk of “cherry picking” different examples for different conditions/analyses. To further address the reviewer’s concern, we now indicate the location of these specific cells in the population data shown in the heat maps in Figures 2A (translations) and 5C (pitch). Additionally, we note that the lack of responses to motor command signals is very consistent, as quantified for the population in Figure 4B ,and we have added an additional Purkinje cell to Figure 4A to illustrate this point.\n13. Page 30, Figure 4A: There is no explanation about the bar graph in the Figure legend.\nWe thank the reviewer for noting this and have added reference to the bar graph in the figure legend.\n14. Page 30, Figure 4B: It is helpful to show the 50 ms time window for Fig. 4B in Fig. 4A.\nWe agree and have added a horizontal bar to indicate the 50 ms pre-movement window and an arrow to indicate movement onset in Fig. 4A.\n15. Page 30, Figure 4B, the bar graph: It should demonstrate modulation from the baseline, rather than the raw firing rate.\nWe appreciate the reviewer’s comment and have revised the Results text (lines 214-218) to improve clarity regarding the analysis. Notably, panel A shows whether example Purkinje cells modulate their activity during attempted head movement, while Panel B evaluates whether firing rate changes systematically when motor commands are issued. Using raw firing rates for this comparison is important because subtracting baseline would artificially introduce variability (as any noise in the two windows would create a non-zero difference). That difference is already captured by the distance from the unity line in the scatter plot of Fig. 4B. The raw firing rate comparison in the bar graph demonstrates that firing rates remain stable across the pre- and post-onset windows, consistent with the absence of efference-copy signals influencing NU Purkinje cell output.\n16. Page 34, Figure 7: It is helpful to show the references in the legend.\nThank you — we are happy that the included reference was helpful."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed my comments well. I do not have further questions.", "reviewer_2": "I really appreciate the authors' efforts to prepare replies for my comments. I am convinced with the revised manuscript."}, "author_response": "We thank the reviewer for their thorough evaluation and valuable feedback, which helped strengthen our manuscript.\nWe appreciate the reviewer's careful consideration and constructive comments throughout the review process."}]

Decision letter