Comparison of Signals from Cerebellar Purkinje Cells and Deep Nuclei during Temporal Prediction in Primates

Abstract

The cerebellum is crucial for predictive motor control and learning, but growing evidence suggests that it also generates forward models for nonmotor functions. Previous studies have reported periodic neuronal activity in the cerebellar dentate nucleus when animals predicted the timing of regularly presented visual stimuli. Since the dentate nucleus is an output structure, this activity likely reflects computations in the cerebellar cortex. Considering that Purkinje cells (PCs), the sole output of the cerebellar cortex, are more numerous than cerebellar nuclear neurons and that nuclear neurons also receive input from mossy and climbing fibers, information integration likely occurs within the cerebellar nuclei. To explore this, we recorded PC activity in the cerebellar crus lobules of three male monkeys trained to detect the omission of periodically flashing visual stimuli and compared it with dentate nucleus data. PCs showed gradually increasing periodic simple spike activity, with amplitudes proportional to the interstimulus intervals. As a population, PC signals slightly preceded those of dentate nucleus neurons and were more temporally variable. However, the individual dentate neuron activity was 84% explained by a linear sum of signals from a small subset of PCs. These results suggest that the main components of cerebellar output signals for temporal prediction may originate from the cerebellar cortex and are integrated within the deep nuclei before being sent to other brain regions. Furthermore, changes in complex spike activity were observed in more than half of the PCs, suggesting that synaptic plasticity in the cerebellar cortex may contribute to modulating these signals.

Significance Statement

Although the role of the cerebellum in motor control is well established, the mechanisms underlying its nonmotor cognitive functions remain unclear. Whether cerebellar computations during motor tasks generalize to nonmotor contexts is a key question in systems neuroscience. This study examined information transfer between the cerebellar cortex and deep nuclei in monkeys performing a periodic temporal prediction task. Purkinje cells (PCs)—the only output of the cerebellar cortex—encoded diverse temporal signals, while neurons in the dentate nucleus showed more phase-specific responses. Notably, the activity of individual dentate nucleus neurons was largely explained by a linear combination of just 16 PCs, suggesting that temporal prediction signals are generated in the cerebellar cortex and selectively integrated in the deep nuclei.

Introduction

The cerebellum has a beautifully organized uniform structure, and many studies have been conducted at the circuit, cellular, and molecular levels. At the systems level, the cerebellum is involved in the predictive control of movement and its adaptive learning (Herzfeld et al., 2020; De Zeeuw et al., 2021), but it is also thought to be associated with a variety of nonmotor functions through interconnection with many brain regions (Strick et al., 2009; Ito, 2011; Sokolov et al., 2017; Schmahmann et al., 2019). Uniformity of the circuit structure suggests that the cerebellum contributes to diverse functions through a shared computational mechanism. However, as few studies have examined the activity of individual neurons in the cerebellum during cognitive tasks (Sendhilnathan et al., 2020; Flierman et al., 2025), the underlying mechanism remains unclear. To understand how the cerebellum works, it is essential to determine whether the same neural mechanisms involved in motor control also apply to nonmotor functions.

The cerebellum is composed of the cortex and deep nuclei. The cortex integrates inputs from mossy and climbing fibers and transmits signals to the deep nuclei via inhibitory Purkinje cells (PCs). The cerebellar cortex plays a major role in information processing, and signals in the deep nuclei likely reflect the outcome of this computation (Person and Raman, 2012; Shadmehr, 2020). However, because both mossy and climbing fibers extend axonal branches to the cerebellar nuclei (Shinoda et al., 1992; Sugihara et al., 2001), these excitatory inputs may also contribute to the generation of signals within the nuclei. Indeed, despite the high spontaneous activity of PCs, most neurons in the deep cerebellar nuclei that receive inhibitory inputs also have high baseline firing rates. This might be attributable to external excitatory inputs in addition to the inherent properties of cerebellar nucleus neurons (Raman et al., 2000).

To elucidate the source of the signals in the deep cerebellar nuclei, this study compared neuronal activity in the cerebellar cortex with that in the nucleus during nonmotor cognitive tasks. We previously showed that neurons in the dentate nucleus of the cerebellum exhibit gradually increasing periodic activity in monkeys trained to detect the omission of regularly flashing visual stimuli (Ohmae et al., 2013; Uematsu et al., 2017; Kameda et al., 2023). Because there was no sensory input at the time of omission, the temporal prediction of the next stimulus is crucial for detecting stimulus omission. Since periodic activity is significantly reduced during passive viewing of repetitive stimuli or during tasks involving the detection of color changes in visual stimuli (Tanaka et al., 2021), this activity may underlie temporal prediction mechanisms. During the recording of these neurons, the administration of a small amount of GABA receptor antagonist in the vicinity attenuated the periodic activity, suggesting that the time-prediction signals in the dentate nucleus originate from the cerebellar cortex (Uematsu and Tanaka, 2022). In the previous study, however, the need to record from single neurons limited the dose of the drug, and its effect on neuronal activity was relatively small. The widespread distribution of dendrites in cerebellar nucleus neurons (Uusisaari et al., 2007) may also be responsible for this result. Furthermore, although the overall changes were not statistically significant, some dentate nucleus neurons showed altered periodic activity during the local administration of glutamate receptor antagonists, suggesting that inputs from mossy fibers or excitatory interneurons in the nucleus might play a role.

Based on these previous observations, the present study explored the neuronal activity in the crus I and II lobules, which send projections to the dentate nucleus of the cerebellum (Kelly and Strick, 2003). Many PCs exhibited periodic simple spike (SS) activity during the task, similar to previously reported neurons in the dentate nucleus. Since the activity of individual dentate nucleus neurons can be approximated by a weighted combination of SS activity from a relatively small number of PCs, sensory prediction signals in the dentate nucleus may primarily originate from the cerebellar cortex.

Materials and Methods

Animal preparation

The experiments were conducted on three male Japanese monkeys (Macaca fuscata, Monkeys H, Q, and W, 9–11 kg, 8–12 years old). All experimental protocols were evaluated and approved in advance by the Hokkaido University Animal Care and Use Committee and were in accordance with the Guidelines for Proper Conduct of Animal Experiments (Science Council of Japan, 2006). The health of the animals was carefully monitored by animal care staff and experimenters, and their food intake, water supply, stool volume, and overall physical condition were recorded daily. Water intake was regulated during weekday training and experiments to motivate the animals to perform the tasks; however, they could drink water ad libitum on weekends. No strict dietary restrictions were imposed, and a variety of vegetables, fruits, and nuts were provided daily.

Prior to the experimental procedures, the animals were trained to sit voluntarily in a custom-made primate chair. A head-holding device was then installed on the skull with titanium screws and dental acrylic using sterile surgical procedures under general anesthesia with isoflurane and nitrous oxide. Analgesics were administered during surgery and for several days postoperatively. After complete recovery, a second surgery was performed under the same surgical conditions to implant a search coil under the conjunctiva to monitor eye movements. The animals were trained for several months on the oddball detection task described below. To allow neuronal recording from the cerebellum, a third surgery was undertaken to implant the recording chamber. The location of the chamber relative to the crus lobules was verified using magnetic resonance imaging (MAGNETOM Prisma 3T, Siemens). Topical or systemic antibiotics were administered as needed during the experiments.

Visual stimuli and behavioral task

During the training and experimental sessions, monkeys were placed in a dark booth with their heads fixed to the primate chair. Visual stimuli were presented on a 27 in liquid-crystal display monitor (BenQ; XL2720Z; refresh rate, 144 Hz) located 40 cm away from the eyes at a viewing angle of 73 × 46°. The experiment was controlled using a Windows-based stimulus presentation and data acquisition system (TEMPO, Reflective Computing) that updated every event at 200 Hz and acquired data at 1 kHz. Horizontal and vertical eye positions were continuously monitored during the training and experimental sessions using the search coil technique (Enzanshi Kogyo).

The animals were well trained on a modified version of the missing oddball detection task developed previously (Ohmae et al., 2013; Kameda et al., 2019). In this task (“hand trial”; Fig. 1A, top), a central fixation point (FP; 0.5° red square) was presented firstly when the monkeys pressed a button that was attached to the primate chair. During the maintenance of eye fixation and holding the button, a brief (35 ms) 4° white square contour surrounding the FP appeared repeatedly at a fixed interstimulus interval (200, 400, or 600 ms; Fig. 1B). Because the interstimulus interval varied from trial to trial, the animals needed to learn the stimulus tempo on each trial. After a random repetition (2,000–4,800 ms), one stimulus was omitted, and the animals were required to release the button within 600 ms to obtain a liquid reward. In a variant of the task (“eye trial”; Fig. 1A, bottom), no hand movements were required, and the additional saccade target appeared 16° left or right of the FP and remained visible during the repetition of visual stimulus that surrounded the FP. In response to stimulus omission, the animals were required to move their eyes to the target within 600 ms. Monkeys Q and W were trained for hand trials, but Monkey H was trained for eye trials. Neuronal activity was recorded after the monkeys were well trained on the task (mean success rates of 86, 74, and 82% for Monkeys H, Q, and W, respectively).

Figure 1.

A, Sequence of events in the missing oddball detection task. During central eye fixation, a white square surrounding the FP was repeatedly presented at regular intervals. After random repetitions, one stimulus was omitted. Monkeys were trained to respond to the stimulus omission by releasing the button (hand trial) or by generating a saccade to the target (eye trial). B, The time course of events. The interstimulus interval was 200, 400, or 600 ms and was constant in each trial. The omission occurred 2,000–4,800 ms from the first stimulus of the sequence.

Physiological procedures

The activity of single PCs was recorded in the crus I and II lobules of the cerebellum in three monkeys. Single tungsten microelectrodes (∼1.0 MΩ at 1 kHz, Alpha Omega Engineering or FHC) were inserted through a 23 gauge stainless steel guide tube using a custom-made grid system. The electrodes were advanced remotely using a micromanipulator (MO-97S, Narishige) attached to the recording chamber. The signals obtained from the electrodes were amplified, bandpass filtered (300 Hz to 10 kHz), and monitored online using a neural data acquisition system (Omniplex, Plexon, or ASD, Alpha Omega Engineering) and an audio device. When a task-related neuron was encountered during the experiments, we attempted to isolate action potential waveforms using software with real-time template–matching algorithm. These neural data, along with task events and eye movement data, were saved in files and later analyzed offline to isolate SS and complex spike (CS) activities generated by each PC. The locations of task-related neurons were verified based on MR images (Fig. 2A) and the stereotaxic coordinates of electrode penetration. Most neurons were recorded from coordinates ranging from 9 to 13 mm posterior to the interaural line and 12–15 mm lateral to the midline (Fig. 2B).

Figure 2.

A, The region of interest on MR images of Monkey W. The red arrow indicates the stereotaxic coordinate of P12 R14. B, Top view of the recording sites in three animals. The coordinates of electrode penetrations are slightly jittered for presentation purposes. C, Examples of SS (blue dots) and CS (red dots) recorded from a PC. D, Superimposed waveforms of simple and CS for the neuron shown in C. E, Cross-correlogram indicates a transient suppression of SS activity after the occurrence of CS in the same PC.

Data acquisition and statistical analyses

Eye position data during the experiments were digitized at a 16 bit resolution, sampled at 1 kHz, and saved in files, along with event timestamps. The neuronal data were stored at 40 kHz for offline spike sorting (Fig. 2C). For all neurons, the spike waveforms were reviewed and sorted after the experiments using commercially or freely available software (Offline Sorter, Plexon, or P-sort; Sedaghat-Nejad et al., 2021). In this study, we only considered the activities of well-isolated PCs and compared them with those recorded previously from the dentate nucleus of the cerebellum (Ohmae et al., 2013). To identify PCs, we reviewed the SS and CS waveforms and constructed a cross-correlogram aligned with CS occurrence for each neuron (Fig. 2D,E). We confirmed that SS firing was transiently suppressed following a CS in all PCs; otherwise, the data were excluded from subsequent analysis.

Data were analyzed using MATLAB (MathWorks). Because the characteristics of neuronal activity during repetition of visual stimuli were similar between animals, neuronal data from different animals were combined and analyzed. To reveal the time course of individual neuronal activity, we aligned data from multiple trials to specific task events and calculated the average firing rate at each millisecond. The resulting signals were then smoothed using a Gaussian kernel (σ = 30 ms) to obtain spike density functions (Fig. 3). Unless otherwise noted, quantitative measures of neuronal activity were based on the modulation of spike density during the task. For quantitative analyses, we focused exclusively on SS activity as it constitutes the primary output of PCs. The periodic activity of SS was verified using a Fourier transform applied to the data from the 1,200 ms period preceding the omission in trials with 400 and 600 ms stimulus intervals. To analyze the periodic activity of CSs, the occurrences of CSs within 16 evenly spaced temporal windows during each 400 ms interstimulus interval were tested against a uniform distribution using the Rayleigh test.

Figure 3.

A,B, Activity of two example PCs exhibiting an increase (A) or decrease (B) of SS firing following each repetitive stimulus. Vertical dashed lines indicate timing of each stimulus. Data are aligned with either the first stimulus (left) or the stimulus omission (right). Spike density profiles for SS and CS activities are shown in blue and magenta lines, respectively. The raster plots below represent the timing of SS (gray dots) and CS (red) occurrence in each trial. Note that PC #1 (A) showed a transient CS activity to each stimulus late in the trial, whereas PC #2 (B) did not. C,D, Activity of two example dentate nucleus neurons that gradually synchronized to the repetitive stimulus. Note the difference in the phase of periodic activity between the neurons.

Because response modulation was small and reproducibility was low during the early phase of each trial, neuronal responses to each visual stimulus were evaluated using regression analysis (Fig. 4; Uematsu and Tanaka, 2022). We first measured the amplitude of neuronal modulation during the period between the last stimulus and subsequent stimulus omission. This segment was then used as a template for the linear fitting of the data from each interstimulus interval to estimate the response gain. When analyzing the timing of the periodic activity (Fig. 5), we averaged the spike density functions from the three cycles preceding stimulus omission. The resulting single-cycle profile was used to identify the timing of the peak and trough of periodic activity.

Figure 4.

A, Time courses of SS firing rate of an example PC for different interstimulus intervals. Stimulus timing is denoted by vertical dashed lines. B, The magnitude of firing modulation during each interstimulus interval as a function of time after the first stimulus for the neuron shown in A. Datapoints on the right indicate the firing modulation for the stimulus immediately before omission. C, Mean and 95% confidence intervals of the magnitude of firing modulation for the first (black) and last stimulus (red) in multiple PCs. D, Neuronal modulation in dentate nucleus neurons, modified from Ohmae et al. (2013). Solid and dashed lines indicate neurons with decreased and increased activity for each repetitive stimulus, respectively.

Figure 5.

A, Heatmap of normalized SS activity in the 400 ms condition for individual PCs. B, Heatmap of normalized activity in the 400 ms condition for individual dentate nucleus neurons. Cyan dots on the right side indicate neurons exhibiting an increase of the firing rate following each stimulus (increase-type neurons, n = 23). C, The polar plot shows the distribution of peak timing of SS activity for PCs. Red solid and green dashed lines indicate the data for 400 ms and 600 ms intervals, respectively. D, Data of dentate nucleus neurons but for the timing of troughs (minima) of activity. E, Comparison of peak timing of SS activity for individual PCs between trials with different stimulus intervals. Solid and dashed lines indicate millisecond and phase unification lines, respectively. F, Same as E but for trough timing of dentate neuron activity. Cyan and black dots represent increase-type and decrease-type neurons, respectively. G, Time courses of PC population activity under different interval conditions, aligned to the peak activity of each neuron. Black, red, and green lines indicate, 200, 400, and 600 ms conditions, respectively. Data for each neuron were subtracted from the average activity before the first stimulus. Arrowheads indicate the timing of the minima. Shaded area represents ± SEM. H, Population activity of dentate nucleus neurons aligned to the trough timing. The timing of peak activity (arrowhead) varies with the interstimulus interval, indicating temporal scaling of neuronal activity. I, The relationship between the timing of SS peak activity and magnitude of firing modulation in individual PCs (400 ms). Red lines connect the means for each 22.5° bin. Note that the response size (radius) is plotted on a logarithmic scale. J, Same as I but for dentate nucleus neurons. The data for dentate neurons shown in the right column of this figure were reanalyzed from previously published data in Ohmae et al., (2013).

To examine how well the cerebellar nuclear activity can be accounted for solely by input from the cerebellar cortex, we fitted the activity of individual dentate nucleus neurons with a linear combination of a subset of PCs activity. For this calculation, we used spike density data consisting of 1,200 ms after the first stimulus and 1,200 ms before omission in trials with 400 and 600 ms stimulus intervals (4,800 data points). Given that PCs are inhibitory, the fitting was performed using the least-squares method with the constraint that the weight coefficient of each neuron was negative. To mitigate the effects of overfitting, we performed the fitting using half of the trials for each PC and evaluated the resulting model using the remaining half. The goodness of fit was evaluated using the adjusted R² corrected for the degrees of freedom. To identify the most parsimonious model for predicting the activity of each dentate neuron, we used backward stepwise regression. Initially, we reconstructed the activity of individual dentate nucleus neurons using all 83 PCs tested at both stimulus intervals. We then excluded one neuron at a time and searched for the combination that yielded the highest R² value. This procedure was repeated to calculate the adjusted R² for each dentate nucleus neuron as a function of the number of PCs used for fitting (Fig. 6D). Among these, the set of PCs that produced the highest R² was defined as the “optimal set.” As controls, we performed the same calculation after replacing the data between different stimulus intervals and also computed the adjusted R² using the optimal set and weights for the data during the response period after stimulus omission (Fig. 6C).

Figure 6.

A, Schematic of the generation mechanism of temporal prediction signals within the cerebellum. B, Activity of a dentate neuron (orange lines) fitted with a weighted sum of the activity of 15 PCs from half of the trials (blue solid lines), aligned to the first stimulus (left panel) or stimulus omission (right panel). The performance of global fit (least squares) was evaluated using reconstructions based on the remaining trials (blue dashed lines). C, Distribution of adjusted R² values calculated using the optimal PC set for each dentate neuron (original). The red horizontal line indicates the median, and the vertical line spans the 25th to 75th percentiles. Shuffled data were generated by replacing different interval conditions in the cross-validated data. The R² values during the response period (movement) were computed using the same optimal PC set and weights but based on neuronal activity within ± 300 ms of movement onset. D, Adjusted R² values from cross-validated fitting of each dentate neuron's activity as a function of the number of PCs used. Each gray line represents an individual dentate neuron, connecting the best-fitting results and terminates at the optimal value obtained across different numbers of PCs. The lower histogram shows the distribution of the number of PCs in the optimal set.

The details of the quantitative measures are reported in the relevant text. For comparisons between the two groups, paired and unpaired t tests were used, and for circular data, the Rayleigh test, Watson–Williams test, and circular–linear correlation test were applied. Statistical calculations were performed using the Statistics and Circular Statistics Toolboxes for MATLAB (Berens, 2009).

Results

Periodic activity in the cerebellar cortex and deep nuclei

We recorded 83 PCs in three monkeys (n = 20, 26, and 37 for Monkeys H, Q, and W, respectively) that showed clear periodic SS activity during the missing oddball task with interstimulus interval of 200, 400, and 600 ms. All neurons exhibiting periodic activity in one stimulus condition also showed more or less periodic activity in the other conditions (Fig. S1A). Overall, the mean power of neuronal activity at the stimulus (fundamental) frequencies in the 400 and 600 ms interval conditions was 9.3 times greater (SD = 5.9, ranging from 2.6 to 32.6) than that at the frequency corresponding to the alternative interval. These values did not differ significantly across monkeys (one-way ANOVA, F_{(2, 80)} = 2.09; p = 0.1; Fig. S1B). Figure 3, A and B, illustrates two representative examples. Both neurons exhibited only weak SS activity during the first few cycles of stimulus flashing, but later in the trial, their activity synchronized with the repetitive visual stimuli and exhibited large periodic responses, although the timing of the peak of periodic activity differed between the PCs. In more than half of the PCs (51/83%, 61%), the CS response also increased gradually and showed periodic activity (Rayleigh test p < 0.05; Fig. 3A), with the peak of CS firing preceding that of the SS by 69.5 ± 68.8 ms (Fig. S1C). However, other neurons showed no periodic CS firing even at the end of the trial (B). As defined (see Materials and Methods), all PCs showed a transient suppression of SS activity immediately after CS for 19.7 ± 6.4 ms (SD; n = 83; ranging from 10 to 51 ms; Fig. 2E).

The temporal profile of these SS activity resembled that of neurons in the dentate nucleus reported earlier by our laboratory. Both dentate nucleus neurons in Figure 3, C and D, initially showed only weak responses, but periodic activity increased gradually as the repetitions progressed. As in the example in Figure 3C, many dentate nucleus neurons transiently decreased their firing rate with the appearance of each stimulus, and the peak of periodic activity was roughly aligned with the stimulus timing. Previous studies have classified such neurons as “decrease-type” neurons based on their activity level 150 ms after stimulus onset (Ohmae et al., 2013; Kameda et al., 2023). The remaining neurons showed an increase in the firing rate following stimulus presentation (Fig. 3D) and were classified as “increase-type.”

This study aimed to determine the extent to which the population activity of PCs can explain periodic activity in the cerebellar nuclei. In subsequent sections, we sought to compare the properties of SS activity in PCs with those of neurons in the dentate nucleus. We only considered SS activity in this study because the CS firing rate is low and SS is thought to be primarily responsible for PC output (Kojima et al., 2010; Herzfeld et al., 2015).

Effects of stimulus repeat and stimulus interval

Neurons in the dentate nucleus represent time-specific information by modulating the amplitude of their periodic activity according to different stimulus tempos (Ohmae et al., 2013; Uematsu et al., 2017). We examined whether the activity of PCs was similarly altered by the interstimulus interval. Figure 4A illustrates the time course of SS activity in a single PC when the task was performed at interstimulus intervals of 200, 400, and 600 ms. When the interval was 400 or 600 ms, the amplitude of the periodic activity increased significantly in each trial. However, when the stimulus interval was 200 ms, the amplitude remained small until the end of the trial. Figure 4B plots the changes in the magnitude of periodic activity of the same neuron at each stimulus interval from the first stimulus to the stimulus omission. Because omissions occurred randomly between 2,000 and 4,800 ms, fewer trials were available in the later period. Therefore, data are plotted only up to the point at which at least half of the trials remained. When the stimulus interval was long, the response magnitude began to increase within 1 s of the first stimulus and reached a plateau ∼2 s later. The time course was similar for the 400 and 600 ms conditions, although the rate of increase was clearly lower for the 200 ms condition. The amplitude of the periodic activity immediately before stimulus omission (open circles on the right) strongly depended on the stimulus interval.

Figure 4C summarizes the results for the 77 PCs examined across all three tempos (see Fig. S1A for the activity in individual neurons). Because trials with different stimulus intervals were presented randomly, the magnitude of firing modulation during the first stimulus interval was similar across conditions (black). However, the magnitude of periodic activity in PCs immediately before stimulus omission was greater at longer stimulus intervals (red; F_{(2, 152)} = 198.9; p = 3.7 × 10⁻⁴³) and did not differ across animals (F_{(2, 152)} = 0.55; p = 0.6; Fig. S1B). For comparison, Figure 4D shows previously published data on neurons in the dentate nucleus [modified from Fig. 3D of Ohmae et al. (2013)]. These neurons were divided into two groups (increase-type and decrease-type neurons), and the effects of stimulus interval were evident in both groups. Thus, SS activity in PCs, as in dentate nucleus neurons, exhibited timing-specific firing modulation. The small modulation of periodic activity observed in the 200 ms condition is likely related to previous findings, including the lack of an inactivation effect of dentate neurons on behavioral performance under this stimulus condition (Ohmae et al., 2013), as well as the inability of humans to predict the timing of the next stimulus when the interstimulus interval is shorter than 250 ms (Ohmae and Tanaka, 2016).

Furthermore, the periodic activity of dentate neurons has been shown to correlate with reaction times for omission detection (Ohmae et al., 2013; Uematsu et al., 2017). Similarly, when individual PC data were divided into three groups according to response latencies, activity around the time of omission (50 ms) tended to be greater in trials with shorter latencies (linear mixed model; p = 0.042 and 0.039 for the 400 and 600 ms conditions, respectively; Fig. S1D).

Comparison of the time course of individual neuronal activity

Because each neuron in the cerebellar nuclei receives input from numerous PCs (Palkovits et al., 1977), signals from the cerebellar cortex must be integrated into the nucleus when generating the cerebellar output. To understand the signals underlying these computations, variations in individual neuronal activity were compared between PCs and neurons in the dentate nucleus. The heat maps in Figure 5, A and B, show the normalized firing rates of individual neurons sorted according to the phase of periodic activity. At both recording sites, a continuum of neurons was active in different phases, although the distribution demonstrated a slight bias. In particular, many peaks of activity in dentate nucleus neurons may occur around the time of stimulus presentation (vertical dashed lines). This is because numerous decrease-type neurons exhibited a transient reduction in activity following stimulus onset, and their recovery to baseline occurred over a time course that depended on the stimulus interval (Kameda et al., 2019). In contrast, the timing of the peak PC activity rarely aligned with stimulus onset and was instead distributed fairly evenly across the interstimulus interval.

To examine the bias in the activity phase in the population at each recording site, the distribution of the timing of the peak PC activity and the timing of the trough of dentate nucleus neuron activity are plotted in Figure 5, C and D, respectively. At both recording sites and under both the 400 and 600 ms conditions, the activity phases were biased and nonuniformly distributed (Rayleigh test, p < 0.001). The distributions of peak PC activity across three monkeys for both the 400 and 600 ms conditions did not differ significantly (all ps > 0.1; Kuiper two-sample test; Fig. S1B). As previously reported, many dentate nucleus neurons exhibit a transient decrease in activity with similar latencies for each repetitive stimulus. This decrease in activity in the dentate nucleus may result from a transient increase in the activity of inhibitory PCs, and in fact, the activity peak of many PCs preceded the troughs of dentate nucleus neuron activity. Specifically, the peak times of PC activity were 159 ± 75 ms (400 ms condition) and 163 ± 104 ms (600 ms condition), whereas the corresponding troughs in dentate nucleus neuron activity occurred 203 ± 65 ms (400 ms condition; Watson–Williams test, p = 0.002) and 211 ± 96 ms (600 ms condition, p = 0.01). However, the distribution of PCs was considerably wider and more dispersed than that of cerebellar nucleus neurons (bootstrap analysis with 10,000 resamples, 95% confidence interval for the difference in SDs, [5.6, 14.8 ms] and [1.1, 15.4 ms] for the 400 and 600 ms conditions, respectively). Thus, diverse signals in the cerebellar cortex may be selected and integrated into time-specific signals in the dentate nucleus.

In Figure 5, C and D, both the excitatory phase of PCs and inhibitory phase of dentate nucleus neurons were differentially distributed according to the stimulus interval (red solid vs green dashed lines). This may be because the changes in the activity of each neuron occurred at a fixed latency from repeated visual stimuli, irrespective of the stimulus interval. To examine this, Figure 5, E and F, compares the response latency of each neuron in trials with different intervals at each recording site. The data show that the timing of the transient response was determined by the time from the stimulus especially in PCs (solid black line; paired t test; PCs, t₍₈₂₎ = −1.3; p = 0.2), whereas that of some dentate nucleus neurons was biased toward the phase of the repetitive stimulus (dashed line; dentate, t₍₁₀₈₎ = 3.2; p = 0.002).

On the other hand, the time course of recovery from the transient response to each stimulus differed significantly between recording sites. When the population activity of the dentate nucleus neurons was aligned to the poststimulus trough, both the magnitude of firing modulation and time to peak depended on the stimulus interval (Fig. 5H). However, when the population activity of PCs was aligned with peak timing, the magnitude of activity still depended on the stimulus interval, although the time course back to baseline showed only weak temporal scaling (Fig. 5G). In individual neurons, the time from trough to peak in dentate nucleus neurons was longer than the time from peak to trough in PCs (unpaired t test; 400 ms condition, t₍₁₉₀₎ = 3.5; p = 5.4 × 10⁻⁴; 600 ms condition, t₍₁₉₀₎ = 5.6; p = 9.3 × 10⁻⁸).

Finally, the relationship between the phase and amplitude of periodic activity also differed between recording sites. Although the preferred phase of PCs was distributed widely, the magnitude of periodic activity did not differ significantly between the phases (circular–linear correlation coefficient, r = 0.24; p = 0.10; Fig. 6I). In contrast, in the dentate nucleus, the magnitude of periodic activity varied clearly with phase, with greater modulation observed in neurons that showed decreased activity 150–300 ms after each stimulus (r = 0.37; p = 5.3 × 10⁻⁴; Fig. 6J). Thus, the information encoded by PCs and dentate nucleus neurons differed, with an overall increase in stimulus phase selectivity at the level of cerebellar output.

Reconstruction of dentate nucleus neuron signals from PC populations

Next, we examined the extent to which the signals in individual dentate nucleus neurons could be explained solely by the population activity of PCs. The periodic activity of each dentate neuron was approximated by the weighted sum of the activities of the selected sets of PCs (Fig. 6A). Because the magnitude of periodic activity was small for a short interstimulus interval, this calculation was performed only for data of 400 and 600 ms interval conditions. In addition, because the PCs are inhibitory, the weight coefficients were constrained to be negative values. To exclude the effects of overfitting on trial-to-trial variability (noise), the goodness of fit was evaluated through cross-validation (see Materials and Methods).

Briefly, the data for each neuron in the dentate nucleus were first fitted (least squares) to a weighted sum of the activities of a certain number of PCs. Only half of the trials for each PC were used for fitting, and the weights obtained and average activity of the remaining half of the trials were used to evaluate the goodness of fit. Figure 6B shows an example of fitting the weighted sum of the activities of 15 PCs (solid blue lines) to that of a single dentate nucleus neuron (orange lines). As shown in this figure, the activity of each neuron in the dentate nucleus can be accurately reproduced by selecting an appropriate combination of PCs and weights. The adjusted coefficient of determination (R²), corrected for the degrees of freedom, was calculated using the population activity of PCs (blue dashed lines) reconstructed from the remaining half of the trials not used for fitting and was used as a measure of goodness of fit.

For each neuron in the dentate nucleus, the optimal weights were initially computed using all 83 PCs, and the adjusted R² was calculated through cross-validation. Subsequently, we iteratively searched for the combination of PCs that yielded the highest goodness of fit by removing one PC at a time from the initial group. The combination that achieved the highest R² value during the iterative process was defined as the optimal set of PCs for a given dentate neuron. The violin plot in Figure 6C displays the distribution of R² values derived from these optimal PC combinations. The mean R² was high (0.84 ± 0.10), with 33% (36/109) exceeding 0.9. To assess the goodness of fit expected by chance, we also performed the same analysis after swapping the PC data between the 400 and 600 ms interval conditions. The actual R² values were consistently and significantly higher than those obtained from the shuffled data (Fig. 6C; paired t test; t₍₁₀₈₎ = 23.1; p = 1.3 × 10⁻⁴³). When fitting was performed using the 200, 400, and 600 ms conditions, the mean R² value was significantly lower than that obtained using only the 400 and 600 ms conditions (0.80 ± 0.11; paired t test; t₍₁₀₈₎ = 5.9; p = 5.1 × 10⁻⁸), likely due to weaker periodic activity in the 200 ms condition.

We further assessed whether the fitting successfully captured the behavioral correlates of neuronal activity. Data for each neuron were divided into two groups based on reaction time to the omission, and the activity of dentate nuclear neurons was predicted using the previously identified optimal set of PCs for matched pairs (early–early and late–late) versus mismatched pairs (early–late and late–early). Matched pairs exhibited significantly higher R² values than mismatched pairs (0.76 ± 0.14 vs 0.72 ± 0.15; paired t test; t₍₁₀₈₎ = 6.3; p = 6.7 × 10⁻⁹), indicating that our reconstruction of dentate activity is sensitive to performance-related neuronal modulation.

Figure 6D shows the adjusted R² values (upper black lines) for individual dentate nucleus neurons when a reduced number of neurons from the optimal set were used. The lower histogram plots the number of PCs in the optimal set. Interestingly, this high level of data reproduction was achievable by appropriately selecting a relatively small number of PCs (mean, 16.2 ± 4.6; median, 16). Overall, the activity of the dentate neuron could be explained with over 85% accuracy using the signals from only 5 PCs in 37% of cases, 10 PCs in 50% of cases, and 20 PCs in 52% of cases.

However, the activity of the dentate nuclear neurons during the response period could not be predicted using the activity of the same PCs. When neuronal activity within ±300 ms of the behavioral response to the omission was predicted using the previously identified optimal set and corresponding weights, the average adjusted R² value was 0.35 ± 0.34 (median, 0.21; Fig. 6C, right; paired t test; t₍₁₀₈₎ = 16.7; p = 1.3 × 10⁻³¹). Furthermore, when the optimal weights were calculated by incorporating the response period, the R² value during stimulus repetition (1,200 ms before omission) was significantly reduced (0.76 ± 0.14; paired t test; t₍₁₀₈₎ = 6.0; p = 2.4 × 10⁻⁸). These results suggest that the activity of dentate nucleus neurons may reflect inputs from different sources, depending on the specific event within each trial.

Discussion

PCs are ∼26 times more abundant than neurons in the cerebellar nucleus and axon terminals of a single PC branch and project to multiple nuclear neurons (Palkovits et al., 1977; Teune et al., 1998). This anatomical organization suggests that signals from the cerebellar cortex are highly integrated into the cerebellar nuclei. Moreover, information transfer from the cerebellar cortex to deep nuclei may involve synchronized SS activity (Person and Raman, 2011), CS activity (Tang et al., 2019), and rebound excitation in the nuclei (Aizenman and Linden, 1999; Wetmore et al., 2008). To understand how signals are integrated, the activity of PCs and nuclear neurons should be quantitatively compared under similar behavioral conditions. A recent study has compared the time course of neuronal activity in the cerebellar nucleus and PCs in monkeys performing a reaching task, demonstrating that the disinhibition from PCs contributes to the generation of motor-related transient activity in the nucleus (Ishikawa et al., 2014). This finding is consistent with the evidence from mice that transient suppression of PC activity by optogenetic stimulation effectively excites neurons in the cerebellar nucleus and evokes eyelid movements (Heiney et al., 2014). The present study examined whether such information transfer during movement control could be generalized to nonmotor cerebellar functions.

Similarities and differences in the activity of PCs and dentate neurons

Many PCs in the crus I and II lobules exhibited periodic SS activity in monkeys performing missing oddball detection tasks. The amplitude of the periodic activity increased gradually as the stimulus was repeated, reaching a plateau at ∼2 s (Fig. 4B). Because stimulus omission occurred 2,000–4,800 ms after the first stimulus, the magnitude of periodic activity during this period was almost constant. The magnitude of neuronal modulation at this time was nearly proportional to the stimulus interval in the range of 200–600 ms (Fig. 4C). These characteristics of SS activity closely resembled those observed previously in dentate nucleus neurons during the same task (Fig. 4D). Given that the cerebellar crus lobules send massive projections to the posterior portion of the dentate nucleus (Ramnani, 2006; Bostan et al., 2013), PC activity likely contributes to the periodic activity in the nucleus.

However, quantitative differences in neuronal activity were observed between these recording sites. For example, many dentate nucleus neurons transiently decreased their activity after each stimulus, whereas PCs often showed increased activity (Fig. 5A,B). This may be explained by the fact that PCs are GABAergic inhibitory neurons. However, the timing of the peak PC activity was more widely distributed than the timing of the trough of dentate neuron activity. In addition, the mean (median) peak latency from stimulus presentation was 159 ms (159 ms) in PCs, compared with a trough latency of 203 ms (213 ms) in the dentate nucleus, which represents a slightly longer delay for transmission across a single synapse. This may reflect the fact that information transfer between PCs and dentate neurons requires considerable temporal and spatial summation (Person and Raman, 2012; Gruver et al., 2024).

Since many dentate nucleus neurons showed decreased activity following each visual stimulus, their activity often peaked near the time of stimulus onset (Fig. 5B; Kameda et al., 2019). Indeed, when the population activity of dentate nucleus neurons was aligned with trough timing, both the size and duration of the firing modulation varied depending on the stimulus interval (Fig. 5H). In contrast, when the population activity of PCs was aligned with the peak, the magnitude of activity depended on the stimulus interval, but the time course of recovery exhibited only partial temporal scaling (Fig. 5G). Furthermore, the relationship between the activity phase and the response magnitude of individual neurons differed between the two recording sites. In the PCs, no significant correlation was identified between the activity phase and response magnitude (Fig. 5I); however, in the dentate nucleus, neurons that showed decreased activity following the stimulus exhibited stronger periodic activity than those that showed increased activity (Fig. 5J). Taken together with the narrower distribution of response timings (Fig. 5D), population activity in the dentate nucleus exhibited a strong dependence on the stimulus phase and conveyed information that was well suited for predicting the timing of the next stimulus, regardless of the stimulus interval. These results suggest that information transmission from PCs to the dentate nucleus is not merely a sign inversion but rather an integrative process that qualitatively transforms the information represented at the population level.

Reconstruction of dentate nucleus signals and its limitations

Although the periodic activity of PCs and dentate nucleus neurons during the omission detection task was similar, several differences were observed at the population level. This might be because the information in the dentate nucleus is not solely derived from PCs but also integrates inputs from the collaterals of mossy and climbing fibers. We performed a quantitative analysis using a linear model to determine the extent to which the activity of individual neurons in the dentate nucleus can be explained by inputs from PCs alone. Approximately 84% of the variance in the periodic activity of cerebellar nucleus neurons could be explained by the linear sum of the PC activity (Fig. 6C). Interestingly, the model revealed that activity in the dentate nucleus could be explained by input from relatively few PCs (Fig. 6D). Because the fitting procedure eliminates redundant inputs, the resulting model likely underestimates physiologically redundant inputs from the PCs. Given the anatomical projections described above, a single cerebellar nucleus neuron is expected to integrate inputs from many PCs. This apparent redundancy might enhance the robustness of information processing and provide flexibility to the cerebellum. Overall, individual PCs exhibited greater diversity in the timing of their periodic activities, whereas neurons in the dentate nucleus displayed more temporally biased and integrated signals.

In contrast, when neurons with periodic activity were analyzed, the combination of PC populations and averaging weights that explained periodic activity in the dentate nucleus failed to accurately account for neuronal responses during movement (Fig. 6C). This may reflect the fact that cerebellar nuclear neurons receive additional input from different PCs or mossy fibers that are specifically active during movement (Gruver et al., 2024). To further investigate this, it will be necessary to examine the activity of individual neurons not only during the omission detection task but also in behavioral tasks that involve voluntary motor control, such as self-timed movement tasks (Ohmae et al., 2013; Kunimatsu et al., 2018).

One limitation of current study is that neurons were selected based on periodic modulation; therefore, our sample may not represent the entire population of PCs projecting to the dentate nucleus. Recent studies have highlighted the coding of saccade parameters by large populations of PCs (Herzfeld et al., 2015; Fakharian et al., 2025). Furthermore, because recordings were made using single electrodes, we were unable to assess the potential impact of synchronized activity among multiple PCs on dentate neuron activity (Person and Raman, 2011). Thus, the contribution of nonperiodic neuronal activity and spike timing in PCs to the generation of periodic predictive activity in the dentate nucleus remain to be elucidated in future studies.

Cerebellar information processing in sensory timing prediction

Interactions between the mossy and climbing fiber inputs are crucial for synaptic plasticity in the cerebellar cortex (Ito and Kano, 1982; Suvrathan et al., 2016). In our behavioral paradigm, the animals learned the stimulus tempo on a trial-by-trial basis and predicted the timing of the next stimulus. It remains entirely unknown whether the mechanism of adaptive learning in the cerebellum, which has been extensively studied in motor control (Lisberger, 2021), also contributes to temporal learning and sensory prediction. However, as shown in Figure 3A, many PCs exhibited periodic activity in both SS and CS, suggesting that synaptic plasticity in the cerebellar cortex may play a role in generating and modulating periodic activity. Further research is needed to clarify this point.

Previous studies using the missing oddball paradigm have shown that in addition to the cerebellum, similar periodic activity occurs in the striatum and motor thalamus (Kameda et al., 2019; Matsuyama and Tanaka, 2021). A recent study found that many neurons in both the cerebellar nucleus and the caudate nucleus of the striatum show periodic activity regardless of stimulus location. However, at the population level, periodic activity in the cerebellum is more strongly modulated by the location of repetitive stimuli, whereas activity in the caudate nucleus is more influenced by the direction of the planned movement (Kameda et al., 2023). Thus, although both regions exhibit periodic activity, the cerebellum is primarily involved in sensory processing, whereas the striatum contributes more to periodic motor preparation. However, the mechanisms underlying these transformations remain a key question for future research.