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Cerebellar Lobulus Simplex and Crus I Differentially Represent Phase and Phase Difference of Prefrontal Cortical and Hippocampal Oscillations

SUMMARY The cerebellum has long been implicated in tasks involving precise temporal control, especially in the coordination of movements. Here we asked whether the cerebellum represents temporal aspects of oscillatory neuronal activity, measured as instantaneous phase and difference between instantaneous phases of oscillations in two cerebral cortical areas involved in cognitive function. We simultaneously recorded Purkinje cell (PC) single-unit spike activity in cerebellar lobulus simplex (LS) and Crus I and local field potential (LFP) activity in the medial prefrontal cortex (mPFC) and dorsal hippocampus CA1 region (dCA1). Purkinje cells in cerebellar LS and Crus I differentially represented specific phases and phase differences of mPFC and dCA1 LFP oscillations in a frequency-specific manner, suggesting a site- and frequency-specific cerebellar representation of temporal aspects of neuronal oscillations in non-motor cerebral cortical areas. These findings suggest that cerebellar interactions with cerebral cortical areas involved in cognitive functions might involve temporal coordination of neuronal oscillations.


INTRODUCTION
Cerebellar function has long been linked to tasks involving precise timing and temporal coordination (Braitenberg, 1967;Ivry et al., 2002) in sensory-motor tasks. Popa and colleagues have shown that cerebellar inactivation disrupts the coherence, i.e., the stability of phase relationships between oscillations in cerebral cortical sensory-motor circuits (Popa et al., 2013). These findings implicate the cerebellum in the temporal or phase alignment of oscillatory activities between cerebral cortical structures. Watson et al. (2014) showed increased theta coherence between the medial prefrontal cortex (mPFC) and the cerebellar fastigial nucleus in freely moving rats during locomotion, but not when the rats were at rest. Granger causality analysis revealed a directionality of the coherence in the fastigial-mPFC direction, suggesting that cerebellar output could modulate the phase of mPFC theta oscillations in a behavior-dependent manner (Watson et al., 2014).
Here we tested whether the phase of spontaneous local field potential (LFP) oscillations in the mPFC and dorsal hippocampal CA1 region (dCA1) is represented in cerebellar Purkinje cell (PC) spike activity in awake, head-fixed mice. We use the term representation in the differences. Our reasoning behind targeting these three areas is based on their potential joint involvement in spatial working memory (SWM) (Lefort et al., 2015) and on findings of increased coherence between mPFC and dCA1 during the decision-making process in a SWM task (Gordon, 2011).
We asked whether phase and/or phase relationship of oscillations in the mPFC and CA1 are represented in the cerebellum and investigated whether representations in lobulus simplex (LS) and Crus I would show site-specific differences with respect to the representation of phase or phase differences. To address this question, we recorded PC simple spike activity in LS or Crus I while simultaneously recording LFP activity in mPFC and dCA1.

Link between Oscillation Phase and PC Activity
We obtained recordings of LFP activities in the mPFC and dorsal CA1 region while simultaneously recording PC simple spike activity in the cerebellar LS or Crus I. Raw data examples of LFP activity recorded in the mPFC and CA1 and single-unit PC spike activity in LS are shown in Figure 1.
All recordings were performed in awake, head-fixed mice at rest. Results from a fast Fourier transform (FFT) analysis of the power spectral densities of LFP activities in the mPFC and hippocampal CA1 region are compatible with awake-state brain activity with limited variability (Figure 2), consistent with previous findings in similar head-fixed recording conditions (Ito et al., 2014).
To determine whether the simple spike activity of PCs in LS was correlated with the instantaneous phase of LFP oscillations in the mPFC or CA1, we quantified PC spike activity as a function of the instantaneous phase for frequencies between 0.5 and 100 Hz. An illustration describing the principle of the spike-phase difference analysis is shown in Figure  3, using single-unit PC spike activity recorded in LS.
The representation of the instantaneous phase of mPFC LFP oscillations across the population of PCs in LS showed two distinct peaks at 2.5 and 68 Hz, corresponding to the conventional delta (0.5-4 Hz) and high gamma (50-100 Hz) frequency bands, respectively ( Figure 4A). The representation of the instantaneous phase of LFP oscillations in CA1 across the population of PCs in LS was similar to that of the mPFC, showing distinct peaks at 1 and 60 Hz ( Figure 4B).
The representation of the instantaneous phase of mPFC LFP oscillations across the population of PCs in Crus I showed distinct peaks at 0.5 and 2.5 Hz, both within the delta frequency range. In contrast to LS, the Crus I PC population representation lacked a distinct peak in the gamma frequency range ( Figure 4C). The representation of the instantaneous phase of CA1 LFP oscillations across the population of PCs in LS was similar to the mPFC, showing distinct peaks around 0.5, 1.5, and 2.5 Hz, all within the delta frequency range ( Figure 4D).

Link between PFC-CA1 Phase Differences and Spike Rate in Individual PCs in LS and Crus I
To determine whether the simple spike activity of PCs in LS is correlated with phase differences between LFP oscillations in the mPFC and CA1, we quantified PC spike activity as a function of mPFC-CA1 oscillation phase difference for frequencies between 0.5 and 100 Hz. The relationship between spike rate and phase difference was quantified for each frequency band by calculating a vector with a direction corresponding to a preferred mPFC-CA1 phase difference and a length representing how strongly spike activity reflected that particular phase difference for PCs in LS ( Figures 5A and 5B) and in Crus I ( Figures 5C and  5D). The statistical significance of spike modulation as a function of mPFC-CA1 phase difference was determined using bootstrap statistical methods (see the STAR Methods section for details). Significant firing rate modulation with mPFC-CA1 phase differences was found in 29 of 32 PCs (90.6%) in LS and in 14 of 17 PCs (82.35%) in Crus I.

PC Activity Modulation Occurs across the Frequency Spectrum of mPFC and dCA1 Oscillations
In an analysis of group data, we asked what fraction of PCs showed significant phasedifference-related rate modulations at each analyzed frequency ( Figure 6). The results suggest that there are clear preferred frequencies in both LS and Crus ( Figure 6A), whose phase differences are represented by large proportions of observed PCs, while other frequencies are not represented. The analysis of LS data revealed that spike rates were most commonly modulated by phase differences in the theta band, with the highest number of PCs representing phase differences for 5 Hz oscillations ( Figures 6B and 6C). Significant results also clustered into modes within each of the other conventional frequency bands: delta (2 Hz), beta (17.5 Hz), low gamma (35 Hz), and high gamma (55 Hz).
PCs in Crus I also represented phase differences only for specific mPFC and CA1 oscillations, with different preferred frequencies, compared to LS PCs ( Figures 6D and 6E). In Crus I, the modal frequencies were 2.5 Hz (delta), 8 Hz (theta), 15.25 Hz (beta), and 45 Hz (low gamma).
We evaluated the strengths of the representation of mPFC-CA1 phase differences for each conventional frequency band for PCs in LS and Crus I by expressing resultant vector length as the ratio (R) of the vector length minus the surrogate distribution median and the difference between the surrogate median and the surrogate 95 th percentile values (see STAR Methods and Figure 3E). For further analysis, R values were grouped by the conventional frequency bands for PCs recorded in LS and Crus I ( Figures 6F and 6G). A comparison of R value distributions revealed no differences between LS and Crus I for any frequency band (Wilcoxon rank-sum test) (results not shown). The average R values across all frequency bands were 1.52 ± 0.43 (mean ± SD) and 1.46 ± 0.41 (mean ± SD) for LS and Crus I, respectively. Comparison among frequency bands within each structure revealed no differences among R value distributions in different frequency bands with LS or Crus I (Wilcoxon rank-sum test) (results not shown).

DISCUSSION
Here we report that PC simple spike activity in LS and Crus I of awake, head-fixed mice represents the instantaneous phase and phase differences of LFP oscillations in the mPFC and dCA1. When evaluating the representation of phase across the populations of PCs, we found that the phase of delta band (0.5-4 Hz) oscillations in mPFC and dCA1 was represented by more than 30% of PCs in both LS and Crus I (Figure 4). By comparison, the phase of most other frequencies was represented by 10% or less of PCs in both cerebellar sites. However, the representation of the instantaneous phase of high gamma band (50-100 Hz) oscillations clearly differentiated between PCs recorded in LS and Crus I. More than 30% of LS PCs represented the instantaneous phase of gamma band oscillations in both mPFC and dCA1. There was no corresponding representation of mPFC or dCA1 gamma phase in Crus I, in which the fraction of PCs representing gamma phase was around or below 10% (compare Figures 4A and 4B with Figures 4C and 4D).
These findings document that the phase of neuronal oscillations in cerebral cortical areas is represented in cerebellar PC spike activity and that the representation is site and frequency band specific, suggesting that oscillations in different cerebral cortical areas are differentially represented in cerebellar cortical sites. Whether such a phase-and frequencydependent map of the cerebral cortex exists in the cerebellum will have to be determined in additional experiments.
In addition to the representation of the instantaneous phase, we found that PCs in both LS and Crus I represented phase differences between mPFC and dCA1 oscillations in one or more of the conventional frequency bands. As for the instantaneous phase, phase differences were not represented equally for all frequencies. We found differences between LS and Crus I in terms of preferred frequencies whose phase differences were represented by the largest proportions of PCs, as reflected in distinct peaks in the plots of fractions of PCs representing phase differences versus frequency ( Figure 6). In LS, those preferred frequencies were 2 Hz (delta), 5 Hz (theta), 17.5 Hz (beta), 35 Hz (low gamma), and 55 Hz (high gamma). In Crus I, the preferred frequencies were 2.5 Hz (delta), 8 Hz (theta), 15.5 Hz (beta), and 45 Hz (low gamma). In addition, in Crus I, three PCs represented phase differences in high gamma but with each cell representing a different frequency. The most prominent difference that distinguishes the activity of PCs in the LS compared to Crus I is the smaller portion of PCs representing delta band phase differences, with 28% of PCs in LS versus 11.7% of PCs in Crus I.
We evaluated the strength of the representation of phase differences between frequency bands within each structure or between the two structures ( Figures 6F and 6G). There were no significant differences in the strengths of representation of phase differences between LS and Crus I. Thus, although there were differences between LS and Crus I regarding the preferred frequencies for which phase differences are represented in PC spike trains, there were no differences with respect to the strengths of these representations.
LS and Crus I are adjacent to each other in the cerebellar cortex. Functional imaging studies suggest that the two lobules have different, as well as common, functional properties. For example, both have been implicated in verbal working memory (Desmond et al., 2005). However, Crus I (together with Crus II) was found to be part of the default mode network that did not include LS (Halko et al., 2014). Tracing studies showed reciprocal connections between Crus I and II and the prefrontal cortex in primates (Bostan et al., 2013) and rodents (Suzuki et al., 2012) but no such connections for LS. However, based on findings of extensive functional connectivity patterns in fMRI studies (Buckner, 2013), future studies are likely to reveal unexpected connections. For example, Watson et al. (2014) showed that the rat cerebellar fastigial nucleus, long believed to interact solely or predominantly with spinal cord circuits, has strong functional connections with the medial prefrontal cortex. We have no conclusive understanding of the similarities and differences between Crus I and LS based on connectivity patterns and involvement in behaviors. Our findings suggest distinct roles for the two areas with respect to the neuronal representation of the oscillatory phase and phase differences in the mPFC and CA1 region.
Although primates and rodents share evolutionarily conserved features in protein expression, neural circuit projection patterns, and gross anatomy, specific adaptations exist, such as expansion of lobules and the functional maps therein. Therefore, although a direct extrapolation of our data into other higher-order species may be challenging, the fundamental basis of how the cerebellum is organized and how it interacts with other brain regions is predicted to share significant homology across mammals (Luo et al., 2017;Sugihara, 2018).
Coherent oscillations between the cerebellum and the cerebral cortex, especially sensory cerebral cortical areas, have been reported previously. O'Connor et al. (2002) showed that coherence of 1-20 Hz oscillations in cerebral and cerebellar whisker-related areas were modulated by behavior, because they increased during active whisking. However, the authors did not investigate the directionality of influence between the two structures. Later, Ros et al. (2009) and Rowland et al. (2010) showed a directionality of influence for low-frequency (<10 Hz) coherence with sensory cerebral cortical areas driving cerebellar cortex and nuclei oscillations.
How cerebellar PC simple spike activity comes to represent phase and phase differences of neuronal oscillations in the mPFC and dCA1 remains to be determined. The phase of cerebral cortical oscillations could be present in the activity of mossy fibers, driven by phase-locked neuronal activity in the mPFC or dCA1. Such a representation could be supported by resonance properties of the Golgi cell network, which would be limited to frequencies of up to 30 Hz (Dugué et al., 2009). However, phase differences would have to be computed either within upstream structures, such as the pontine nuclei, or within the cerebellar network. Considering that any phase difference can be represented as a time interval, a possible neuronal mechanism, at least for higher frequencies, can be derived from the cerebellar network architecture. Parallel fibers could serve as delay lines, transforming phase-difference encoding delays between mossy fiber spike events into synchronous inputs to PCs as proposed by Braitenberg et al. (1997).
Although the behavioral significance of our findings remains to be determined, we would like to point out that the cerebellum, mPFC, and dCA1 are jointly implicated in spatial processing and SWM (Lefort et al., 2015;Spellman et al., 2015) and the process of decisionmaking in working memory involves temporary stabilization of phase differences (i.e., increased coherence) between mPFC-dCA1 oscillations (Gordon, 2011). How the cerebellum contributes to SWM is not understood, but our results uncover the compelling possibility of a cerebellar role in modulating mPFC-dCA1 coherence, which is concordant with findings by Popa et al. (2013), who showed that normal coherence between sensory and motor cortical areas requires an intact cerebellum. Coherence has been proposed as a mechanism for the coordination of neuronal communication between brain regions (Bastos et al., 2015). Our findings thus suggest cerebellar involvement in the temporal coordination of oscillatory phase relationships, a function that would be in line with the long-standing notions of cerebellar timing and temporal coordination functions (Braitenberg, 1961;Ivry et al., 2002).

STAR★METHODS CONTACT FOR REAGENT AND RESOURCE SHARING
Further information and requests for resources and data should be directed to and will be fulfilled by Dr. Samuel S. McAfee (Stuart.McAfee@STJUDE.ORG) or Dr. Detlef H. Heck (dheck@uthsc.edu).

EXPERIMENTAL MODEL AND SUBJECT DETAILS
Experiments were performed on a total 11 adult male C57BL/6J (B6) mice, (> 8 weeks old, 18-25 g body weight). Mice were housed in a breeding colony with 12-hour light/dark cycles in standard cages with ad libitum access to food and water. All experiments were performed during the light cycle, between 12:00 noon and 17:00 hours. None of the mice had undergone any previous experimental procedure. All animal experimental procedures adhered to guidelines approved by the University of Tennessee Health Science Center Animal Care and Use Committee. Principles of laboratory animal care (NIH publication No. 86-23, rev. 1996) were followed. Founder animals were originally purchased at Jackson Labs (Stock # 000664).

METHOD DETAILS
Surgical procedures-Mice were initially anesthetized in an induction chamber with 3% Isoflurane in oxygen controlled by a vaporizer (Highland Medical Equipment, CA) and then transferred to a stereotaxic head frame. Anesthesia was maintained at the lowest concentration at which mice failed to show toe-pinch reflexive withdrawal, typically 1% −2.5% Isoflurane in oxygen. Core body temperature was maintained at 37°C using a feedback-controlled heating pad with a rectal thermometer (FHC Inc., Bowdoinham, ME).
The skull was exposed and craniotomies were made over the left mPFC (lat. 0.5 mm, ant. 2.8 mm) and dCA1 (lat. 2.0 mm, ant. −2.3 mm) and over the right cerebellar LS (lat. 2.0 mm, ant. −5.52 mm, 6 mice) or right Crus I (2.5 mm, ant. −6.25 mm, 5 mice). Cylindrical recoding chambers were placed over each craniotomy. Recording chambers and a head fixation bar were anchored to the skull with three small skull screws and acrylic cement (Co-Oral-Ite Manufacturing, USA). Mice recovered for 3 to 4 days prior to recording.
Electrophysiological recordings-Recording procedures were as described previously (Liu et al., 2017). A 7-electrode micromanipulator (System Eckhorn; Thomas Recording, Germany) with a custom-made set of guiding tubes was used to record simultaneously from the three brain areas. Extracellular recording electrodes (3-7 MΩ) were advanced through the intact dura. In this system the metal guiding tubes serve as the electrical reference forthe extracellular recordings. Guiding tubes are immersed in saline, which is used to fill the recording chambers during experiments and established electrical contact between the guiding tubes and the surface of the targeted brain area. Hippocampal recording electrodes were advanced until sharp wave ripples (SWRs), a high-frequency local field potential (LFP) oscillation characteristic for the hippocampus (Buzsaki, 2015), were detected ( Figure 1A). Cerebellar PCs were identified by the presence of complex spikes (Thach, 1968). Prefrontal cortical sites were targeted following stereotaxic coordinates (Paxinos and Franklin, 2001) and verified anatomically using small electrolytic lesions.
LFPs and spike signals were separated by band-pass filtering at 0.1 to 200 Hz and at 200 Hz to 8 kHz, respectively (FA32; Multi Channel Systems, Germany), digitized (sampling rate: > 20 kHz for action potentials and > 1 kHz for LFPs) and stored on hard disk, using a 16 bit A/D converter (CED power1401) and Spike2 software (both Cambridge Electronic Design, UK). Electrode depths were adjusted to obtain stable LFP recordings in mPFC and dCA1 and single unit PC activity in the cerebellum.
Recording sessions were repeated on three successive days for each mouse. After completion of each recording session, the chambers were rinsed and re-filled with triple antibiotic ointment and mice were returned to their home cages.
Histology-At the end of the last recording sessions electrolytic lesions were created at the final recording sites in the mPFC, dCA1 and LS by passing a small current (5 μA/10 s) through the recording electrodes ( Figure 1B). Within 12 hours of creating the lesion, mice were euthanized and then transcardially perfused. After perfusion, the brain was removed and post-fixed in 4% formaldehyde for 24 h. Brain tissue was cut into 50 μm thick coronal sections, which were mounted and stained with cresyl violet. The location of lesion sites was determined using a stereotaxic atlas of the mouse brain (Paxinos and Franklin, 2001).
Analysis of PC activity-Single-unit spike activity was recorded from 32 PCs located in LS (6 mice) and 17 located in Crus I (5 mice). PCs were identified based on location, firing characteristics and the presence of complex spikes (Thach, 1970) (Figure 1). Simple spike activity was identified offline using a shape-based spike-sorting algorithm of the Spike2 software. PCs simple spike firing rates ranged from 36.5 to 157.9Hz, with a mean of 89.1 Hz, consistent with previously reported rates in awake mice (Cao et al., 2012) and primates (Thach, 1970). Complex spikes were excluded from the analysis because their low frequency (~1 Hz) resulted in too small a number of incidents for a meaningful evaluation.
Pre-preprocessing of LFPs-Only sections of data with stable single-unit spike isolation and LFP recordings, which were free of movement artifacts, were included in analysis. dCA1 recording sites were included only if they showed clear sharp wave ripples (Figure 1, dCA1 LFP). 60Hz noise was diminished using a hum-removal algorithm in Spike2 that subtracted 60Hz components rather than applying a notch-filter, which left the power spectrum of LFP signals at that frequency intact (Figure 2).

QUANTIFICATION AND STATISTICAL ANALYSIS
Analysis of LFP power spectral density-Power spectral density for LFP activity recorded in the mPFC and hippocampal CA1 regions were calculated using Fast Furier Transform (FFT) in MATLAB. FFT analysis was applied to subsequent, non-overlapping 10 s wide windows for individual recordings to determine temporal variability of power spectral density as a measure of brain states. The average power spectral density was also calculated across all datasets from all 11 mice, expressing the variability power spectral density across the group as standard error of the mean (SEM).
Estimation of LFP phase and phase relationships-In order to determine phase and phase relationships of LFP oscillations in PFC anddCA1 overtime, LFPs were band-pass filtered for frequencies between 0.5-100Hz. FIR filters were applied in frequency steps of 0.25Hz with bandwidth ranging from 0.5-10Hz with increasing frequency. Filter order was determined to be the number of samples within 5 cycles of the center frequency. The Hilbert transform was performed on each band-pass-filtered signal, and instantaneous phase values were defined as the angular value derived from the complex-valued analytic signal. The frequency specific phase relationship between mPFC and dCA1 oscillations was determined by subtracting the instantaneous mPFC phase from dCA1 phase.
Instantaneous phase and phase difference values were analyzed using an angular binning approach to produce a mean spike incidence (spike density) value for each phase. The choice to implement vector mean analysis over more conventional vector sum statistics was made primarily to account for potential inherent bias in the distribution of observed phase relationships (i.e., mPFC-dCA1 phase relationship preferences), and isolate the statistical relationship between spike rate and phase. Furthermore, the vector mean test can reveal significant PC silence during frequently-observed phases, which may be functionally relevant.
The phase or phase difference values were designated into 30 angular bins of 12° width, and the corresponding spikes within each bin were counted. The spike count in each bin was divided by the total number of angular samples in the bin to return a measure of spike density. Each bin was then treated as a vector with an angular value of the phase or phase difference and magnitude of the spike density in order to calculate a resultant vector with magnitude reflecting degree of modulation and direction of preferred phase or phase difference.
Statistical analysis-Bootstrap statistical analysis of the relationship between spike activity and PFC-CA1 phase/phase differences was performed by calculating vector lengths for 200 surrogate datasets. Each surrogate dataset was created by randomly shifting the spike sequence, leaving the original spike sequence unchanged. The resulting 200 surrogate vector values were rank-ordered for each frequency and the 95 th and 99 th percentile values were determined. Real vector values greater than the 95 th percentile of the surrogate vector distribution were considered statistically significant, and those greater than the 99 th percentile were selected for further group analysis. The magnitude of all significant resultant vectors was further quantified by first subtracting the surrogate median from each vector value and the corresponding 95 percentile boundary values and then calculating the ratios of those two values, as illustrated in Figure 3. The resulting ratio was termed R. For further analysis R values were grouped by frequency bands and evaluated separately for LS and Crus I PCs (Figures 6F and 6G).