Cerebellar control of a unitary head direction sense

Abstract

The head-direction (HD) system, a key neural circuit for navigation, consists of several anatomical structures containing neurons selective to the animal's head direction. HD cells exhibit ubiquitous temporal coordination across brain regions, independently of the animal's behavioral state or sensory inputs. Such temporal coordination mediates a single, stable, and persistent HD signal, which is essential for intact orientation. However, the mechanistic processes behind the temporal organization of HD cells are unknown. By manipulating the cerebellum, we identify pairs of HD cells recorded from two brain structures (anterodorsal thalamus and retrosplenial cortex) that lose their temporal coordination, specifically during the removal of the external sensory inputs. Further, we identify distinct cerebellar mechanisms that participate in the spatial stability of the HD signal depending on sensory signals. We show that while cerebellar protein phosphatase 2B-dependent mechanisms facilitate the anchoring of the HD signal on the external cues, the cerebellar protein kinase C-dependent mechanisms are required for the stability of the HD signal by self-motion cues. These results indicate that the cerebellum contributes to the preservation of a single and stable sense of direction.

Keywords: anterodorsal thalamic nucleus; cerebellum; head-direction cell; retrosplenial cortex; temporal coordination.

Fig. 1.

Suppression of cerebellar PKC-dependent plasticity causes directional firing instability in dark conditions. (A) Schemes illustrating the targeted structures for HD cell recordings. ADN, anterodorsal thalamic nucleus; RSC, retrosplenial cortex. (B) Spikes and HD tuning curves for a representative HD cell from RSC of a control mouse across light and dark sessions. Top, scheme illustrates the protocol for electrophysiological recordings under the light condition (with the presence of an external cue) and the dark condition (without the cue). Middle, spikes (black) are superimposed on the animal's trajectory (cyan). Bottom, spikes from the Middle panel are compiled in polar plots visualizing average FRs as a function of the animal’s head direction. (C) The activity of representative HD cells from control and L7-PKCI mice over time and under light and dark conditions. Top, from a control mouse; Bottom, from an L7-PKCI mouse. Left, HD cell activity by time. Right, data in the Left panel is accumulated to generate directional firing distributions for a 10-min session. In this example, HD cell from the L7-PKCI group displayed degraded directional activity over time under dark condition. FR, firing rate. (D) Left, representative HD cells from the ADN structure of a control (Left column) or an L7-PKCI (Right column) mouse. The same cell is shown across light (Top) and dark (Bottom) conditions. The HD tuning curve of each cell is visualized by polar plots demonstrating average FRs as a function of the animal’s head direction. HD cells from L7-PKCI mice exhibit drastic changes in the HD tuning curve under dark conditions. Right, HD cells from L7-PKCI mice exhibit lower directional stability in the dark. Right-top, population average of directional stability of HD cells across light and dark sessions relative to another light session (***P < 0.001). For each cell, the Pearson correlation between polar tuning curves of the first and second half of that session was assigned as the directional stability of the cell. The relative stability is after a normalization over the directional stability of the same cell in the first light session. Right-bottom, nonparametric comparison of directional stability of HD cells from the L7-PKCI group in the dark compared to random sampling distribution. The median of distributions is used as a criterion. Random sampling was made 100,000 times from a pool mixed of control and L7-PKCI groups (n_L7-PKCI = 102, n_Resampling = 165). CI, confidence interval. (E) Data are presented as in D for HD cells from RSC structure (**P < 0.01; n_L7-PKCI = 46, n_Resampling = 93). CI, confidence interval.

Fig. 2.

Temporal coordination between HD cell structures in the dark requires cerebellar PKC-dependent plasticity. (A) Two sets of representative simultaneously recorded HD cells from ADN and RSC of L7-PKCI mice which remap differently under dark conditions. In the first set (Left), HD cells from ADN show a directional drift over time in the dark while cells from RSC fire in random directions. In the second set (Right), cells from ADN maintain their PFD in the dark while the cells from RSC exhibit a shift in PFD as well as firing in random directions. (B) Left, the activity of representative HD cell pairs from control over a 10-s time window superimposed on the animal momentary head direction during light and dark conditions. Spikes are shown as colorful circles as well as raster lines. The gray line represents the animal’s momentary head direction. Right, accumulated FR for each cell for the whole session. Cells 1 and 2 were recorded from ADN and cell 3 was recorded from RSC. Both cell pairs fire in concert under both dark and light conditions. Cells 1 and 2 discharge in separate time windows and cells 3 and 4 exhibit codischarge within a small time window, under both light and dark conditions. (C) The discharge correlation for HD cell pairs from B during light and dark conditions. Normalized histograms with a value of 1 represent the chance level. Cell pairs exhibit a similar discharge correlation around the central time lag bin (τ = 0) across light and dark conditions. (D) Data are presented as in C for all HD cell pairs from control mice. Cell pairs are sorted based on the value of correlation at the central bin from the light session. (E) Data are presented as in B for representative cells from L7-PKCI mice. Cells 1 and 2 recorded from ADN exhibit a drift in firing direction under dark but retain their temporal coordination (discharge in separate time windows) similar to light conditions. Cell 1 from ADN and cell 3 from RSC exhibit codischarge within a small time window under the light and however often discharge in separate time windows under the dark. (F) The discharge correlations for HD cell pairs from E during light and dark conditions. Top, cell pair (1×2) from ADN represent similar discharge correlation under both light and dark conditions. Bottom, cells 1 and 3, respectively, from ADN and RSC, exhibit a different discharge correlation under the dark compared to light conditions (Bottom). (G) Data are presented as in F for all HD cell pairs from L7-PKCI mice. Cell pairs were separated into groups within structures (Top, within ADN and within RSC) and between structures (Bottom, ADN × RSC). Cell pairs are sorted based on the value of cross-correlation at the central bin from the light session. Note the difference in cross-correlation around the central time lag bin (τ = 0) for the ADN × RSC group. (H) The discharge correlations of HD cell pairs within structures (ADN or RSC) from both control and L7-PKCI groups are maintained under both light and dark conditions. Left, data from D is reprocessed for comparisons of central correlation values, only for cell pairs within ADN or within RSC. Central correlation values (correlation values at the central time lag bin) in a reference light session are plotted against that of another light (green) or dark (purple) session. The P value is after the two-sided Fisher z-transformed correlation values followed by Bonferroni correction for multiple comparisons. Middle, data are presented as left for the L7-PKCI group. Right, distribution of discharge correlation variations from light to dark compared to the chance-level CIs generated by random sampling. The median value was used as the criterion. CI, confidence interval. (I) The discharge correlations of HD cell pairs between ADN and RSC from the L7-PKCI group are decreased under dark conditions. Data are presented as in H, for cell pairs between structures (ADN × RSC). Left, the discharge correlation of cell pairs between structures from control in the dark was indifferent to light. Middle, the discharge correlation of cell pairs between structures from L7-PKCI in the dark was significantly weaker than in light. Right, the median variation of discharge correlation from light to dark for cell pairs between structures from L7-PKCI was significantly larger than the 95th percentile of random sampling distribution (P < 0.001, single-sided test). The median value was used as the criterion. CI, confidence interval.

Fig. 3.

Suppression of cerebellar PP2B-dependent plasticity disrupts HD cell anchoring to the landmark cue without affecting the temporal organization of the HD system. (A) Scheme illustrating the recording protocol across standard light conditions. (B) Two representative HD cells from the ADN of L7-PP2B mice with directional instability during a standard light session. Left, spike raster indicated by circles overlaid on HD samples. Middle and Right, HD tuning curves during each 2-min section (for visualization clarity of cell 1, FR is only shown for the first and last 2-min sections). Cell 1 exhibits directional drift over time. Cell 2 exhibits a subsequent increase in FR over time. For cell 2, the spike raster of the first and last 2-min section is also shown on the bottom for visualization of the change in FR. FR, firing rate. (C) Spike waveforms (tetrode recording) of the cells from panel B are shown for the first and last 2-min sections of the sessions. Note the stability of spike waveform across these two sections. Raw waveforms, in red; average waveforms, in black. Horizontal scale bar, 0.5 ms; vertical scale bar, 100 μV. (D) HD cells from L7-PP2B group exhibited significantly lower directional stability within standard light sessions. Left, data are presented as median (red line) with 25th and 75th percentiles (box) overlaying data points. Right, nonparametric comparison of median directional stability of HD cells from L7-PP2B group compared to the distribution of medians for random sampling. Random sampling was made 100,000 times from a pool mixed of control and L7-PP2B groups from all standard light sessions (n_L7-PP2B = 199, n_Resampling = 754). The median value of directional stability for HD cells from L7-PP2B is lower than the first percentile of the random sampling distribution. CI, confidence interval. (E) Stability of neuronal recordings within standard light sessions was similar between control and L7-PP2B groups. Left, spike waveform stability for a given session is estimated by the Spearman correlation between the average spike waveform of the first and second half of that session. Middle, relative changes in amplitude of average spike waveform from the first to the second half of sessions. Right, distribution of relative change in the peak-trough duration of average spike waveform from the first to the second half of sessions. Data for the Left and Middle panels are presented as median (red line) with 25th and 75th percentiles (box) overlaying data points. (F) Scheme illustrating the recording protocol under cue manipulation conditions. (G) HD cells from ADN in L7-PP2B mice weakly follow the cue rotations. Left, polar tuning curves of representative HD cells from ADN of a control (Left column) and an L7-PP2B (Right column) mouse. Inset values, peak FR in hertz (Hz); the degree of shift in tuning curve (°). The degree of shift in the tuning curve in the rotation session represents the amount of shift in the tuning curve compared to the light session. The degree of shift is calculated after rotating the tuning curve of the rotation sessions from −180° to 180° (in steps of 6°; positive degrees represent counterclockwise rotations), and finding the shift value that yields the highest Spearman correlation between the tuning curve of the cue-rotation session and previous light session. Right-top, the degree of shift in the tuning curve after the rotation session (R) for all cells. Each circle represents one HD cell. Right-bottom, the degree of shift in tuning curve following a light session or a cue rotation session. Following the cue rotation, HD cells from ADN in L7-PP2B mice exhibited significantly lower average rotation in comparison to the control (71.2 ± 2.6° control, 48.7 ± 5.9° L7-PP2B). *****P = 0.00001. (H) Data are presented as in G for HD cells from RSC. Following the cue rotation, HD cells from RSC in L7-PP2B mice exhibited significantly lower average rotation in comparison to the control (92.1 ± 5.7° control, 47.6 ± 9.5° L7-PP2B). **P = 0.0017. (I) The discharge correlations for all HD cell pairs from L7-PP2B mice under a light and cue rotation session. (J) The discharge correlations of HD cell pairs in L7-PP2B mice are maintained following the cue rotations compared to the light session. Data are presented as in I, for central correlation values in a reference light session plotted against another light (green) or cue rotation (Rot., purple) session. The P value is after the two-sided Fisher z-transformed correlation values followed by Bonferroni correction for multiple comparisons. (K and L) The discharge correlations of HD cell pairs in L7-PP2B mice compared to control. Data from the control and L7-PP2B group were resampled to create a chance-level statistic of correlation variations from light to cue-rotation session, and the median value used as a criterion. The median of data from L7-PP2B was compared to the chance-level statistic (random sampling, one-sided tests). Comparisons were made separately for cell pairs from within structures (K; within ADN and within RSC) and between structures (L; ADN × RSC). Median variation of discharge correlation from light to rotation session for cell pairs for both within and between structures did not surpass the 95th percentile of bootstrap distribution (P > 0.9, within structures; P > 0.7 between structures; one-sided test). CI, confidence interval.

Fig. 4.

Intact AHV and linear speed cell discharges during directional firing instability in L7-PKCI and L7-PP2B mice. (A) Firing characteristics of speed cells under dark sessions were indistinguishable between control and L7-PKCI groups. Changes in speed score in a light or dark session relative to a standard light session were compared between groups for both ADN (Left) and RSC (Right). (B) Firing characteristics of a representative speed cell (Left and Middle) from ADN simultaneously recorded with an HD cell with directional instability under the dark (Right). Note the similarity of speed cell firing in light and dark and directional instability of HD cell under the dark session. Left, speed tuning curve for a speed cell; Inset, Pearson’s correlation r. Middle, speed by HD tuning curves of the speed cell for visualizing a firing independent of head direction. Right, head direction tuning curves of a directionally unstable HD cell under the dark; Inset, peak polar FR. FR, firing rate; HD, head direction; Bin, the FR was estimated by binning the speed data; Mle, the FR was estimated using a maximum likelihood estimator (SI Appendix, Supplemental Experimental Procedures) (C) Firing characteristics of AHV cells under dark sessions were indistinguishable between control and L7-PKCI groups. Changes in the AHV score in a light or dark session relative to a standard light session were compared between groups for both ADN (Left) and RSC (Right). (D) Firing characteristic of a representative AHV cell (Left and Middle) from ADN was simultaneously recorded with an HD cell (Right). Note the similarity of AHV cells firing in light and dark and the directional instability of HD cell under the dark session. Left, AHV tuning curve for an AHV cell. Middle, AHV by HD tuning curves of the AHV cell for visualizing a firing independent of head direction. Right, head direction tuning curve of a directionally unstable HD cell under the dark; Inset, peak polar FR. FR, firing rate; HD, head direction; Bin, the FR was estimated by binning the AHV data; Mle, the FR was estimated using a maximum likelihood estimator (SI Appendix, Supplemental Experimental Procedures). (E–H) Data are shown as A–D for the L7-PP2B group. Comparison in ADN was not possible for AHV cells due to the lack of recorded cells. n.s., not significant.