Head-direction cells escaping attractor dynamics in the parahippocampal region

Navigation depends on the activity of head-direction (HD) cells. Computational models postulate that HD cells form a uniform population that reacts coherently to changes in landmarks. We tested whether this applied to HD cells of the medial entorhinal cortex and parasubiculum, areas where the HD signal contributes to the periodic firing of grid cells. Manipulations of the visual landmarks surrounding freely-moving mice altered the tuning of HD cells. Importantly, these tuning modifications were often non-coherent across cells, refuting the notion that HD cells form a uniform population constrained by attractor-like dynamics. Instead, examination of theta rhythmicity 1revealed two types of HD cells, theta rhythmic and non-rhythmic cells. Larger tuning alterations were observed predominantly in non-rhythmic HD cells. Moreover, only non-rhythmic HD cells reorganized their firing associations in response to visual land-mark changes. These findings reveal a theta non-rhythmic HD signal whose malleable organization is controlled by visual landmarks.

. 31 Continuous attractor network models provide a mechanistic framework explaining 32 how the HD signal is generated (Skaggs et al., 1995;Redish et al., 1996;Zhang, 1996). 33 In these models, neurons are allotted positions in a circle according to their preferred 34 firing direction. The connectivity between neurons depends on their relative position. 35 While neighboring cells with similar preferred HD excite each other, distant cells tend 36 to inhibit each other. This connectivity leads to the emergence of an activity packet 37 which represents the moment-to-moment HD of the animal. These models predict that 38 preferred HD differences between HD cells never change because the connections 39 within the network are immutable. 40 Most empirical data support attractor network models of HD cells. For example, 41 rotation of a peripheral visual landmark in an environment causes an equivalent rota- The recording environment was an elevated square platform surrounded by four walls. Two distinct visual patterns (vp1 and vp2) made of LED strips were attached to two adjacent walls. A standard paper cue card was attached to a third wall. b, Recording sessions comprised a sequence of forty 2-min trials that alternated between vp1 and vp2 trials. c, Sagittal brain sections showing representative recording sites in the MEC and PaS. Red circles indicate tetrode tips. d, Distribution of tetrode tips across brain regions and different layers of the MEC. PaS: parasubiculum, PrS: Presubiculum, RSA: retrosplenial agranular cortex, Ctx: cortex. e, HD firing rate polar plots for four HD cells recorded during the two light conditions (numbers indicate HD score and peak firing rate). f, Scatter plot showing HD scores and peak firing rates of all neurons during vp2 trials. Each dot represents one cell. Lines indicate thresholds for HD cells identification. Red dots are HD cells.
ing the vp1 and vp2 trials. At the population level, HD scores, peak firing rates and 121 mean firing rates of HD cells were not significantly different between the two trial types Numbers indicate peak firing rates and preferred HD during vp1 and vp2 trials. Middle: preferred HD of the same cells during individual 2-min trials. Changes in preferred HD were often readily visible on a single trial basis. Right: observed change in preferred HD between vp1 and vp2 trials (red line) and distribution of preferred HD changes when trial labels were reassigned randomly. b, Examples of two HD cells with different HD selectivity during vp1 and vp2 trials. Left: HD tuning curves during vp1 (black) and vp2 (blue) trials. Numbers indicate peak firing rates and HD scores during vp1 and vp2 trials. Middle: HD scores of the same two cells for individual trials. Right: observed difference in HD score between vp1 and vp2 trials (red line) and distribution of HD score differences when trial labels were reassigned randomly. c, Distribution of shifts in HD preference between vp1 and vp2 for all HD cells (red). Inset: the median of observed shifts (red line) with the distribution expected by chance (gray). d, Same as c but for changes in HD score between vp1 and vp2.   | Firing rate changes induced by visual landmarks. a, Six HD cells that significantly changed their firing rate depending on visual landmarks. For each cell from left to right: HD tuning curves for vp1 (black) and vp2 (blue) trials, instantaneous firing rates (standard deviation Gaussian kernel 25 s, window size 1 s) as a function of time, and average firing rates during vp1 and vp2 trials. Numbers indicate the relative change in rate of each HD cell. b, Distribution of relative change in firing rate for all HD cells (red). Inset: the median of observed rate change (red line) with the distribution expected by chance (gray). c, Pie chart illustrating the fractions of HD cells with significant changes in preferred direction, HD score or mean firing rate.
in preferred direction, v = 127, P < 10 -15 ; change in HD score, v = 4, P < 10 -16 ). 149 It was previously shown that HD cells located in the presubiculum and anterodor-150 sal thalamic nucleus maintained their average firing rate when an animal explored dif-151 ferent environments (Taube et al., 1990b;Taube and Burton, 1995;Goodridge et al., 152 1998). We therefore tested whether the mean firing rate of HD cells in the MEC/PaS 153 was also preserved when visual landmarks were manipulated. We observed HD cells 154 that showed pronounced alterations in their firing rate in response to different visual 155 patterns ( Figure 3a). For these cells, the instantaneous firing rate oscillated in time, 156 in line with the trial type ( Figure 3a). To test whether these changes were signifi-157 cant, we calculated the relative change in firing rate for each neuron: | r vp1 −r vp2 r vp1 +r vp2 |. We 158 found that 40.9% (38 out of 93) of the HD cells significantly altered their mean fir-159 ing rate in response to distinct visual landmarks. At the population level, observed 160 rate changes were larger than those obtained from surrogate data (Figure 3b; paired 161 Wilcoxon signed-rank test, v = 12, P < 10 -16 ). Thus, these results demonstrate that 162 the mean firing rate of HD cells in the MEC/PaS is modulated by visual landmarks. 163 The majority of neurons in the MEC are spatially selective (Diehl et al., 2017). It 164 could therefore be argued that the changes in the firing properties of HD cells between 165 vp1 and vp2 trials were caused by an altered spatial input to HD cells (Cacucci et al.,166 2004). To rule out this possibility, we focused our analysis on a subset of HD cells with 167 no significant spatial modulation (non-significant sparsity score; 36 out of 93 HD cells). 168 Within this population of non-spatial HD cells, 86.1% (31 out of 36) had a significant 169 change in preferred direction, HD score or mean firing rate between the vp1 and vp2 170 trials. This proportion was comparable to that observed when considering spatially 171 selective HD cells (Pearson's Chi-squared test: χ 2 = 0.3543, df = 1, P = 0.55). Thus, 172 the changes in HD cell properties did not result from an altered spatial signal between 173 vp1 and vp2 trials. 174 We also tested whether a similar proportion of HD cells showed landmark-driven that bidirectionality was not caused by instability of a single preferred direction. 194 Bidirectional HD cells were defined as HD cells for which the BD score was larger 195 than 0.2, the peak firing rates of the two peaks were larger than 2 Hz, and the ratio be-  From left to right: tuning curves during vp1 and vp2 trials, with numbers indicating the peak firing rates and bidirectionality (BD) scores during vp1 and vp2, and evolution of the BD score during the recording session. Bidirectionality of the tuning curved changed with the two trial types. b, Example of a bidirectional HD cell during the transition from vp2 to vp1 trials at a shorter time scale. Top panel: polar plots during 30 second blocks showing that the two preferred HDs are expressed together in short time periods during vp1 trials. Bottom panel: preferred HD and HD score of the cell over time. c, Distribution of angles between the two preferred HDs of bidirectional HD cells. d, Distribution of change in BD score between vp1 and vp2 for HD cells with a bidirectional HD tuning curve (red, n = 14). Inset: the median of observed changes in BD score (red line) with the distribution expected by chance (gray).

Within condition Between conditions
Pref. (second column) trials. The numbers above each polar plot indicate the difference in preferred HD (HD Pairs 1 and 2), in HD score (HD Pair 3) or in mean firing rate (HD Pair 4). Right: temporal evolution of the difference in preferred HD, HD score or mean firing rate for the cell pairs shown on the left. b, Correlation between the differences in preferred HD, in HD score and in instantaneous firing rate (IFR) association of HD cell pairs for trials with the same or different visual patterns. Data are shown for vp1 and vp2 trials (left, between conditions) or for two mutually exclusive subsets of vp1 trials (right, within condition). r values are correlation coefficients. c, Reorganization of preferred HD, HD score and IFR association of HD cell pairs between vp1 and vp2 trials (between conditions) or between two subsets of vp1 trials (within condition). Plots show mean ± 95% confidence intervals. **: P < 0.01, ***: P < 0.001.
to vp2 were not coherent. For example, two HD cell pairs modified their difference 220 in preferred direction depending on which visual pattern was presented (HD Pairs 1 221 and 2). These pairwise changes could be detected during single 2-min trials ( Figure   222 5a, right). A similar uncoupling of simultaneously recorded HD cell pairs was also 223 observed for HD selectivity (   These results indicate that the reorganization of firing associations was specific to non-326 rhythmic HD cells. 327 We also tested whether visually-driven reorganization between HD cells can be 328 predicted based on their synchronous activity at theta frequency. We obtained power   . 407 A core tenet of HD cell models is that cells within the network have a fixed con-408 nectivity and that differences in preferred direction between HD cells do not change 409 (Skaggs et al., 1995;Zhang, 1996;Redish et al., 1996). Although the HD signal is

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The raw data (spike trains, position data and histology) together with the com-471 puter code of this study will be freely available on digital repositories upon publication. Wire Company). Mice were anaesthetized with isoflurane (1-3%) and fixed to the 487 stereotaxic instrument. The skull was exposed and 4 miniature screws were inserted 488 into the skull. Two screws located above the cerebellum served as ground electrodes. 489 The skull above the MEC/PaS was removed and the tetrode bundles were implanted   Firing rate maps were generated by dividing the square platform in 2 x 2 cm bins. 570 The time in seconds spend in each bin was calculated and this occupancy map was 571 smoothed with a Gaussian kernel (standard deviation of 3 cm). The number of spikes 572 in each bin was divided by the smoothed occupancy map to obtain a firing rate map. A 573 smoothing kernel (standard deviation of 3 cm) was applied to the firing rate map. Only 574 periods when the mouse ran faster than 3 cm/s were considered. 575 To identify HD cells, vp1 and vp2 tuning curves were calculated by concatenating 576 data from all vp1 and all vp2 trials, respectively. A HD score was defined as the mean 577 vector length of the tuning curve. The preferred direction of the neuron was the circular 578 mean of the tuning curve. HD cells had to have a HD score larger than 0.4 and a peak 579 firing rate larger than 5 Hz during vp1 trials or vp2 trials or both to be selected. The where R P was the firing rate in one bin of the firing rate map and T P (θ) was the time 593 spent facing HD θ in that bin. A distributive ratio, DR, was then calculated to estimate 594 the similarity between the observed and predicted HD tuning curve: 595 DR = |ln((1 + R Obs (θ))/(1 + R P red (θ)))|/N, where N was the number of bins in a HD tuning curve. A DR of zero indicated that 596 the observed HD tuning curve was well predicted by a combination of spatial selectivity 597 and bias in HD sampling. Higher value indicated that the HD tuning curve was poorly 598 predicted by the spatial selectivity of the cell and that its firing rate was modulated by 599 HD. Cells had to have a DR larger than 0.2 to be considered putative HD cells. 600 Grid cells were identified based on the periodicity in each firing rate map. A spatial 601 autocorrelation matrix was calculated from the firing rate map. Peaks in the autocorre-602 lation matrix were defined as more than 10 adjacent bins with values larger than 0.1. 603 The 60 • periodicity in the spatial autocorrelation matrix was estimated using a circular Significance thresholds for grid scores were obtained by shifting the position data by at 609 least 20 s before recalculating grid scores. This procedure was repeated 100 times for 610 each neuron to obtain surrogate distributions. The 99th percentiles of the null distribu-611 tions were used as significance thresholds. 612 Spatial selectivity was measured using a sparsity score, adapted so that high 613 scores reflected high sparsity: where N was the number of bins in the firing rate map, p i and λ i were the occupancy 615 probability and firing rate in bin i, respectively. Significance levels for sparsity score 616 were obtained with the same shuffling procedure as for grid scores. 617 The firing rate modulation by running speed was estimated using the speed score 618 (Kropff et al., 2015), which was defined as the correlation coefficient between the run- Theta oscillations were detected using one wire of every tetrode. The signal was 682 bandpass filtered at delta (2-4 Hz) and theta (6-10 Hz) frequencies and the power of the 683 filtered signals (root mean square) was calculated in non-overlapping 500 ms windows. 684 Windows with a theta/delta power ratio larger than 2 were defined as theta epochs. 685 Individual theta cycles within theta epochs were identified using the bandpass filtered  and vp2 trials. a, Directional distributive ratio (DR) for two representative HD cells with low (cell 1) and high DR (cell 2). Left: HD dependent spatial firing rate maps. The central firing rate map is direction independent. Surrounding maps show firing rate maps for specific HDs in 45 deg bins. Top right: polar plot showing the HD tuning curve of the neuron. Numbers indicate peak firing rates and HD scores. Bottom right: Observed (red lines), expected firing rate (black lines) as function of HD and corresponding DR scores. A DR near 0 indicates that the observed tuning curve of a neuron can be explained by its spatial selectivity. b, Distribution of DR for all putative HD cells. c, Box-and-whisker plots showing DR across different functional cell types: HD cells (HD), grid cells (Grid, n = 219), and other low firing rate cells (other, firing rate < 10 Hz, n = 335). DR was computed during vp1 trials. HD cells had significantly higher DR compared to other functional cell types (Wilcoxon rank-sum test, HD vs. grid cells, W = 20085, P < 10 -16 , HD vs. other cells W = 29717, P < 10 -16 ). d, Pie chart illustrates the fractions of HD cells with significant spatial sparsity or speed scores. e, Distributions of grid scores, sparsity scores, mean firing rates and speed scores for HD cells (red lines), grid cells (blue lines), and other cells (black lines). Asterisks indicate significant difference in scores between HD and grid cells (blue), and HD and other cells (black). f, HD scores, peak and mean firing rates for HD cells (paired Wilcoxon signed-rank test, n = 93, HD score: V = 2015, P = 0.52; peak firing rate: V = 2267, P = 0.76; mean firing rate: V = 2234, P = 0.85). g, Average running speed (left) and average head angular velocity (right). Magnitude of changes between the two trial types was small (paired Wilcoxon signed-rank test, n = 68 recording sessions containing HD cells, median running speed, vp1: 13.7 cm/s, vp2: 13.8 cm/s, V = 788, P = 0.02; median head angular speed, vp1: 73.0 deg/s, vp2: 75.7 deg/s, V = 522, P < 10 -5 ). ns.: not significant, *: P < 0.05, **: P < 0.01, ***: P < 0.001. Time   . r values are correlation coefficients. b, Reorganization scores of grid cell pairs and HD cell pairs between conditions (vp1 and vp2, gray) or within condition (green). Grid cells significantly changing their map similarity or average firing rate between vp1 and vp2 trials showed no reorganization in their IFR association (top) or pairwise map similarity between conditions (bottom). ns.: not significant, *: P < 0.05, ***: P < 0.001. Plots show mean ± 95% confidence intervals.