Efficient navigation in mammals depends on several classes of spatially selective neurons. The animal’s sense of direction is encoded by head-direction (HD) cells that track ongoing angular movements of the head (Taube et al., 1990a; Valerio and Taube, 2012; Butler et al., 2017). Each HD cell fires maximally when the head of an animal points in a particular direction, with different cells having different preferred directions. HD cells are located in both subcortical and cortical areas including the dorsal tegmental nucleus, lateral mammillary nucleus, anterodorsal thalamic nucleus, nucleus reuniens, postsubiculum, retrosplenial cortex, parasubiculum, and the medial entorhinal cortex (Taube et al., 1990a; Chen et al., 1994; Taube, 1995; Stackman and Taube, 1998; Sharp et al., 2001; Cacucci et al., 2004; Sargolini et al., 2006; Jankowski et al., 2014). The HD signal is generated in subcortical areas, possibly in the dorsal tegmental and lateral mammillary nuclei, and depends on intact vestibular inputs (Stackman and Taube, 1997; Muir et al., 2009; Yoder and Taube, 2009; Valerio and Taube, 2016). This signal reaches cortical areas via the thalamocortical excitatory projections of the anterodorsal thalamic nucleus. Accordingly, lesions to the subcortical components of the HD system strongly impair HD representations in cortical areas (Goodridge and Taube, 1997; Bassett et al., 2007; Winter et al., 2015).

Continuous attractor network models provide a mechanistic framework explaining how the HD signal is generated (Skaggs et al., 1995; Redish et al., 1996; Zhang, 1996). In these models, neurons are conceptually arranged in a circle according to their preferred firing direction. The connectivity between any two neurons depends on their relative position. While neighboring cells with similar preferred HD excite each other, distant cells tend to inhibit each other. This connectivity leads to the emergence of an activity packet which represents the moment-to-moment HD of the animal. These models predict that the differences between the preferred directions of HD cells never change because the connections within the network are immutable, and most empirical data support this prediction. For example, rotation of a distal visual landmark in an environment causes an equivalent rotation of the preferred direction of all HD cells (Taube et al., 1990b). When distal and proximal cues are rotated in opposite directions, HD cells in the anterior thalamus rotate coherently with one of the two sets of cues (Yoganarasimha et al., 2006). The firing associations of HD cells (i.e. their tendency to fire together) have also been compared across different brain states (Tsanov et al., 2014; Peyrache et al., 2015). As predicted by the models, firing associations of HD cells during exploratory behavior are maintained during sleep. In addition, reliable spike transmission is observed between HD cells in the anterodorsal thalamic nucleus and the presubiculum (Peyrache et al., 2015), suggesting that cortical cells inherit their preferred HD from thalamic HD cells.

All models of HD cells require a mechanism to anchor the preferred direction of HD cells to the external world, thereby preventing error accumulation inherent to head-movement integration (Skaggs et al., 1995; Redish et al., 1996; Zhang, 1996; Bicanski and Burgess, 2016). In these models, the anchoring mechanism involves the interaction between HD cells and cells encoding information about visual landmarks. Recent experimental work has shown that a subset of directional cells in the retrosplenial cortex are indeed controlled primarily by local visual landmarks, and that these cells can change their preferred directions independently of classic HD cells (Jacob et al., 2017). These observations suggest that cortical regions containing both classic HD cells and cells controlled by visual landmarks might be key sites where visual landmarks gain control over the head direction signal (Goodridge and Taube, 1997; Clark et al., 2010).

The medial entorhinal cortex and parasubiculum (MEC/PaS) are located at the top of hierarchical ascending HD pathways (Clark and Taube, 2012). There, HD cells intermingle with speed cells and grid cells (Sargolini et al., 2006; Boccara et al., 2010; Kropff et al., 2015). It has been proposed that a key function of these cells is to compute an estimate of the animal’s position in space, which is optimally represented by the activity of modularly organized grid cells (McNaughton et al., 2006; Stensola et al., 2012; Herz et al., 2017). To keep track of the animal’s position during movement, the grid cell network is thought to integrate direction and speed of movement using the activity of HD and speed cells, respectively (McNaughton et al., 2006; Sargolini et al., 2006; Kropff et al., 2015). Thus, this spatial code likely depends on the properties of its HD inputs (Winter et al., 2015).

The MEC/PaS also receive important visual and visuospatial inputs from the postrhinal and retrosplenial cortices (Wyss and Van Groen, 1992; Burwell and Amaral, 1998; Czajkowski et al., 2013; Koganezawa et al., 2015). Indeed, recent studies have established that a substantial fraction of MEC/PaS neurons encode information about visual patterns or contexts (Pérez-Escobar et al., 2016; Diehl et al., 2017; Ismakov et al., 2017). The presence of cells influenced by visual landmarks in the MEC/PaS raises the possibility that the MEC/PaS is a site of interaction between information about HD and visual cues. We therefore investigated whether some MEC/PaS neurons express a conjunctive code for HD and visual landmarks. We recorded the activity of HD cells in the MEC/PaS and tested whether their activity was also controlled by visual landmarks. The recording environment consisted of an elevated platform surrounded by four walls. Two distinct light patterns located on different walls were turned on and off. We report that HD cells in the MEC/PaS could be divided into two classes: non-rhythmic and theta-rhythmic HD cells. Changing which visual pattern was presented caused alterations in the tuning curves of both non-rhythmic and theta-rhythmic HD cells, but the magnitude of the changes was larger for non-rhythmic HD cells, with some non-rhythmic HD cells switching from active to nearly silent when the light pattern changed. Simultaneous recordings from multiple HD cells revealed that while theta-rhythmic HD cells maintained their firing associations when landmarks changed, the tuning changes of non-rhythmic HD cells were often non-coherent, demonstrating that non-rhythmic HD cells were not constrained by attractor-like dynamics but rather controlled by visual landmarks. We suggest that landmark-controlled non-rhythmic HD cells might contribute to setting the preferred directions of classic HD cells when an animal enters visually distinct environments.

To investigate the impact of visual landmarks on the HD signal, we recorded the activity of MEC/PaS neurons together with oscillatory field potentials using multichannel extracellular techniques in freely behaving mice. Nine mice were trained to explore an elevated square platform surrounded by four walls (Figure 1a). Two distinct visual patterns (vp1 and vp2) made from different arrangements of LED strips were attached to two adjacent walls. In addition, a standard cue card attached to one wall remained at the same location throughout the experiment (Figure 1a). The two distinct visual patterns were switched on and off in turn, without any interleaving dark periods. Recording sessions included forty 2-min trials alternating between vp1 and vp2 trials (Figure 1b).

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Histological analysis revealed that the final locations of most recording sites were in the MEC (63.0%, 34 out of 54; Figure 1c–d, Figure 1—figure supplement 1). Half of the remaining recording sites were found in the PaS (16.7%, 9 out of 54). Of the recording sites in the MEC, 82.4% (28 out of 34) had entered layer II of the MEC before the end of the experiment (Figure 1d). The final location of all visible tetrode tips is presented in Supplementary file 1.

A total of 944 neurons were recorded over 167 recording sessions. The number of cells recorded in each animal is presented in Supplementary file 1. The HD tuning curve of each neuron was calculated separately for trials with vp1 and vp2 (Figure 1e). The HD score, which was defined as the mean vector length of the tuning curve, served as a measure of HD selectivity. Cells with a HD score exceeding 0.4 and a peak firing rate larger than 5 Hz during vp1 or vp2 trials were considered putative HD cells (106 out of 944 neurons, Figure 1f). To ensure that HD selectivity was not a byproduct of spatial selectivity coupled with unequal HD sampling across the recording environment, we calculated a directional distributive ratio for each HD cell (Muller et al., 1994; Cacucci et al., 2004) (Materials and methods and Figure 1—figure supplement 2a–c). A directional distributive ratio approaching 0 indicated that the observed HD tuning curve could result from spatial selectivity coupled with biased HD sampling. Only HD cells with a directional distributive ratio larger than 0.2 were included in further analysis (N = 104). Out of 104 HD cells, 10.6% (N = 11) were conjunctive grid x HD cells and were excluded from the HD cell category, leaving a total of 93 HD cells. Of the remaining HD cells, 29.0% were speed modulated, 62.3% had significant spatial sparsity scores, and 31.2% were HD selective only (Figure 1—figure supplement 2d).

HD cells expressed similar levels of directional tuning during vp1 and vp2 trials. At the population level, HD scores, peak firing rates and mean firing rates of HD cells were not significantly different between the two trial types (Figure 1—figure supplement 2f). Preferred directions of HD cells were randomly distributed during both trial types (Rayleigh test of uniformity, vp1: test statistic = 0.0931, p=0.4466; vp2: test statistic = 0.0479, p=0.81). Moreover, the behavior of mice was comparable between the two different trial types (Figure 1—figure supplement 2g).

Theta rhythmicity reveals two HD cell populations

A substantial proportion of MEC/PaS neurons shows prominent rhythmic activity in the theta frequency band (6–10 Hz) (Alonso and García-Austt, 1987; Cacucci et al., 2004; Mizuseki et al., 2009). Surprisingly, we observed a large variability in the theta rhythmic activity of HD cells, with a group of HD cells firing rhythmically at theta frequency (Figure 2a) and a second group showing no clear rhythmic activity in this frequency range (Figure 2b).

Figure 2

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To quantify this observation, we first calculated for each neuron a power spectrum from the instantaneous firing rate. We found a large variability in the power at theta frequency between neurons. A theta index was calculated by comparing the power in the theta frequency band (6–10 Hz) to that of two adjacent frequency bands (3–5 and 11–13 Hz). The distribution of theta indices for all HD cells is shown in Figure 3a. The theta index distribution was best fit by a model with two components (see Materials and methods; Gaussian finite mixture models: log-likelihood = 98.25, df = 5, BIC = 173.83). In line with Alonso and García-Ausst’s work (Alonso and García-Austt, 1987), these two components corresponded to non-rhythmic and theta-rhythmic cells (Figure 3a and Figure 3—figure supplement 1a, N = 34 non-rhythmic, N = 59 theta-rhythmic, theta index threshold = 0.07). Similar results were obtained when the lower adjacent frequency band used to calculate the theta index was lowered to 1.5–3 Hz in order to minimize the influence of subharmonic theta.

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We investigated the relationship between HD cell firing activity and theta oscillations of the local field potentials. For each cell, the firing probability as a function of theta phase, together with the mean vector length and the preferred theta phase of its spikes were calculated. Spikes of theta-rhythmic HD cells had larger mean vector lengths than non-rhythmic HD cells (Figure 3b, left; Wilcoxon rank-sum test, w = 19, P < ${\displaystyle {10}^{-15}}$). Theta-rhythmic HD cells fired preferentially at the end of the descending phase of theta oscillations (Figure 3b, right; mean preferred phase: 59.27${}^{\circ }$; Rayleigh test of uniformity, test statistic = 0.2685, p ${\displaystyle <{10}^{-19}}$), whereas non-rhythmic HD cells did not show such preference (test statistic = 0.2685, p=0.09). Theta phase modulated the firing rate of all theta-rhythmic HD cells (Rayleigh test of uniformity). Even though non-rhythmic HD cells displayed weak theta phase modulation, the firing rate of 94.1% (32 out of 34) of non-rhythmic HD cells was still significantly modulated by theta phase.

These substantial differences in theta modulation were not caused by differences in the local field potential theta power recorded in the proximity of the cell bodies. For each HD cell, we calculated the power spectrum from the local field potentials of its respective tetrode. The power at theta frequency in the local field potentials was similar for non-rhythmic and theta-rhythmic HD cells (Figure 3—figure supplement 1b, Wilcoxon rank-sum test, peak theta power: w = 1024.5, p=0.87). There was no significant difference between theta indices of cells recorded in hemispheres in which all tetrode tips were located in the MEC compared to those in which some tetrode tips were in the PaS (w = 2433.5, p=0.75).

The HD selectivity and mean firing rate of non-rhythmic and theta-rhythmic HD cells during vp1 trials were similar (Figure 3c, Wilcoxon rank-sum test, HD score: w = 881, p=0.33, mean firing rate: w = 993, p=0.94), demonstrating that theta-rhythmic and non-rhythmic HD cells displayed similar levels of directional tuning.

Theta-cycle skipping was observed in a minority of theta-rhythmic HD cells. When using a theta-cycle skipping index of 0.1 as threshold (see Materials and methods), 10% (6 out of 59) of theta-rhythmic HD cells showed theta-cycle skipping. This was slightly lower than what had been previously reported in rats (Brandon et al., 2013).

We then investigated whether non-rhythmic and theta-rhythmic HD cells form anatomically segregated populations within the MEC/PaS region. By analyzing pairs of HD cells simultaneously recorded on the same tetrode (N = 17), we found only one mixed non-rhythmic/theta-rhythmic pair, suggesting that the two cell populations were partially anatomically segregated. Also, fewer non-rhythmic HD cells were recorded on the same tetrode as grid cells compared to theta-rhythmic HD cells (Figure 3—figure supplement 1c, N = 9 and 42, respectively) (Chi-squared test: ${\chi }^2$ = 15.66, df = 1, p ${\displaystyle <{10}^{-5}}$). Finally, non-rhythmic HD cells tended to be recorded during earlier recording sessions compared to theta-rhythmic HD cells (Figure 3d, w = 497, p ${\displaystyle <{10}^{-5}}$), suggesting that non-rhythmic HD cells were located closer to the dorsal border of the MEC/PaS or in deeper layers.

To confirm the anatomical localization of non-rhythmic HD cells, we implanted four additional mice in which the minimal spacing between tetrodes was increased to approximately 0.5 mm, making it possible to assign each cell to a tetrode track. These mice were trained on a shorter recording protocol (60 min per session instead of 80 min) and perfused with the tetrode left in place as soon as non-rhythmic HD cells were recorded. Out of the seven recording sites with non-rhythmic HD cells that were recovered, four were in the MEC (Figure 3e). Interestingly, three recording sites were in the postrhinal cortex (Figure 3—figure supplement 2), suggesting that the postrhinal cortex might also contain non-rhythmic HD cells. Note that stopping this experiment as soon as non-rhythmic HD cells were encountered biased our sampling toward more dorsal locations.

Analysis of the spike waveforms in the two populations revealed that non-rhythmic HD cells had longer trough-to-peak durations (Figure 3f, N = 30 and 52, w = 1347, p ${\displaystyle <{10}^{-8}}$) and larger spike asymmetry, compared to theta-rhythmic HD cells (Figure 3f, w = 463, p=0.002). Taken together, these results demonstrate that HD cells in the parahippocampal region can be divided into non-rhythmic and theta-rhythmic HD cells. These two cell types appear partially anatomically segregated and have distinct intrinsic biophysical properties.

Visual landmarks alter the tuning curves of HD cells

Having established that HD cells of the MEC/PaS form two populations, we asked whether HD cells responded to changes in visual landmarks. Inspection of the tuning curves during vp1 and vp2 trials suggested that the preferred direction of some HD cells changed with the different visual patterns (Figure 4a). For some HD cells, these changes could be observed between consecutive trials, causing the preferred direction of the neurons to oscillate in time (Figure 4a). To test whether the change in preferred direction of each cell was statistically significant, we compared the observed change to a surrogate distribution of changes obtained by randomly reassigning trial labels (vp1 and vp2) (Figure 4a, see Materials and methods). Observed changes that were larger than 99% of the surrogate changes were considered significant. We found that 63.4% (59 out of 93) of the HD cells significantly altered their preferred HD between vp1 and vp2 trials.

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A similar analysis was performed to test whether the level of directionality of HD cells changed with the visual patterns presented to the animal (Figure 4b). We observed HD cells that changed their selectivity depending on the visual patterns (Figure 4b). These changes could often be observed between single trials (Figure 4b). Overall, 47.3% (44 out of 93) of the HD cells significantly altered their HD score between trial types.

We next compared the responses of non-rhythmic and theta-rhythmic HD cells to visual landmark manipulations. Non-rhythmic HD cells showed larger changes in preferred HD between vp1 and vp2 trials than theta-rhythmic HD cells (Figure 4c, w = 1465, p=0.00012). Likewise, non-rhythmic HD cells also showed larger changes in HD selectivity (Figure 4d, w = 1618, p $<{10}^{-7}$). This indicates that visually driven changes in tuning curves were more pronounced in non-rhythmic HD cells compared to theta-rhythmic HD cells.

It was previously shown that HD cells located in the presubiculum and anterodorsal thalamic nucleus maintained their firing rate when an animal explored different environments (Goodridge et al., 1998; Taube and Burton, 1995; Taube et al., 1990b). We therefore tested whether the firing rate of HD cells in the MEC/PaS was preserved when visual landmarks were manipulated. We observed HD cells with pronounced alterations in their firing rate with some cells being almost silent in response to one of the two different visual patterns (Figure 5a). For these cells, the instantaneous firing rate oscillated in time, in line with the trial type (Figure 5a). To test whether these changes were significant, we calculated the relative change in firing rate for each neuron: $\left|\frac{r_{\text{vp}1}-r_{\text{vp}2}}{r_{\text{vp}1}+r_{\text{vp}2}}\right|$. We found that 40.9% (38 out of 93) of the HD cells significantly altered their mean firing rate in response to changes in visual landmarks. Thus, these results demonstrate that the mean firing rate of HD cells in the MEC/PaS is modulated by visual landmarks. The magnitude of the firing rate changes was significantly larger for non-rhythmic than for theta-rhythmic HD cells (Figure 5b, w = 1641, p $<{10}^{-7}$).

Figure 5c summarizes the different types of changes observed in the non-rhythmic and theta-rhythmic HD cell populations. The percentage of cells with a significant visually driven change was 94.1% and 74.5% for non-rhythmic and theta-rhythmic cells, respectively (Figure 5c, ${\chi }^2$ = 3.4465, df = 1, p=0.06). Taken together, these results show that the tuning curves of MEC/PaS HD cells are affected by the visual landmarks. The tuning curves of non-rhythmic HD cells showed larger landmark-driven changes than those of theta-rhythmic HD cells.

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The majority of neurons in the MEC are spatially selective (Diehl et al., 2017). It could therefore be argued that the changes in HD tuning between vp1 and vp2 trials were caused by altered spatial firing patterns of HD cells. To rule out this possibility, we focused our analysis on a subset of HD cells with no significant spatial modulation (non-significant sparsity score; 36 out of 93 HD cells). Within this population of non-spatial HD cells, 86.1% (31 out of 36) had a significant change in preferred direction, HD score or mean firing rate between the vp1 and vp2 trials. This proportion was comparable to that observed when considering spatially selective HD cells (Pearson’s Chi-squared test: ${\chi }^2$ = 0.3543, df = 1, p=0.55). Thus, the changes in HD tuning curves did not result from an altered spatial signal between vp1 and vp2 trials.

We also tested whether a similar proportion of HD cells showed landmark-driven changes when limiting the analysis to cells recorded from hemispheres in which all tetrode tips were positioned in the MEC. We found that 83.6% (56 out of 67) of the MEC HD cells displayed significant changes in preferred direction, HD selectivity or mean firing rate between trial types. A similar percentage was obtained when analyzing HD cells from hemispheres containing recording sites in the PaS, presubiculum or cortex (76.9%, 20 out of 26 cells, ${\chi }^2$ = 0.1996, df = 1, p=0.66).

It was previously shown that the width of a prominent visual landmark could affect the width of the HD tuning curves of hippocampal neurons during navigation in a virtual environment (Acharya et al., 2016). In the same study, a prominent visual landmark could also bias the distribution of preferred directions toward the landmark. To address whether these two effects could contribute to the differences observed between vp1 and vp2 trials, we analyzed selectively HD cells that showed a tuning curve change between vp1 and vp2 trials. No difference in HD scores was observed between vp1 and vp2 trials (Figure 4—figure supplement 2a). Moreover, there was no clear indication of an accumulation of preferred directions toward either vp1 or vp2 (Figure 4—figure supplement 2b).

Finally, one explanation of the strong response of non-rhythmic HD cells to landmark manipulations is that these cells might encode egocentric landmark bearing information instead of allocentric HD. Egocentric landmark bearing cells fire when a landmark is located at a given position in the animal’s field of view (Bicanski and Burgess, 2016). If a HD cell is an egocentric landmark bearing cell, its preferred HD should change systematically as a function of the animal’s position within the arena due to the parallax effect. We could not detect clear evidence for such systematic changes in HD as a function of position in non-rhythmic HD cells (see Figure 5—figure supplement 1).

Bidirectionality of HD cells is affected by visual landmarks

Inspection of the HD cell tuning curves also revealed that a subpopulation of HD cells had two preferred directions (Figure 6a, see also Figure 1e-Cell-4, Figure 4a-Cell-3). Some of these tuning curves were similar to those previously reported for the retrosplenial cortex (Jacob et al., 2017), but the two peaks were not always at an 180${}^{\circ }$ angle to each other. The bidirectionality of these cells often varied with the trial types (Figure 6a).

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To quantify these observations, a bidirectionality (BD) score was defined as the firing rate ratio of the two largest peaks in the tuning curve (see Materials and methods). For some cells, the BD score changed on a trial-by-trial basis (Figure 6a). The bidirectionality in the tuning curves could be observed over short periods of 30 s (Figure 6b), suggesting that bidirectionality was not caused by inter-trial instability of a single preferred direction.

Bidirectional HD cells were defined as HD cells for which the BD score was larger than 0.2, the peak firing rates of the two peaks were larger than 2 Hz, and the ratio between the firing rate of the second largest peak and the trough in the HD tuning curve with the highest firing rate between the peaks exceeded 1.25. These criteria had to be reached during vp1 or vp2 trials. Note that a bidirectional cell with equally dominant peaks at 180 degrees to each other during both trial types would not have been classified as HD cell in either trial type and, therefore, would not have been included in the analysis.

The analysis showed that 15.1% (14 out of 93, eight non-rhythmic and six theta-rhythmic) of the HD cells were classified as bidirectional, with two cells being bidirectional only during vp1 trials, and 6 cells only during vp2 trials. The remaining six cells were bidirectional during both trial types. The distribution of angles between the two preferred directions of bidirectional HD cells had two modes, close to 90${}^{\circ }$ and 180 degrees (Figure 6c). In some HD cells, the changes in HD score and preferred direction between vp1 and vp2 trials could be explained by a change in bidirectionality (Figure 6a–b). The changes in the BD scores between vp1 and vp2 trials were larger than chance levels (Figure 6d; paired Wilcoxon signed-rank test, N = 14, v = 12, p=0.009). Overall, non-rhythmic HD cells showed larger changes in their BD score compared to theta-rhythmic cells (Figure 6e, w = 1366, p=0.004). Including bidirectional cells that were not classified as HD cells (N = 36) did not affect this conclusion (Figure 6—figure supplement 1).

Non-rhythmic HD cells reorganize their firing associations

Computational models of HD cells predict that differences in the preferred directions of HD cells are preserved at all times. Support for these models comes from numerous studies showing coherent rotation of the preferred directions of HD cells in response to landmark manipulations (Taube et al., 1990b; Yoganarasimha et al., 2006). However, these findings were obtained from recordings in subcortical areas or in the presubiculum, and it is still not known whether HD cells in the MEC/PaS display the coherence predicted by computational models. We therefore tested whether visually driven tuning curve changes observed in our protocol were coherent across simultaneously recorded HD cells.

We first inspected the tuning curves of simultaneously recorded HD cells (N = 37 HD cell pairs). Figure 7a shows examples of HD cells for which changes from vp1 to vp2 were not coherent. For example, two HD cells modified their difference in preferred direction depending on which visual pattern was presented (Figure 7a, HD Pair 1). A similar uncoupling of simultaneously recorded HD cell pairs was also observed for HD selectivity (Figure 7a, HD Pair 2) and mean firing rate (Figure 7a, HD Pair 3).

Figure 7

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To quantify these non-coherent changes in HD cell activity, we correlated the differences in preferred direction of HD cell pairs observed during vp1 and vp2 trials (between conditions) (Figure 7b, top left panel). As a control, we calculated the correlation coefficients of the same scores obtained from two mutually exclusive subsets of vp1 trials (within condition) (Figure 7b, top right panel). The correlation coefficient between conditions (r = 0.65) was significantly lower than that observed within condition (r = 0.99; difference, Fisher Z-transformation: Z-score = 7.72, p ${\displaystyle <{10}^{-14}}$). Similarly, differences in HD scores were less correlated between conditions than within condition (Figure 7b, middle panels; between conditions: r = 0.32, within condition: r = 0.98, difference: Z-score = 8.11, p ${\displaystyle <{10}^{-16}}$). We also assessed the firing associations of HD cells in the time domain. The instantaneous firing rate (IFR) of each HD cell was calculated and IFR association was defined as the correlation coefficient between IFR vectors of two HD cells. The stability of IFR associations was lower between conditions (r = 0.60) than within condition (r = 0.98) (Figure 7b, bottom panels; difference: Z-score = 6.62, p=10 ${\displaystyle <{10}^{-11}}$).

To further quantify non-coherent changes within the HD cell population, a reorganization score for preferred HD, HD score and IFR association was computed. After obtaining differences in preferred HD, HD score or IFR association for each cell pair, the absolute difference between the values from vp1 and vp2 trials or from two mutually exclusive subsets of vp1 trials served as reorganization score between or within condition, respectively (see Materials and methods). We compared reorganization scores of HD cell pairs formed by two theta-rhythmic or two non-rhythmic HD cells (Figure 7b). We found that theta-rhythmic HD cell pairs did not show significant reorganization when visual landmarks were altered (Figure 7b, N = 20, preferred HD: v = 65, p=0.14, HD score: v = 72, p=0.23, IFR association: v = 69, p=0.19). In contrast, visual landmark manipulations caused a reorganization of firing associations in non-rhythmic HD cell pairs (N = 9, preferred HD: v = 2, p=0.01, HD score: v = 1, p=0.00781, IFR association: v = 0, p=0.00391). These results indicate that the reorganization of firing associations was specific to non-rhythmic HD cells. Thus, the activity of HD cells is not entirely constrained by attractor-like dynamics.

We also tested whether visually driven reorganization between HD cells can be predicted based on their synchronous activity at theta frequency. We obtained time-frequency power spectra from spike-time crosscorrelations of simultaneously recorded HD cell pairs (Peyrache et al., 2015) (Figure 7c). Theta synchrony was defined as the average power in the time widow of 0$\pm$25 ms at theta frequency (6–10 Hz). From this, the distribution of theta synchrony scores was used to identify low-theta synchronous (LTS) and high-theta synchronous (HTS) HD cell pairs (Figure 7d, LTS $<$ 0.2, N = 19, HTS $>$ 0.2, N = 18). HTS HD cell pairs did not show significant visually-driven reorganization (Figure 7e, preferred HD: v = 69, p=0.50, HD score: v = 51, p=0.14, IFR association: v = 67, p=0.44). In contrast, LTS cell pairs showed significant reorganization when visual landmarks were altered (preferred HD: v = 14, p=0.00042, HD score: v = 16, p=0.00065, IFR association: v = 18, p=0.00097). These results show that HD cells which synchronized at theta frequency did not undergo visually driven reorganization. In contrast, non-synchronous HD cells reorganized their firing associations based on visual landmarks.

Stable firing associations between grid cells

The above results indicate that one population of HD cells in the MEC/PaS shows visually-driven reorganization of their firing associations. This contradicts the prediction of current attractor network models of HD cells which states that the firing associations between HD cells are static. Another cell population in this brain region that is thought to be governed by attractor-like dynamics is that of grid cells (McNaughton et al., 2006). For this reason, we sought to determine whether the activity of simultaneously recorded grid cells remained coherent when visual landmarks were manipulated.

We recorded the activity of 219 grid cells during vp1 and vp2 trials (Figure 8a and Figure 8—figure supplement 1a). To investigate whether grid cells altered their firing properties in response to manipulation of visual landmarks, we assessed the stability of their firing rate maps. The firing rate map similarity between the two trial types was significantly lower than chance level (Figure 8b; paired Wilcoxon signed-rank test, N = 219, v = 439, p ${\displaystyle <{10}^{-16}}$). We found that 48.4% (106 out of 219) of the grid cells showed significant changes in map similarity, preferred HD, or average firing rate between the vp1 and vp2 trials (Figure 8c).

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Next, we examined whether the grid cell changes were coherent across simultaneously recorded grid cells (N = 223 grid cell pairs, Figure 8d), as predicted by attractor network models. Firing associations based on instantaneous firing rates were highly preserved between vp1 and vp2 trials (Figure 8e, top left panel, r = 0.96). Likewise, pairwise map similarity from the vp1 and vp2 trials was also strongly correlated (Figure 8e, bottom left panel, r = 0.95). In addition, reorganization levels for pairs of grid cells and pairs of HD cells were compared (Figure 8f). Only HD cells showed significant reorganization of their IFR association and of their firing rate maps between different trial types (reorganization of grid cell pairs between vs. within condition for IFR associations: v = 10911, p=0.10; map similarity: v = 10661, p=0.058). Similar results were obtained when considering only grid cell pairs, with at least one grid cell showing significant visually-driven changes of either map similarity, average firing rate or preferred HD (Figure 8—figure supplement 1b–c, N = 106 grid cell pairs, IFR association: v = 2296, p=0.089; map similarity: v = 2247, p=0.064). These findings suggest that the firing associations of grid cells were not significantly altered in response to changes in visual landmarks.

HD cells of the MEC/PaS are at the top level of the HD circuit hierarchy. Because a substantial fraction of MEC/PaS neurons encode information about visual patterns or contexts (Pérez-Escobar et al., 2016; Diehl et al., 2017; Ismakov et al., 2017), we set out to test whether HD cells in the MEC/PaS express a conjunctive code for visual landmarks and HD. We found that HD cells could be divided into two functionally distinct classes based on whether they fired rhythmically at theta frequency. Theta-rhythmic and non-rhythmic HD cells showed significant changes in their tuning curves when visual landmarks were manipulated, but the magnitude of the changes was larger for non-rhythmic HD cells. Moreover, non-rhythmic HD cells displayed non-coherent responses to visual landmark manipulations, whereas theta-rhythmic HD cells showed stable firing associations.

These properties of MEC/PaS HD cells set them apart from classic HD cells. Indeed, in the anterodorsal thalamic nucleus and presubiculum the peak firing rate and directional tuning of HD cells were unchanged when an animal explored visually distinct environments (Taube et al., 1990b; Yoder et al., 2011). These results suggest that, in these two brain regions, HD cells are driven mainly by self-motion cues derived from vestibular, proprioceptive, and motor efference information (Stackman and Taube, 1997; Yoder and Taube, 2014) and the principal effect of visual landmarks on HD cells is to anchor the HD signal to the external world (Skaggs et al., 1995; Yoder and Taube, 2009; Yoder et al., 2011). Our findings demonstrate that the impact of visual information on MEC/PaS HD cells extends beyond this anchoring mechanism. The firing rate of several non-rhythmic HD cells was strongly modulated by the two visual landmarks, with some cells being almost silent with one of the two landmarks. This indicates that some HD cells are driven by visual landmarks, rather than being simply anchored by them. We suggest that a significant proportion of HD cells in the MEC/PaS express a conjunctive code for HD, visual landmarks and position. The origin of this 2D visual landmark modulation of HD cell activity is still unknown. Two possible origins are other MEC neurons changing their firing patterns depending on visual landmarks (Pérez-Escobar et al., 2016; Diehl et al., 2017), or afferent connections from visual cortical areas (e.g., postrhinal or retrosplenial cortex) (Burwell and Amaral, 1998; Czajkowski et al., 2013; Koganezawa et al., 2015).

A core tenet of HD cell models is that cells within the network have a fixed connectivity and that differences in preferred direction between HD cells do not change (Skaggs et al., 1995; Zhang, 1996; Redish et al., 1996). Although the HD signal is generated at the level of the dorsal tegmental nucleus and the lateral mammillary nucleus, the evidence supporting this assertion has been obtained mainly from recordings performed in the anterodorsal thalamic nucleus, presubiculum or cortical areas (Taube et al., 1990a; Stackman et al., 2003; Yoganarasimha et al., 2006; Peyrache et al., 2015). This suggests that the attractor-like network dynamics of the HD signal generator propagate from subcortical networks to cortical areas via ascending excitatory connections (Peyrache et al., 2015). In the current study, we found that the firing pattern of non-rhythmic HD cells within the MEC/PaS is not strictly controlled by these attractor-like network dynamics. Indeed, the firing associations of non-rhythmic HD cells reorganized when visual landmarks were changed. This result indicates that the firing associations of non-rhythmic HD cells are malleable and controlled by visual landmarks.

A recent study also reported the existence of a population of HD cells in the dysgranular retrosplenial cortex that was controlled by local landmarks (Jacob et al., 2017). In a two-compartment environment in which the compartment cue cards had the opposite orientation to one another, some HD cells had unimodal tuning curves within each compartment but their preferred direction rotated by 180${}^{\circ }$ when the animal moved across compartments. A second population of HD cells had bimodal tuning curves within each compartment, and their direction associated with the highest firing rate rotated 180${}^{\circ }$ across compartments. Thus, the preferred direction of these cells was likely controlled by the visual landmarks in each compartment. Importantly, bidirectional cells were recorded simultaneously with classic HD cells that did not change their tuning curves across compartments, demonstrating that bidirectional HD cells could re-align independently of the main HD system. The data currently available on non-rhythmic HD cells and bidirectional HD cells of the retrosplenial cortex suggest that, despite being both being controlled by visual landmarks, they might operate differently. One potential difference is their internal coherence as a population. Whereas bidirectional cells rotated coherently with one another when the animal moved across compartments, changing the visual landmarks in our experiment caused a reorganization of firing associations within the non-rhythmic HD cell population. Whether this difference originates from distinct cell properties will need to be investigated more directly by testing the two populations in similar recording conditions. Taken together, these findings suggest that the HD signal in cortical areas is more heterogeneous than in the anterodorsal thalamus or the presubiculum.

The different firing properties of theta-rhythmic and non-rhythmic HD cells suggest that they support different functions. Theta-rhythmic HD cells showed no reorganization during our experiment. This coherent HD signal could be well suited for providing directional information to grid cells. Indeed, computational models of grid cells assume that the HD signal remains coherent, and recordings from grid cells indicates that they do not show major reorganization after visual cue manipulations (Hafting et al., 2005; Pérez-Escobar et al., 2016). The theta modulation of rhythmic HD cells might also play an important role in the integration of the HD signal by grid cells. It has previously been proposed that the HD signal needs to be transformed into a theta-modulated signal to be used for navigation (Cacucci et al., 2004). Moreover, the segregation of HD cell ensembles during individual theta cycles might also contribute to grid periodicity (Brandon et al., 2013). We therefore suggest that an important function of theta-rhythmic HD cells is to provide a directional input to the grid cell network.

One function of non-rhythmic HD cells might be to act as an interface between visual landmarks and the coherent HD signal (Bicanski and Burgess, 2016). These non-rhythmic HD cells show large, non-coherent tuning changes upon landmark manipulations. An interesting mechanism that links visual landmarks to the HD signal has been put forward by Jacob and colleagues based on their recordings in the dysgranular retrosplenial cortex (Jacob et al., 2017; Page and Jeffery, 2018). In this model landmark-controlled HD cells could mediate a two-way interaction between visual landmarks and a coherent HD signal. This idea can be applied to the two HD cell populations identified in our study. The tuning curves of non-rhythmic HD cells would be established partly based on landmark-dependent inputs. The HD selectivity of these cells would make them co-active with a subgroup of classic HD cells (e.g. theta-rhythmic HD cells) with similar HD preferences. Over time, if the visual landmarks controlling the non-rhythmic HD cells remain stable, the association between the non-rhythmic HD cells and the coherent HD signal would be strengthened, allowing stable visual landmarks to gain preferential control over the coherent HD signal. This way, the population activity of landmark-controlled HD cells could contribute to setting the preferred directions of theta-rhythmic HD cells when an animal enters visually distinct environments. One interesting possibility is that this interaction between non-rhythmic and rhythmic HD cells might contribute to the orientation of grid cells within each grid module (Stensola et al., 2012).

Our data suggest that theta-rhythmic and non-rhythmic HD cells could form anatomically distinct populations. The differences in spike waveforms indicate that the two populations have distinct intrinsic biophysical properties. Moreover, the low incidence of pair recordings comprising a theta-rhythmic and a non-rhythmic cell HD suggests that the two populations are only partially overlapping in the MEC/PaS area. Histological analysis also points to the possibility that non-rhythmic cells could be preferentially located in the dorsal-most portion of the MEC. This could potentially correspond to the large cytochrome-oxidase positive, putatively parasubicular, patches previously described (Burgalossi et al., 2011). The high degree of HD selectivity in anatomically identified neurons located in these patches is consistent with this idea, although we note that most neurons in the large patches had strong theta modulation (Burgalossi et al., 2011).

In conclusion, our results establish that HD cells of the MEC/PaS comprise two functionally distinct types of cells. Theta-rhythmic HD cells react coherently when visual landmarks are altered and resemble more closely classic HD cells recorded in the anterodorsal thalamic nucleus or presubiculum. In contrast, non-rhythmic HD cells not only show larger responses to visual landmark manipulations, but also respond non-coherently to these manipulations. This study therefore reveals the existence of landmark-driven reorganization within a population of HD cells. Previous work has shown that non-periodic place selective neurons of the MEC react to alterations in the recording environment by shifting the location of their firing fields (Diehl et al., 2017). The findings presented here indicate that an equivalent context-dependent reorganization occurs within the MEC/PaS HD code.

Data analysis was performed in the R software environment and the source code is available from GitHub (Kornienko and Allen, 2018; copy archived at https://github.com/elifesciences-publications/prog_kornienko_2018). The raw data (spike trains, position data and histology) of this study are available from the Dryad Digital Repository (doi:10.5061/dryad.202m6h0) (Kornienko et al., 2018).

All data generated or analysed during this study are available.

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Author details

1. Olga Kornienko

   Department of Clinical Neurobiology, Medical Faculty of Heidelberg University and German Cancer Research Center, Heidelberg, Germany

   Contribution

   Conceptualization, Software, Formal analysis, Visualization, Methodology, Writing—original draft, Writing—review and editing

   For correspondence

   o.kornienko@dkfz-heidelberg.de

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1936-8414

2. Patrick Latuske

   Department of Clinical Neurobiology, Medical Faculty of Heidelberg University and German Cancer Research Center, Heidelberg, Germany

   Contribution

   Investigation, Writing—review and editing

   For correspondence

   patrick.latuske@boehringer-ingelheim.com

   Competing interests

   No competing interests declared

3. Mathis Bassler

   Department of Clinical Neurobiology, Medical Faculty of Heidelberg University and German Cancer Research Center, Heidelberg, Germany

   Contribution

   Investigation

   For correspondence

   m.bassler@dkfz-heidelberg.de

   Competing interests

   No competing interests declared

4. Laura Kohler

   Department of Clinical Neurobiology, Medical Faculty of Heidelberg University and German Cancer Research Center, Heidelberg, Germany

   Contribution

   Investigation, Writing—review and editing

   For correspondence

   l.kohler@dkfz-heidelberg.de

   Competing interests

   No competing interests declared

5. Kevin Allen

   Department of Clinical Neurobiology, Medical Faculty of Heidelberg University and German Cancer Research Center, Heidelberg, Germany

   Contribution

   Conceptualization, Software, Formal analysis, Supervision, Funding acquisition, Methodology, Writing—original draft, Writing—review and editing

   For correspondence

   allen@uni-heidelberg.de

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5319-3721

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