The medial entorhinal cortex (MEC) is thought to create a map of space through a set of functionally distinct cell types: grid cells, border cells, head direction cells, and speed cells (Rowland et al., 2016). Each functional cell type follows its own developmental trajectory (Bjerknes et al., 2014; Langston et al., 2010; Wills et al., 2010), suggesting that the functional identity of the cell is hardwired during development. A reasonable hypothesis is therefore that these functional cell types map onto the diversity of morphologically or molecularly defined cell types found in the MEC. Layer II of the MEC contains two largely distinct populations of principal cells: stellate cells and pyramidal cells. Stellate cells express reelin (Pesold et al., 1998; Kitamura et al., 2014; Fuchs et al., 2016; Winterer et al., 2017), have large sag potentials (Dickson et al., 2000), superficially branching dendrites (Canto and Witter, 2012), and, at least in rodents, sub-threshold membrane potential oscillations in the theta range (Alonso and Llinás, 1989). Pyramidal cells form tight clusters (Kitamura et al., 2014; Ray et al., 2014), express calbindin and WFS-1 (Kitamura et al., 2014), have thick apical dendrites (Canto and Witter, 2012), and receive strong cholinergic input from the medial septum (Ray et al., 2014). Within the local circuit, the two-cell populations form largely distinct microcircuits: pyramidal cells are connected via 5-HT 3a positive interneurons (Fuchs et al., 2016), while stellate cells are connected via fast-spiking parvalbumin (PV+) cells and slower spiking somatostatin-positive cells (Fuchs et al., 2016). However, the two subnetworks are not entirely independent; it has been estimated that up to 14% of pyramidal cells project to stellate cells (Winterer et al., 2017) and some cells express an intermediate stellate/pyramidal identity (Fuchs et al., 2016).

The functional identity of stellate cells and pyramidal cells has implications for the broader hippocampal-entorhinal circuit. Nearly every stellate cell projects to the DG, CA3 and/or CA2 regions of the hippocampus, where terminals from stellate cells make up the main, and nearly exclusive, excitatory input from the MEC (Kitamura et al., 2014; Ray et al., 2014; Varga et al., 2010). The targets of layer II pyramidal cells remain largely unclear. A subset of the cells project to the CA1 region (Kitamura et al., 2014) and to the contralateral hemisphere of the MEC (Varga et al., 2010), but importantly, they do not terminate in the DG, CA3 or CA2 regions (Kitamura et al., 2014; Ray et al., 2014). Because some theoretical models propose that the spatial specificity of cells in the DG and CA fields are formed in large part by combining input from grid cells (Solstad et al., 2006; McNaughton et al., 2006; Savelli and Knierim, 2010; Monaco et al., 2011; de Almeida et al., 2012), determining the functional identity of the two MEC layer II populations is critically important.

Previous attempts to functionally characterize stellate cells have produced mixed results. Intracellular recordings of stellate and pyramidal cells in mice running on a virtual linear track have shown that both types could be putative grid cells (Domnisoru et al., 2013; Schmidt-Hieber and Häusser, 2013) and imaging studies of freely moving animals have found the same (Sun et al., 2015). These findings contrast with those of another study, which assigned cells into putative stellate or pyramidal cells based on their phase locking to the ongoing theta oscillation. Based on this classifier, only 3 of 94 putative stellate cells (near chance levels) were grid cells (Tang et al., 2014), calling into question the role of grid cells in enabling spatial firing in target regions of stellate cells, such as the hippocampus. Here, we attempt to reconcile these differences using a mouse line in which the inhibitory opsin ArchT (Chow et al., 2010; Han et al., 2011) is expressed almost exclusively in stellate cells. Using ArchT expression and optogenetic inhibition to identify stellate cells, we first showed that approximately one in four stellate cells are grid cells. We then revisited the previously published classifier using an extended dataset of over 1300 cells and 400 grid cells recorded in layer II. Consistent with prior observations (Latuske et al., 2015), we found that neither the classifier’s cell assignment nor the relationship between the firing of the cell and the theta oscillation cleanly separated grid cells from other cell types. Taken together, the results suggest that substantial fraction of the stellate cells are grid cells, although they can have other functional identities as well, and the relationship between the cell’s firing and the theta oscillation is a poor predictor of the functional identity of the cell.

We sought to characterize the functional properties of stellate cells using an optogenetic tagging approach. To gain genetic access to stellate cells, we used the ‘EC-tTA’ line (Yasuda and Mayford, 2006) that expresses almost exclusively in the parahippocampal region (entorhinal cortex together with the pre- and para- subiculum). Within the MEC, where we targeted our tetrodes, the expression is confined to layer II (Figure 1). Previous work on the ‘EC-tTA’ line has shown that the transgene-expressing cells in layer II of the MEC have stellate-like morphologies, project to the dentate gyrus and CA3 regions of the hippocampus (Rowland et al., 2013), and often show distinctive circular gaps in expression (Kanter et al., 2017), which presumably correlate with circular clusters of calbindin-positive pyramidal cells (Kitamura et al., 2014) and would be expected if the transgene-expressing cells were stellate cells. Because the tTA-line allows expression of our transgene of interest in stellate cells, we crossed the line to a tetO-ArchT-GFP (Weible et al., 2014) line to enable functional characterization of these cells through optogenetic tagging. To characterize expression of ArchT in this particular cross, we combined an in situ hybridization staining for the transgene with antibody staining for either calbindin, a marker for pyramidal cells (Figure 1A,B), or in situ staining for reelin, a marker for stellate cells (Figure 1C,D), on alternating sections of one mouse. Arch-expressing cells avoided clusters of calbindin-positive cells (Figure 1B) but overlapped extremely well with reelin (Figure 1D). Overall, only a small minority of the Arch-expressing MEC cells expressed calbindin (3 of 303 Arch-expressing cells expressed calbindin, ~ 1%; 3 of 433 calbindin expressing cells expressed Arch, less than 1%) while 97.2% expressed reelin (315 of 324 ArchT-expressing cells expressed reelin; 315 of 967 of reelin expressing cells expressed ArchT, 32.5%; Figure 1C,D). The fact that not all stellate cells express Arch raises the possibility that the EC-tTA line targets a subclass of stellate cells, but we could not test for that because there are no known markers for any subclass. To check for consistency across animals, we also examined the overlap between ArchT and reelin in three additional mice and each additional mouse showed a very similar pattern (Figure 1—figure supplement 1). Finally, to confirm that the ArchT-expressing cells project to the hippocampus, we checked for GFP-labeled fibers in the molecular layer of the dentate gyrus and CA3, the expected termination zones of MEC stellate cells, and found intense labeling in these areas (Figure 1—figure supplement 2). The cross therefore drives expression of ArchT almost exclusively in stellate cells in MECII.

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To functionally characterize the transgene-expressing cells, we implanted a bundle of four tetrodes glued to an optic fiber (see Materials and methods) into the MEC (Figure 1—figure supplement 3) of seven double positive EC-tTA x tetO-ArchT-GFP mice. After recovery from surgery, single units were recorded as the mice foraged for food in a 0.8 or 1 m wide square open field (Figure 2A). Immediately following the open-field session, the mice were placed in a smaller box (27cm × 20 cm×14 cm height) and connected to a 532 nm green laser via a patch cable for an optogenetic tagging session. Optogenetic tagging is typically performed using excitatory opsins (Lima et al., 2009; Zhang et al., 2013). However, inhibition has been used for the same purpose (Wolff et al., 2014) and has the advantage that it circumvents the problem of false positives caused by recurrent excitation. Previous work has shown that Arch silences cells with near-zero latency (Chow et al., 2010; Wolff et al., 2014), and we therefore reasoned that we could reliably tag ArchT-expressing cells using short (10 to 20 ms) pulses of light delivered thousands of times at 1–4 Hz (Figure 2B,C; additional examples in Figure 2—figure supplement 1). The large number of trials was necessary to have sufficient data for reliable statistics and to accurately estimate the latency to inhibition because the cell needs to be active precisely when the light comes on. We spike-sorted the baseline and tagging sessions together to avoid cluster assignment errors, and only analyzed cells with fewer than 1% of spikes between 0 and 2 ms in the interspike interval histogram and with high waveform correlations (r > 0.99) between the baseline and tagging session. We considered the cell to be silenced if the activity in the baseline period was more than during the laser-on period (two sided t-test with stringent cutoff of p<0.001). The latency to inhibition was determined using a change point analysis (Wolff et al., 2014). Most of the cells had near-zero millisecond latencies (median latency = 0.85 ms, Figure 2C–E), making it highly improbable that silencing was caused through a network mechanism. We applied a latency threshold of 5 ms, which eliminated three outlier cells and left a total of 75 tagged cells from a population of 578 (~13% tagged cells). The non-tagged population included non-expressing or non-responsive stellate cells as well as all other cell types (see below).

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To assign the cells into functional classes, we computed standard scores for speed modulation, head directionality, gridness, and border-related firing (see Materials and methods). We then shuffled the spike times of each cell 200 times, recalculated the measures each time, and used the 95th percentile of the shuffled distribution as a cutoff for assigning cells to a particular class. For head direction cells, we additionally required that the correlation of the directional firing of the first half and the second half of the trial exceed 0.6. Cells that passed more than one criterion were considered mixed (light blue portion of bars in Figure 3A) and counted in all supra-threshold categories (thus, the sum exceeds 100%). The tagged population included grid cells (25.3%; 16% pure, 9.3% mixed), head direction cells (12%; 9.3% pure, 2.7% mixed), speed cells (16%; 8% pure, 8% mixed), border cells (1.3%; 1.3% pure, 0% mixed), and unclassified cells (56.0%). To control for the possibility that accidental resampling of cells between sessions created spurious results, we downsampled our data to cells recorded 4 or more days apart, when the electrodes had been turned approximately 100 microns. The downsampled population had similar proportions in each functional class as the full dataset, suggesting that percentages described here are representative of the functional diversity in layer II of the MEC (Figure 3—figure supplement 1). We next compared the properties of the tagged cells to the untagged population. The untagged population likely included layer II pyramidal cells, non-expressing stellates (i.e reelin-expressing cells that do not express Arch, Figure 1C,D) and possibly even some layer III cells that fell within the ~100 micron recordable distance of the tetrodes (Gray et al., 1995; Harris et al., 2000). The untagged population therefore represents the properties of superficial layer cells of multiple morphologically- and molecularly- defined cell types. The untagged population included grid cells (35.6%; 26.8% pure, 8.8% mixed), head direction cells (9.1%; 6.1% pure, 3% mixed), speed cells (18.9%; 10.1% pure, 8.8% mixed), border cells (5.8%; 4.6% pure and 1.2% mixed), and unclassified cells (41.6%). We next compared the raw scores between the populations using two-sided, non-parametric statistics (Figure 3B). The untagged population had lower head direction scores (two-sided Mann-Whitney U test, U = 22869.0, p=0.003), higher grid scores (Mann-Whitney U test, U = 14225.0, p=0.0037), and lower spatial information content (two-sided Mann-Whitney U test, U = 21692.0 p=0.036) compared to the tagged cells. There was no significant difference in border score (two-sided Mann-Whitney U test, U = 16536.0, p=0.085), or speed score (two-sided Mann-Whitney U test, U = 18307.0, p=0.68). We also tested whether the grid scores of cells categorized as grid cells (two-sided Mann-Whitney U test, U = 1786.0, p=0.72), head direction score of head direction cells (two-sided Mann-Whitney U test, U = 208.0, p=0.99), and speed score of speed cells (two-sided Mann-Whitney U test, U = 461.0, p=0.28) differed between the tagged and untagged populations, and we found no significant differences. The number of border cells was too small to do a statistical comparison. In summary, the tagged and untagged populations were heterogeneous but notably both groups included substantial numbers of grid cells (approximately 1 in 4 for tagged cells and 1 in 3 for untagged cells).

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These results contrast with a previous study by Tang and colleagues (Tang et al., 2014). Tang et al. assigned extracellularly recorded cells into putative pyramidal and stellate classes based on depth of modulation and preferred firing phase relative to the ongoing theta oscillation. The authors concluded that stellate cells were grid cells only ~3% of the time (near chance levels) but were more frequently border cells (~11%). In contrast, putative pyramidal cells were more often grid cells (~19%) and less often border cells (~1%). We first asked how well the classifier approach worked to identify our tagged cells. We found that the classifier identified our tagged cells as putative stellate cells 81.3% of the time (Figure 4A). Most of the misidentified cells were clearly in the putative pyramidal region and the tagged grid cells showed a similar distribution as the other tagged cells (Figure 4—figure supplement 1; mean distance to decision boundary for the misidentified cells = 0.87). Because the untagged population also includes stellate cells, among others, we cannot determine the number of cells falsely identified as stellate cells and therefore cannot fully evaluate the classifier. Nevertheless, we note that our calculated true positive rate for stellate cells is only around 80%. Therefore, there is currently no available substitute for identifying stellate cells with high precision besides more labor intensive options like functional imaging combined with a marker of stellate cells (Sun et al., 2015), intracellular recordings with post-hoc reconstructions (Domnisoru et al., 2013; Schmidt-Hieber and Häusser, 2013; Burgalossi et al., 2011), or optogenetic tagging, as we have done here.

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The Tang et al. results also suggested that theta phase and strength could be used to predict the functional identity of the cells. We therefore evaluated their classifier on an extended dataset of 1332 cells including 411 grid cells. This extended dataset included recordings from the EC-tTA x tetO-ArchT-GFP mice and three additional mice with histologically confirmed layer II recordings (N = 270 putative pyramidal cells, 999 putative stellate and 63 cells in the guard zone). We observed a similar distribution in plots of the preferred firing phase and strength of theta modulation as Tang et al. (Figure 4B). The preferred firing phase of the cells was not evenly distributed across the theta cycle (Rayleigh test for non-uniformity, p=3.79 × 10⁻⁹) and there were two peaks in the distribution: one near the peak and one near the trough of the oscillation (Figure 4B, Figure 4—figure supplement 2; see also [Newman and Hasselmo, 2014]). In contrast to the Tang et al. findings, however, we found that cells classified as stellate cells had overall higher grid scores than cells that were classified as pyramidal cells (two-sided Mann-Whitney U test, U = 114913, p=0.0003). Correspondingly,~32% of the putative stellates were grid cells, compared to ~23% of the putative pyramidal cells (Figure 4C,D). We did not find a significant difference in border scores between the two populations (two-sided Mann-Whitney U-Test, U = 127330.5, p=0.158, Figure 4C).

We then considered whether grid cells preferentially fired at a particular phase of the theta oscillation. Individual grid cells showed large diversity in their preferred firing and depth of theta modulation (Figure 4B,E) as expected given the propensity of layer II grid cells to phase-precess (Hafting et al., 2008). Clustering of the cells using an agglomerative clustering approach captured one population that fired near the peak and one that fired near the trough of the theta oscillation. Similar to what we found when we used the classifier, the clustering approach revealed higher grid scores in the peak-preferring population but cells with high grid scores in both populations (Figure 4—figure supplement 2). Border scores were not significantly different between the two populations.

We then asked whether grid cells had stronger theta modulation than non-grids. As a group, despite having many strongly modulated example cells, grid cells were significantly less theta modulated, as measured by the mean vector length of the cell firing with respect to the theta oscillation, than non-grids (Figure 4F; two-sided Mann-Whitney U test, U = 162644.0, p=9.28×10⁻⁵), perhaps again reflecting the strong phase precession of layer II grid cells (Hafting et al., 2008). Consistent with these results, the strength of theta modulation had a very weak but significant negative correlation to grid score (Pearson’s r = −0.15, p=6×10⁻⁸; Figure 4—figure supplement 3). We next compared the depth of theta modulation by class. To avoid comparing cells against themselves, we compared only cells that were ‘pure’ (i.e. above threshold in just one category; number of pure grid cells = 327, pure speed cells = 127, pure border cells = 68, pure head direction cells = 121). Pure grid cells were not significantly different in theta modulation compared to pure border cells (two-sided Mann-Whitney U test, U = 22816, p=0.087, Figure 4G), but had less theta modulation than pure speed cells (two-sided Mann-Whitney U test, U = 16548.0, p=0.0002) and more theta modulation than pure head direction cells (two-sided Mann-Whitney U test, U = 23391.0, p=0.003). In summary, theta modulation is prevalent across all functional cell types in the MEC but with some small, although significant, differences between groups. For example, we observed a small negative correlation between grid score and depth of theta modulation but the correlation accounted for approximately 2% of the variance. These results show that, despite some differences between groups, the large diversity in theta modulation and preferred theta phase within cell types makes the relationship between the firing of the cell and the theta oscillation a poor predictor of the functional identity of the cell, in close agreement with the results of Latuske et al., 2015.

We have shown that stellate cells in layer II of the MEC can belong to multiple functional cell classes and that approximately one in four are grid cells. These results serve to reconcile conflicting evidence in the field. On the one hand, in vivo whole cell recordings and functional imaging of stellate cells have both found approximately equal or greater numbers of putative grid cells in the stellate population than in the pyramidal cell population (Domnisoru et al., 2013; Schmidt-Hieber and Häusser, 2013; Sun et al., 2015). On the other hand, it has been reported, in work where cell identity was classified on the basis of locking to the theta phase, that putative stellates are almost never grid cells (Tang et al., 2014). We addressed this controversy in two ways. First, we optogenetically tagged stellate cells using a mouse line that expresses transgenes almost exclusively in stellate cells of MEC layer II. Second, we used the previously published classifier (Tang et al., 2014) on a dataset of 1332 cells and 411 grid cells.

Optogenetic tagging showed that roughly 25% of stellate cells are grid cells. The actual proportion of grid cells may be larger than this estimate, for three reasons: (i) spike sorting errors can lead to misassignment of cells into the wrong functional class (Navratilova et al., 2016), (ii) boundary-induced distortions of the grid pattern could, in theory, cause a grid cell to fall below the cutoff (Stensola et al., 2015), and (iii) grid cells with inter-field spacing larger than our 0.8–1.0 meter recording box would be missed in our analysis (Stensola et al., 2012). The widespread presence of grid cells in the stellate cell population was corroborated by the use of the theta classifier, which showed that putative stellate cells are more likely to be grid cells than putative pyramidal cells, in agreement with a previous study re-testing the same classifier (Latuske et al., 2015). The classifier results should be taken with a note of caution, because our data and the Tang et al. data suggest that the classifier correctly assigns stellate cells only around 80% of the time. One unanswered question is why the classifier assigned grid cells almost exclusively to the putative pyramidal category in the original Tang et al. study, but not in the present study and the Latuske et al. study. One clear difference is that the number of cells and animals recorded in the present study and the Latuske et al. study is higher than in the Tang et al. study. A second difference is the fraction of grid cells reported in the studies. We report approximately 30% grid cells in our layer II recordings using the 95th percentile cutoff and the Latuske study reported around 20% using the 99th percentile cutoff. In contrast, the Tang et al. study reported only 10% grid cells at the 95th percentile cutoff, well below any other published estimate with layer II tetrode recordings in rodents. As there are now clear indications from imaging work that grid cells are not homogeneously distributed in layer II (Heys et al., 2014), one possibility is that Tang et al. did not sample from a large enough region of layer II to get a representative sample. However, the lack of histology in the Tang et al. paper makes it impossible to compare recording locations between the studies.

Although the suggestion that one of four stellate cells probably is an underestimate, the majority of stellate cells are probably not grid cells. The remaining cells include smaller fractions of cells of all functional types, as well as a large number of unclassified cells, which might include the recently discovered object vector cells (Hoydal et al., 2018). This is consistent with recent observations of the role of PV+ cells, which contact stellate cells but not pyramidal cells (Fuchs et al., 2016). On the one hand, PV+ cells are preferentially connected with grid cells in vivo (Buetfering et al., 2014) and manipulations of the PV+ network alters grid cell firing (Fuchs et al., 2016). On the other hand, the effects of manipulating the PV+ network are not strictly limited to grid cells alone (Buetfering et al., 2014; Miao et al., 2017). Moreover, although we cannot address the functional identity of layer II pyramidal cells using our approach due to the high numbers of non-expressing stellate cells, it is very likely that grid cells are present also among pyramidal cells, along with other functional cell types (Domnisoru et al., 2013; Sun et al., 2015). Taken together, the observations suggest that there is no 1:1 relationship between morphological and functional cell types in layer II of the MEC. One possibility is that grid cells are specific subclasses of pyramidal and stellate cells, perhaps with a distinct molecular expression profile. In agreement with this possibility, in vitro recordings have found some heterogeneity among both stellate cells and pyramidal cells (Fuchs et al., 2016; Ferrante et al., 2017; Giocomo et al., 2007; Giocomo and Hasselmo, 2009; Shay et al., 2016). Alternatively, the cell class or subclass might make little difference for the functional identity of the cell. In the visual cortex, where there are also functionally defined cell types such as simple and complex cells, a cell’s morphology, projection pattern, and layer assignment does not define its functional class in a straightforward manner (Gilbert and Wiesel, 1979). Further studies are needed to establish exactly what determines the functional identity of the cells in the MEC.

The diversity of functional cell types in the stellate population is consistent with the proposal that grid cells contribute to, but are not the sole determinant of, place cell firing (Zhang et al., 2013). The observation fits with earlier results that place cells show mature firing patterns before grid cells in development (Langston et al., 2010; Wills et al., 2010; Bjerknes et al., 2018) and place cells can maintain some significant spatial tuning even when grid cells lose their hexagonal firing patterns (Brandon et al., 2011; Koenig et al., 2011). Such residual tuning could be upheld by border cells in MEC, which are present from the earliest days that place cells have been recorded in the hippocampus (Bjerknes et al., 2014; Muessig et al., 2015), and whose spatial modulation is retained under circumstances that compromise the spatial periodicity of grid cells (Miao et al., 2017). These cells, as well as the recently discovered entorhinal object-vector cells (Hoydal et al., 2018), may provide vector-based spatial information to hippocampal place cells, as proposed by theoretical models proposing cells with such properties in the MEC or elsewhere (O'Keefe and Burgess, 1996; Hartley et al., 2000; Burgess et al., 2000). Whether border cells and object-vector cells are stellate cells remains to be determined, since only one of the tagged cells was a border cell in the present study. The low number of tagged border cells may reflect either that such cells are not stellate cells or that we missed the border cells, given their low abundance in MEC (5–10% [Bjerknes et al., 2014; Solstad et al., 2008; Boccara et al., 2010]) and the patchy organization of the MEC network (Kitamura et al., 2014; Burgalossi et al., 2011; Heys et al., 2014). Finally, theoretical work (Savelli and Knierim, 2010; de Almeida et al., 2012; Rolls et al., 2006) has suggested that place cells may also be formed by inputs from cells with weak spatial modulation in the MEC (Zhang et al., 2013; Diehl et al., 2017), or the LEC (Hargreaves et al., 2005), or elsewhere. By showing that grid cells account for only a fraction of the hippocampal stellate-cell input, the present findings point to multiple functional classes of MEC cells as possible sources for place-cell formation.

Taken in combination with previous recording and imaging efforts (Domnisoru et al., 2013; Schmidt-Hieber and Häusser, 2013; Sun et al., 2015; Latuske et al., 2015), our findings settle the controversy over whether stellate cells can be grid cells and suggest a major but not exclusive role for grid cells in the formation and maintenance of place cells and other spatially modulated cells in CA3 and dentate gyrus of the adult hippocampus. Taken together with recent work showing that stellate cells are required for path integration behaviors (Tennant et al., 2018), our data also implicate grid cells in path integration, in agreement with a large body of present and past theoretical models of grid cells (McNaughton et al., 2006; Couey et al., 2013).

Data and python code required to reproduce Figures 3 and 4 are available on GitHub (https://github.com/davidcrowland/archdata; copy archived at https://github.com/elifesciences-publications/archdata). Unprocessed electrophysiological data are archived on Norstor (https://archive.sigma2.no/pages/public/datasetDetail.jsf?id=10.11582/2018.00025).

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Author details

1. David C Rowland

   Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway

   Contribution

   Conceptualization, Software, Funding acquisition, Investigation, Methodology, Writing—original draft, Writing—review and editing

   For correspondence

   david.c.rowland@ntnu.no

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2735-2730

2. Horst A Obenhaus

   Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway

   Contribution

   Resources, Software, Formal analysis, Validation, Investigation, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

3. Emilie R Skytøen

   Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway

   Contribution

   Investigation, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

4. Qiangwei Zhang

   Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway

   Contribution

   Investigation, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

5. Cliff G Kentros

   Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway

   Contribution

   Supervision, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

6. Edvard I Moser

   Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Investigation, Writing—original draft, Project administration, Writing—review and editing

   Competing interests

   No competing interests declared

7. May-Britt Moser

   Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway

   Contribution

   Resources, Supervision, Funding acquisition, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   may-britt.moser@ntnu.no

   Competing interests

   No competing interests declared

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