## Introduction

The dentate gyrus (DG) is largely hypothesized to implement a ‘pattern separation’ operation1,2,3,4 allowing similar but not identical input patterns from the entorhinal cortex (EC) to be distinctly encoded in CA3. Specifically, the DG network is believed to generate distinct activity patterns for slightly distinct EC inputs, and the supply of this differentiated information to CA3 is believed critical to prevent the merging of information by CA3 pattern completion2,4,5,6. While lesion studies largely support this hypothesis7,8,9,10, how pattern separation is implemented by the DG remains unclear.

One behavior paradigm that requires intact DG function is the detection of small changes in the spatial layout of objects in an environment. Animals tend to spend more time exploring the location of displaced objects; however, they do not show such behavior when DG functions are impaired8,10. How the activity of DG cells is altered by small changes in object layout is largely unknown. Yet, we can envision that several factors might compel the DG to produce distinct representations. First, granule cells (GCs) are believed to be especially predisposed to produce sparse and orthogonal cell assemblies2,11,12 due to a strong inhibition that promotes competition between GCs13 and to extensive divergence of EC-to-GC afferents, as GCs outnumber EC cells by a ratio of at least 5:1 (possibly reaching 10:1)14,15. Second, GC place fields are suggested to be contingent on both object and spatial information9,16,17 and therefore sensitive to object displacements. Activity patterns related to objects, boundaries and path integration are reported in the lateral (LEC) and medial (MEC) divisions of the EC18,19,20,21,22. Specifically, GC place fields may emerge from the conjunction of MEC grid cells18,22,23, MEC object-vector cells24 and LEC object-specific cells21. Third, mossy cells (MCs) exhibit activity patterns sensitive to changes in local cues25,26 and are hypothesized to convey a novelty signal, which could help transform GC representations via MC-to-GC excitation and disynaptic inhibition27,28,29.

Despite the importance of an intact DG for detecting changes in the spatial layout of objects7,8,9,10, experiments that examine DG cell responses to small changes in object layout are missing. Here, we used silicon probes with integrated light guides30,31, two mouse lines (POMC-Cre and DRD2-Cre) expressing Chronos32 in GCs and MCs25,27,33,34, and a treadmill apparatus on which mice ran head-fixed through a sequence of visual-tactile cues fixed on the belt35,36,37. We identified putative GCs and MCs and examined their spatial and temporal responses to the addition of a visual-tactile cue to the familiar layout of the belt. We implemented a computational model of the GC network that incorporated grid cell, object-vector cell, MC and feedback inhibitory inputs, and evolved via Hebbian synaptic modifications13,38,39. We showed that spatial representations reconfigure differently for GCs and MCs in ways that are consistent with MCs detecting changes first, GCs operating as a competitive network, and MCs enabling the spreadout of GC remapping in locations distant from the cue.

## Results

### Recording and photostimulation of dentate units on the treadmill

AAV/hSyn-Flex-Chronos-GFP was injected into the DG of 8 mice (5 DRD2-Cre and 3 POMC-Cre mice) to selectively express Chronos in MCs (n = 5) or in GCs (n = 3). Following a period of 7 days to recover from surgery, the mice were trained for 3 weeks to run head-fixed on a 211-centimeter-long treadmill belt enriched with visual-tactile cues, with water rewards provided via a lick port on every trial (belt cycle) at a fixed position of the belt. Then, for simultaneous recordings of electrophysiological activity and photoexcitation of DG neurons, a silicon probe with integrated optical fibers30,31 was chronically implanted in the dorsal DG (Fig. 1a). The electrode position in the DG was assessed by the profile of local field potential (LFP) type 2 dentate spikes (DS2s), whose polarity is positive in the hilus and reverses above the granule cell layer25,40 (Fig. 1b), and confirmed by the concentration of recorded cells below the DS2 reversal point and the detection of optogenetic cell responses. For DRD2-Cre mice, GFP-labeled cells were visible in the hilus and colocalized with the MC markers calretinin and GluR2/326,27,33,41,42,43, while for POMC-Cre mice, GFP-labeled cells populated the GC layer and colocalized with the GC marker calbindin27,44,45 (Fig. 1c). POMC is typically used as a marker for immature GCs because its expression is limited to the 1-month period following cell mitosis46. While we cannot be sure, Chronos expression may have been biased toward mature adult-born GCs (>5–6-week old47) at the time of the recordings 4 weeks after virus injection.

To excite GCs and MCs that expressed Chronos, a series of sine-wave-shape photostimuli (>300 single sine waves, 50 µW, 100-ms duration, every 3 s) was delivered. Compared to a short pulse, such a gradual stimulus waveform is more likely to induce asynchronous spiking as cells reach spike thresholds at distinct phases of the stimulus (because of differences in excitability, proximity to the light source and virus expression), thereby improving spike detection30,48,49 and reducing the chance of indirect cell excitation. The peri-stimulus histograms of a fraction of cells showed excitatory responses (Fig. 1d,e). For the next analysis, we considered excitatory responses having a Z-score > 5 (comparing the peak of the response with the 1-s period preceding the stimulus; DRD2: 49 out of 752 cells; POMC: 25 out of 318 cells).

### Identification and characterization of putative GCs and MCs

To allow the identification of putative GCs and MCs based on physiological criteria, we searched differences in spike features for DRD2 and POMC light-excited cells (Fig. 1f–i). First, we found that spike autocorrelogram profiles were characteristic of short-interval burst activity for POMC light-excited cells and showed large humps flanking a wide refractory gap for DRD2 light-excited cells (Fig. 1f), consistent with the GC and MC autocorrelogram profiles obtained from in vivo intracellular recordings50. To quantify this difference, we measured an ACG refractory gap, defined as the duration for the autocorrelogram to reach 75% of its peak value, for each cell (Fig. 1g). As expected, DRD2 light-excited cells had, on average, higher ACG refractory gap values than POMC light-excited cells (Fig. 1g; DRD2, 15.5 ± 1.2 ms; POMC, 9.8 ± 1.7 ms; p = 0.0055, unpaired t-test). Furthermore, compared to DRD2 light-excited cells, POMC light-excited cells had shorter spike durations (Fig. 1h; DRD2, 0.7 ± 0.01 ms; POMC, 0.6 ± 0.03 ms; p = 0.0050, unpaired t-test) and more negative spike asymmetry values (Fig. 1h; DRD2, −0.05 ± 0.01; POMC, −0.1 ± 0.02; p = 0.045, unpaired t-test). Finally, POMC light-excited cells showed a preference to discharge before the troughs of local field potential gamma oscillations (30–80 Hz; measured in the hilus), while DRD2 light-excited cells showed no clear bias (Fig. 1i).

The light stimuli allowed only the detection of a subset of GCs or MCs in a mouse. To identify all putative GCs and MCs in all mice, we measured the above spike features for all cells and examined the overlaps with the spike features of POMC/DRD2 light-excited cells25 and putative excitatory neurons (identified from cell-pairs cross-correlogram analysis51). We first excluded a group of cells categorized as putative interneurons based on their high firing rates, low ACG refractory gap values, and the lack of overlap with putative excitatory neurons (Fig. 2a). Then, we found that the combination of features that best separated POMC and DRD2 light-excited cells was the cells’ ACG refractory gap together with the cells’ preferred gamma phase. Putative GCs (n = 252) were characterized by a narrow ACG refractory gap, a preference to discharge during the troughs of gamma oscillations and an overlap with POMC light-excited cells (Fig. 2b,d, Right). In contrast, putative MCs (n = 116) were characterized by a wide ACG refractory gap, a preference to discharge at other phases of gamma oscillations and an overlap with DRD2 light-excited cells (Fig. 2b,d, Left).

Next, we examined the relative position of putative GCs, MCs and local field potential (LFP) type 2 dentate spike (DS2)25,40 along the electrode shanks (Figs 1a and 2c; See methods). Consistent with anatomical data, putative GCs were located closer to the site of DS2 polarity reversal, which is located above the granule cell layer, while putative MCs were shifted toward the positivity of the DS2, i.e., toward the hilus (Fig. 2c). As previously reported25,43, putative GCs had higher spatial information compared to putative MCs (Fig. 2e; p = 7.03e-04, Wilcoxon rank-sum test).

### Addition of a landmark

The next experiment was performed with 5 of the 8 mice (2 DRD2 and 3 POMC). For the analyses, we considered cells with a mean firing rate > 0.5 Hz and stable place fields (for which spatial correlation between session halves > 0.5; GC, n = 40; MC, n = 40), and POMC and DRD2 data were pooled and analyzed together, as we observed no qualitative difference between the two groups.

In a second recording session in which no photostimuli were delivered, we fixed a new visual-tactile cue on the belt after 10 to 15 trials. We first examined individual cell responses by plotting firing rate maps for trials before (pre) and after (post) the object addition (Fig. 3b,c) and by computing spatial correlations (pixel-by-pixel correlation coefficient) and firing rate changes between ‘pre’ and ‘post’ rate maps (Fig. 3d). GCs showed a range of responses. While some GCs were not much affected, other GCs developed a place field near the object position or exhibited changes in firing rate (Fig. 3c). Most MCs were affected by the manipulation (Fig. 3b), as only a small fraction of MCs showed very high spatial correlation (Fig. 3d Left). However, MC alterations were more partial than GC alterations, as MCs showed fewer spatial correlations that were very low and exhibited, on average, smaller changes in firing rate (Fig. 3d; mean rate, p = 0.0037; peak rate, p = 2.91e-04, F-test).

### Spatiotemporal profiles of changes for GC and MC firing rates

To examine the spatiotemporal profiles of GC and MC responses, we first examined how firing rates changed depending on belt positions, trials and time. To examine the spatial profile of firing rate changes, we computed firing rate changes for each position of the belt using ‘pre’ rate maps as references and implemented color-coded matrices displaying individual cells as well as cell population averages (Fig. 4a). For both individual cell and population average displays, firing rate changes were seen throughout the whole belt; however, the largest effect was in the vicinity of the added cue (average change within cue versus > 10 cm away from cue; MC: 0.21 ± 0.02 versus 0.15 ± 0.007, p = 0.010; GC: 0.21 ± 0.03 versus 0.13 ± 0.01, p = 0.008, paired t-test). Furthermore, the peak of the response was shifted to after the cue for GCs, whereas the peak was aligned with the cue for MCs (MC: −0.4 ± 1.8 cm from middle of cue; GC: +6.6 ± 2.2 cm from middle of cue; p = 0.021, unpaired t-test; cell averages using cells with peak changes <10 cm away from the cue).

To examine the dynamics of cell responses, we computed trial-by-trial changes in firing rate for individual cells using ‘pre’ rate maps as references and implemented color-coded matrices displaying individual cells as well as cell population averages (Fig. 4b). In both GC and MC populations, firing rates were increased for a subset of cells while decreased for another (Fig. 4b, color-coded). However, at the population level, the average cell firing rates were relatively unaltered (Fig. 4b, middle), suggesting that the firing rate elevations and reductions were relatively balanced in both the GC and MC populations. Therefore, we also computed average firing rate changes using the absolute values of changes for each cell (Fig. 4b, bottom). GCs and MCs showed distinct dynamics. While the magnitude of GC firing rate changes progressively increased and reached a plateau value after 15 trials, the MC response was more immediate, reaching a plateau value after 4 trials.

Interestingly, an initial transient decrease was visible in the population average firing rates (Fig. 4b, middle). To precisely examine this transient component, we computed cell firing rate changes over a 300-s time period using the 50-s period preceding the cue addition as a reference and implemented color-coded matrices displaying individual cells as well as cell population averages (Fig. 4c). A transient decrease in firing rate, lasting approximately 1 minute, was visible for some MCs (Fig. 4c, color coded) and detectable in the MC population average (Fig. 4c, bottom). Such an effect is reminiscent of the one-minute transient inhibition of hilar cells observed following the stimulation of the locus ceruleus52.

### Spatiotemporal profiles of changes for GC and MC population vectors

We next examined how population vectors25,53 were altered depending on belt position and trials. For this, we computed MC and GC population vector correlations for each position of the belt and for either single trials or block of 8 trials, using ‘pre’ rate maps as references (Fig. 5a). While population vectors were altered throughout the whole belt for both MCs and GCs, the alteration peaked in the vicinity of the cue (within cue versus > 10 cm away from cue; MC: 0.2 ± 0.04 versus 0.6 ± 0.01, p = 0.78e-23; GC: 0.6 ± 0.05 versus 0.8 ± 0.01, p = 1.57e-09; paired t-test) and the peak was shifted to after the cue for GCs but aligned with the cue for MCs (Fig. 5a; MC: 0.4 ± 1.2 cm from middle of cue; GC: +9.3 ± 0.7 cm from middle of cue; p = 5.50e-07, paired t-test).

Importantly, the alteration of the population vector was stronger for MCs than for GCs, a phenomenon that was observed in all positions of the belt initially (Fig. 5a; trial 1–8 population vector correlation before cue: GC, 0.7 ± 0.01, MC, 0.5 ± 0.03, p = 3.5e-05; within cue: GC, 0.4 ± 0.02, MC, 0.2 ± 0.03, p = 2.5e-04; after cue: GC, 0.6 ± 0.01, MC, 0.4 ± 0.05, p = 0.01; unpaired t-test). However, the difference was reduced over trials as GC population vector correlation progressively decreased while MC population vector correlation was unchanged, a phenomenon that was also observed in all positions of the belt (Fig. 5b; Before cue: GC, p = 0.012, MC, p = 0.89; Within cue: GC, p = 0.0010, MC, p = 0.24; After cue: GC, p = 0.0037, MC, p = 0.48; All positions: GC, p = 0.0003, MC, p = 0.81; Pearson correlation coefficient).

### Modeling of the GC response to cue addition

The dentate gyrus is often modeled as a competitive network in which discrete place field representations are produced through ‘competitive learning’, that is, through the combination of Hebbian synaptic plasticity and GC competition13,38,39,54. Therefore, we tested whether GC responses to cue addition could be replicated by a competitive network model of the DG in which place field representations were initially developed through competitive learning. We incorporated only the mechanisms necessary to replicate the response features of experimental data in the model. The model was therefore simplistic. Briefly, 3000 GCs received excitatory inputs, with randomly assigned synaptic weights, from 300 EC grid cells, 75 EC object-vector cells and 30 MCs, and were subject to feedback inhibition (Fig. 6a, See methods). The firing patterns of the inputs were generated with Gaussian functions and were periodic for grid cells, matched the positions of a pair of cues (slightly shifted toward after the cues) for object-vector cells and were randomly distributed for MCs. The activity of a GC in a given position was the weighted sum of EC and MC activity minus the inhibition. The inhibition was proportional to the summed activity of GCs. In each model iteration, the EC-to-GC synapses were modified via synaptic potentiation and scaling mechanisms (Fig. 6b).

Importantly, a critical factor to reproduce the progressive aspect of GC population vector changes was a partial scaling of synaptic weights per iteration. For the value of the parameter ß = 3 used so far (Fig. 6b), the sum of synaptic weights was shifted closer (but not made equal) to 1 on each iteration, and the GC population vector correlation showed a gradual development similar to that observed in the experimental data. However, such gradual development could not be reproduced when the values of ß were much higher or lower, i.e., when synaptic scaling operation leaned toward normalization or no scaling, respectively (Fig. 7c). A partial scaling of synaptic weights per iteration is consistent with the gradual restoration of total synaptic weight observed after synaptic potentiation in vitro55.

Finally, because MCs displayed transient changes in firing rate and are suggested to contribute feedforward inhibition to GCs52,56,57, we examined the effect of transiently modulating the inhibition parameter α. Interestingly, increasing and reducing α changed the GC population vector correlation in a similar direction (Fig. 7d). Hence, the degree of GC remapping can be dynamically tuned via the modulation of inhibition, and MCs are well positioned to control such operation.

## Discussion

Despite the critical involvement of the DG in detecting changes in object locations8,10,19, the impact of local changes in object layout on DG cell activity has not been investigated. With the combination of silicon probe recording, optogenetic techniques and running behavior on a cue-enriched treadmill, we identified putative GCs and MCs and monitored their trial-by-trial responses to the introduction of a local cue.

The method used to identify putative GCs and MCs differed from those used in previous studies25,42,43 and presented both potential advantages and limitations. We used Cre-dependent virus injections in DRD2-Cre and POMC-Cre mice to express Chronos in MCs and GCs, respectively. Virus expression in DRD2-Cre mice was reported to be quite specific to MCs in the DG but present in interneurons of the CA hippocampal regions58. Additionally, Chronos expression may have been biased toward mature adult-born GCs47 because POMC expression is limited to the 1-month period following cell mitosis46 and because recordings were carried out 4 weeks after virus injection such that a large fraction of virus-infected GCs were likely mature (>5–6 week old47) by the time of the recordings.

We used sine-wave-shape light stimuli to excite GCs and MCs expressing Chronos. This type of stimulus was used for several reasons. First, long sine waves have been shown to be better than short pulses for the detection and isolation of light-triggered spikes30. Indeed, short light pulses tend to produce synchronous cell activation, generating an overlap of spike waveforms of cells that compromise spike sorting. In contrast, with the progressive change in light intensity generated by the sine wave, cells are likely to reach spike thresholds at distinct phases of the stimulus because of differences in excitability, proximity to the light source and Chronos expression. Second, the asynchronous cell activation generated by the sine wave should reduce the chance of disynaptic cell activation. Third, light excitation of cells is in some respects better than light silencing of cells (using halorhodopsin59 for instance). To detect the effect of cell silencing, the baseline firing rates of cells should be high, which is not the case for GCs11,60,61. Additionally, while the possibility of an indirect effect exists in both approaches, the effect of light excitation is more easily observed in real time than that of light silencing, allowing for the adjustment of the light intensity to minimal levels (to reduce indirect effects).

We found that the two features providing the best separation for putative GCs and MCs, based on POMC and DRD2 light-excited cell data, were the spike autocorrelogram profile and spike gamma phase of cells. The wide profile of MC spike autocorrelograms was consistent with in vivo intracellular recording data in which MCs were identified via intracellular labeling50. Additionally, a difference in spike gamma phase between GCs and MCs was observed in another study25, but to a smaller extent. This discrepancy might not necessarily reflect a difference in cell classification but differences in the locations where local field potential gamma oscillations were measured. Finally, the differences in MC and GC activity patterns and spatial responses were largely consistent with other studies reporting that MCs have wider and more numerous firing fields and show stronger remapping than GCs25,42,43.

With the addition of a local cue on the belt of the treadmill apparatus, we could observe both temporal and spatial aspects of cell responses. The GC response was characterized by a reconfiguration of place fields that peaked in the vicinity of the added cue. This local peak likely arose from the addition of local object-vector inputs, as illustrated by the model. Interestingly, the peak was shifted slightly after the cue, possibly because of a similar shift of object-vector representations or local network computations. Despite the additional cue and the reconfiguration of spatial representations, the overall firing activity of the GC population was relatively unchanged as the increase and decrease in cell activity were relatively balanced, suggesting the existence of mechanisms preserving the scale of GC activity. Furthermore, changes in GC population activity developed progressively over trials (Figs 4 and 5), suggesting the involvement of synaptic plasticity mechanisms. The model reproduced this feature using two types of synaptic plasticity mechanisms: synaptic potentiation akin to Hebbian long-term potentiation (LTP)54,62 and synaptic scaling, which is necessary to prevent exponential growth of synaptic weights13,38,39. While LTP appears immediately after LTP inducing stimuli54,55,63, synaptic scaling is a slower process, developing over 30 minutes in vitro via heterosynaptic depression55 and partly taking place during slow-wave sleep/sharp-wave ripple activity in vivo64,65. Consistent with this time scale, the rate of synaptic scaling had to be relatively low for the model to reproduce the progressive decrease in GC population vector correlation.

MCs are suggested to play a role of sentinels that inform GCs of object layout changes by deciphering changes from semilunar GC inputs66,67,68,69. The differences between MC and GC responses were consistent with this hypothesis. First, the MC response was stronger25,43, more immediate, and peaked earlier on the belt than the GC response (Figs 4 and 5), consistent with MCs not being controlled by GC-to-MC inputs and MCs preceding GCs in detecting change. Second, in contrast to GCs, several MCs displayed a one-minute-long transient response (Fig. 4c). One-minute-long cell responses have been reported in the hilus for stimulations of the locus ceruleus52, a structure that shows phasic activation to change in environmental contingencies70,71 and releases both noradrenaline72 and dopamine73. Although hilar cells were generally called interneurons in this study, MCs, the most common cell type in the hilus74, likely expressed such responses, considering that the large majority of recorded cells did. The transient response we observed for MCs might therefore be generated by a novelty-related neuromodulatory signal from the locus ceruleus. Hence, consistent with the sentinel hypothesis27, MCs were not controlled by GC-to-MC inputs and likely received novel cue information from other afferents, such as semilunar GCs27,66,67,68,75, direct EC afferents28,76 and the locus ceruleus. MCs could then contribute to changes in GC encoding via both direct and indirect inputs to GCs5,27,28,74,75.

An alteration of both MC and GC population vectors was visible in locations distant from the added cue, a feature that did not arise from noise as it developed over time (Fig. 5). While the mechanism underlying this feature is unclear for MCs, a possible scenario is that it originates from the abovementioned transient neuromodulatory effect, which should overlap with all belt positions due to its minutes-long duration. Importantly, the model did not predict such feature for GCs when only a set of EC object-vector cell inputs was added in the cue position but did so when MC activity was altered throughout the whole belt as in the experiment. Hence, an important function of MCs might be to spread the alteration of GC representations in locations distant from the added cue. Because MC-to-GC feed-forward inhibition77,78,79 was not incorporated in the model, MC-to-GC excitation might alone be sufficient to support this function. However, MC-to-GC feed-forward inhibition and other mechanisms such as presynaptic inhibition of EC inputs27,28,52, likely also contribute. For instance, the remapping of MCs is expected to generate a remapping of inhibitory inputs to GCs, which should alter GC population activity considering the effects of modulating model inhibition reported in Fig. 7d. In terms of function, the spread of GC remapping to distant locations might support enhanced exploratory behaviors in areas surrounding displaced objects8,10,80 and be critical for binding information of novel cues and contingencies that are part of the same event but not spatially contiguous. Future experiments using cell-type specific inactivation might directly test MC contribution to the spatial extent of GC remapping and exploratory behaviors.

## Methods

### Animals

All experiments conformed to the Guide for the Care and Use of Laboratory Animals (NRC 2011). The experimental protocols were approved by the Institutional Animal Care and Use Committee of the Korea Institute of Science and Technology.

Data were collected from 8 mice, 5 DRD2-Cre (B6.FVB(Cg)-Tg(Drd2-cre)ER44Gsat, GENSAT) and 3 POMC-Cre (B6.FVB(Pomc-cre)1LowI/J, The Jackson Laboratory) mice aged between 11 and 12 weeks at the time of recordings. Male mice were used for all experiments to avoid gender-related variability. Mice were housed in groups of 2 or 3 per cage in a vivarium with a 12-h light/dark cycle. Training and recording sessions were conducted during the light cycles.

### Virus injection and preparation for head fixation

Part of the surgery procedure has been described previously81. Briefly, under isoflurane anesthesia (supplemented by injections of buprenorphine 0.1 mg/kg, s.c), a viral vector expressing Chronos and GFP (AAV-hSyn-FLEX-Chronos-GFP, UNC vector core) was injected bilaterally into the dorsal dentate gyrus (−2.1 mm anteroposterior; −1.5 mm mediolateral; −1.6 and −1.7 mm dorsoventral; 50 nL per location) using a glass micropipette and custom-made injector (using the Narishige mo-10 manipulator). Two screws were inserted into the skull overlying the cerebellum to serve as ground and reference electrodes. A head plate designed to be conveniently fastened to a metal holder was fixed to the skull using dental cement31.

### Behavioral training and apparatus

After a recovery period of 7 days, mice were put under a water restriction scheme (1 ml per day) and trained (1 h session per day for 3 weeks) to run on a treadmill with their head restrained. The treadmill consisted of a 211-cm velvet belt stretched between two 3D printed wheels and was not motorized such that mice moved the belt themselves. Pairs of visual-tactile cues were fixed on the belt. Each cue consisted of a double array (15 to 20-cm-long) of small erect objects lined along the edges of the belt and provided visual-tactile stimulation to both sides of the mice without interfering with their locomotion. Three types of objects were used: ~2-cm-high glue spines, ~2-cm-high shrink tubes, and ~1-cm-high pieces of folded Velcro.

To induce consistent running trajectories, a water reward was delivered through a lick port on each trial (belt revolution) at the same belt position. Mice typically ran 100 to 150 trials over 45-minute sessions after 2 weeks of training.

### Silicon probe with integrated fibers

A 64-channel silicon probe (Neuronexus, Buzsaki64sp) was mounted on a custom made microdrive31. Optical fibers were chemically etched on one end (down to 15-µm diameter) and fixed on every other shank of the silicon probe (3 out of 6 shanks) with the fiber tip positions 100 µm above the recording sites30. Optical fiber connectors (Precision Fiber Products Inc, single-mode LC ferrule) were fixed on the unetched end of the fibers and cemented to a custom-made support31.

### Chronic implantation of the electrode

Detailed procedures for chronic implants of silicon probes were described previously81. Briefly, a craniotomy was performed under isoflurane anesthesia. The silicon probe was inserted in the dentate gyrus under microscope supervision and electrophysiological activity monitoring. The electrode was slowly lowered to the granule cell layer of the dentate gyrus, which was detected by the emergence of unit activity following an ~500-μm silent zone below the CA1 pyramidal layer. Then the electrode was retracted 200 μm. The microdrive was cemented to both the skull and head plate. A mixture of bone wax and mineral oil was used to cover the skull opening. The next day, the silicon probe was slowly lowered to the granule cell layer using the microdrive. A plastic cap was used to protect the microdrive/silicon probe assembly.

### Recording sessions

On the recording day, two consecutive sessions were implemented while mice were on the treadmill. In the first session, we delivered multiple light stimuli (single ~50-µW amplitude sine waves of a 100-ms duration every 3 s) during periods when the animal was immobile. In the second session, a landmark was added to the belt after 10 to 15 trials. The object was a 15-cm-long double array of glue spines identical to the one already fixed on the belt (Fig. 3a).

### Anatomy, opsin expression and immunohistochemistry

The mice were anesthetized with isoflurane and perfused transcardially with 4% paraformaldehyde in PBS. The brain was removed and kept overnight in 4% paraformaldehyde, after which it was cut into 100-µm-thick coronal sections using a vibratome (Leica, VT1200S). Brain sections were processed for fluorescent immunohistochemistry82. The sections were permeabilized with 1% Triton X-100 in 1X Tris-Buffered Saline (1X TBS: 50 mM Tris, 150 mM NaCl, pH 7.4 adjusted with 1 M HCl) and incubated in blocking solution (5% normal donkey serum (Jackson, 017-000-12) and 0.4% Triton X-100 in 1X TBS). Rabbit anti-calretinin (1:1000; Swant, 7697) and rabbit anti-GluR2/3 (1:100; Millipore, AB1506) were used as primary antibodies (4 °C overnight incubation) for DRD2-Cre mice, while rabbit anti-calbindin-D28k (1:1000; Swant, CB38) was used for POMC-Cre mice. Donkey anti-rabbit Alexa Fluor 594 (1:500–1000; Jackson ImmunoResearch, 711-585-15) was used as a secondary antibody (3-h incubation at room temperature). Slices were washed in TBS and mounted using Vectashield mounting medium with DAPI (Sigma-Aldrich). Images of DAPI, GFP and Alexa 594 fluorescence were acquired separately with a confocal microscope (Nikon A1).

### Behavior control and photostimulation

The forward and backward movement increments of the treadmill were monitored using two pairs of LED and photosensors that read patterns on a disc coupled to the treadmill wheel, while the zero position was implemented by an LED and photosensor couple detecting a small hole on the belt. From these signals, the mouse position was implemented in real time by an Arduino board (Arduino Uno, arduino.cc), which also controlled the valves for the reward delivery. Position, time and reward information from the Arduino board was sent via USB serial communication to a computer and recorded with custom-made LabView (National Instruments) programs.

To deliver the photostimuli, a blue diode laser (Vortran Laser Technology, StradusTM 473) was divided and collimated into 4 optical fibers (Thorlabs HPSC10-CUSTOM) using fiber ports (Thorlabs, PAFA-X-4-A). The optical fibers were connected to the electrodes’ fibers via LC connectors (single mode LC ferrule, Precision Fiber Products Inc). The waveform of the light stimulus was controlled using LabVIEW (National Instruments) and a USB Interface Board (Intan Technologies, RHD2000) communicating with the analog port of the laser.

### Data acquisition and spike sorting

Wideband neurophysiological signals were acquired continuously at 30 kHz on a 250-channel recording system (Intan Technologies, RHD2132 amplifier board with RHD2000 USB Interface Board and custom-made LabView interface). The wideband signals were digitally high-pass filtered (0.8–5 kHz) for spike detection, whereas they were low-pass filtered (0–500 Hz) and downsampled to 1000 Hz for local field potentials (LFPs). Spikes from each shank of the silicon probe were clustered separately with automatic algorithms83 followed by manual adjustments in custom-made MATLAB routines implementing spike autocorrelation, cross-correlation and cluster isolation statistics. Only clusters with well-defined cluster boundaries and clear refractory periods were included in the analyses84.

### Gamma phase of spikes

The LFP was bandpass filtered between 30–80 Hz. A vector of instantaneous phase was derived using the Hilbert transform. The gamma phase of each spike was interpolated from the vector of the instantaneous phase.

### Implementation of a single-neuron firing rate map

The length of the belt was divided into 100 pixels. For each cell, the number of spikes occurring in each pixel (spike count vector) and the time the animal spent in each pixel (time spent vector) were calculated. Both spike count and time spent vectors were smoothed with a Gaussian function and spike count was divided by time spent to obtain a firing rate map.

### Estimation of cell position on electrode shanks

To estimate the position of a cell with respect to the recording sites of a shank, we assumed that the amplitude of spike signals attenuated as 1/d2 (see notes below), where d is the distance of the site to the cell soma, such that the amplitude measured at a given site is as follows:

$${{\rm{a}}}_{{\rm{i}}}={\rm{A}}/{{{\rm{d}}}_{{\rm{i}}}}^{2}$$

where A is the spike amplitude exactly at the cell position. For the several recording sites on one shank, this means the following:

$${\rm{A}}={{\rm{a}}}_{1}\ast {{{\rm{d}}}_{1}}^{2}={{\rm{a}}}_{2}\ast {{{\rm{d}}}_{2}}^{2}={{\rm{a}}}_{3}\ast {{{\rm{d}}}_{3}}^{2}={{\rm{a}}}_{4}\ast {{{\rm{d}}}_{4}}^{2}={{\rm{a}}}_{5}\ast {{{\rm{d}}}_{5}}^{2}\cdots$$

Therefore, to estimate the position of a cell, we simply found the position where this condition was optimally fulfilled. To do this, we divided the volume around each shank in 1-µm3 pixels and calculated the Euclidean distances of recording sites for each pixel.

Then, we defined the value S as follows:

$${\rm{S}}={\sum }_{{\rm{ij}}}|{{\rm{a}}}_{{\rm{i}}}\ast {{{\rm{d}}}_{{\rm{i}}}}^{2}-{{\rm{a}}}_{{\rm{j}}}\ast {{{\rm{d}}}_{{\rm{j}}}}^{2}|$$

where i and j varies to generate all combinations of possible sites. The pixel with the smallest value of S was defined as the cell position.

Note: The electric potential of dipoles attenuate to 1/d2 and that of monopoles attenuates by 1/d. We tested the method using both forms and found the resultant cell positions to be very similar.

### Spatial information

Spatial information85 was calculated using the following equation:

$${\rm{Information}}\,{\rm{per}}\,{\rm{spike}}={\sum }_{{\rm{i}}}{{\rm{P}}}_{{\rm{i}}}\cdot \frac{{{\rm{R}}}_{{\rm{i}}}}{{\rm{R}}}\cdot {\log }_{2}\cdot \frac{{{\rm{R}}}_{{\rm{i}}}}{{\rm{R}}}$$

where i is the pixel number, Pi is the probability of occupancy of pixel i, Ri is the mean firing rate in pixel i, and R is the overall mean firing rate.

### Model

Three hundred and seventy-five EC cells (300 grid cells and 75 object-vector cells) were connected to 3000 GCs with synaptic weights initially set randomly and selected from a gamma distribution (shape parameter = 0.008). EC cells had firing fields generated with Gaussian functions (half-width of 15 cm) and included 3 groups of grid cells of different periodicities (70/√2 cm, 70 cm, 70*√2 cm)86 and 3 groups of object-vector cells encoding a range of positions within 10 cm from the tube, Velcro and spine cues (Fig. 6a). In addition, 30 MCs provided inputs to GCs, with synaptic weights set randomly and selected from a uniform distribution. MCs had several firing fields generated with Gaussian functions (half-width of 30 cm) of randomly varying amplitude and spread at random position on the belt (Fig. 6a). The overall contribution of MC-to-GC synapses was set to be weaker than that of EC-to-GC synapses by setting a constant γ = 0.5 (Fig. 6b (1)). The relative number of cells roughly matched the ~1:5 to 1:10 EC:GC ratio and the 1:100 MC:GC ratio14,15.

The excitation received by a GC in a given belt position was equal to the weighted sum of EC cell activity plus the weighted sum of MC activity (Fig. 6b (1)). The feedback inhibition was set proportional (using a constant α = 0.5) to the summed activity of GCs in a given belt position (Fig. 6b (2)). If the excitation exceeded the inhibition, the activity of the GC was equal to the excitation minus the inhibition; otherwise, the activity was set to zero (Fig. 6b (2)). To induce experience-dependent learning, EC-to-GC synaptic weights were incremented proportionally to the level of co-firing of EC-GC pairs (using a synaptic learning rate constant k), similar to Hebbian forms of long-term synaptic potentiation54 (Fig. 6b (3)). Then, the synaptic weights were scaled using a function that pulled the sum of synaptic weights for individual GCs toward normalization at a rate adjusted by a constant ß (Fig. 6b (4)).

The simulation was divided into two stages. In the first stage, 10 iterations were implemented to mimic the 3-week period of familiarization to the belt, which produced single place field representations (Fig. 6c) as previously reported25,43. For this stage, the synaptic learning rate was set to k = 20, and synaptic rescaling was set to produce complete synaptic weight normalization (ß = ∞). In the second stage, a new place field was added to the firing pattern of object-vector cells that encoded the spine cue in the position of the added spine cue (Fig. 6c). MC activity was reorganized by changing the amplitude of MC firing fields, with the direction of change randomly chosen and the magnitude of change decreasing exponentially with distance from the added cue to generate a similar profile of MC population vector correlation as observed in the experimental data (Fig. 6a). Five iterations were implemented to reproduce the trial-by-trial changes observed within the recording sessions. For this stage, the synaptic learning rate was reduced to k = 1 to generate small trial-by-trial synaptic learning increments, and synaptic scaling rate was reduced to ß = 3 (a feature we found critical to produce a gradual development of population vector and firing rate). The simulation was run 10 times with different sets of random values to obtain mean and standard error values for population vector correlations.

### Statistical analysis

All statistical analyses were performed in MATLAB (MathWorks). The number of animals and the number of recorded cells were similar to those generally employed. For each distribution, a Kolmogorov-Smirnov test was used to test the null hypothesis that the sample distribution was derived from a standard normal distribution. If normality was uncertain, we used nonparametric tests as stated in the main text or figures. Otherwise, Student’s t-tests were used to test the sample mean. Correlations were computed using the Pearson correlation coefficient. The results were considered significant if the p-value was < 0.05.