Recalibration of path integration in hippocampal place cells

Abstract

Hippocampal place cells are spatially tuned neurons that serve as elements of a 'cognitive map' in the mammalian brain¹. To detect the animal's location, place cells are thought to rely upon two interacting mechanisms: sensing the position of the animal relative to familiar landmarks^2,3 and measuring the distance and direction that the animal has travelled from previously occupied locations^4-7. The latter mechanism-known as path integration-requires a finely tuned gain factor that relates the animal's self-movement to the updating of position on the internal cognitive map, as well as external landmarks to correct the positional error that accumulates^8,9. Models of hippocampal place cells and entorhinal grid cells based on path integration treat the path-integration gain as a constant^9-14, but behavioural evidence in humans suggests that the gain is modifiable¹⁵. Here we show, using physiological evidence from rat hippocampal place cells, that the path-integration gain is a highly plastic variable that can be altered by persistent conflict between self-motion cues and feedback from external landmarks. In an augmented-reality system, visual landmarks were moved in proportion to the movement of a rat on a circular track, creating continuous conflict with path integration. Sustained exposure to this cue conflict resulted in predictable and prolonged recalibration of the path-integration gain, as estimated from the place cells after the landmarks were turned off. We propose that this rapid plasticity keeps the positional update in register with the movement of the rat in the external world over behavioural timescales. These results also demonstrate that visual landmarks not only provide a signal to correct cumulative error in the path-integration system^4,8,16-19, but also rapidly fine-tune the integration computation itself.

Extended Data Figure 1:. Representative histology.

Coronal slices from the five rats used in this study. Arrows point to tetrode tracks in different stages of advancement towards CA1. Note that these are not always the termination of these tetrodes, simply one section along their tracks. In one animal (Rat 576), the histology was inconclusive due to poor fixation and slice quality; however, we determined that the tetrodes were correctly placed in CA1 by the medio-lateral placement of the bundle, tracks in the few sections that we could analyze, and features in the EEG signals observed during recording (e.g., sharp wave/ripples). In one animal, (Rat 638), two of the most medial tetrodes (not shown) appeared to record from the fasciola cinereum, rather than CA1.

Extended Data Figure 2:. Examples of failure of landmark control.

a, (top) Experimental gain, G (blue), and hippocampal gain, H (yellow), for Epochs 1–3 of a session where G_final was 0.231. Note that the two curves overlap until ~lap 40, when they start to diverge. (middle) Spikes from three putative pyramidal cells (colored dots) in the lab frame. Alternate gray and white bars indicate laps in the lab frame. (bottom) The same spikes in the landmark frame. At the point of landmark control failure, the place cells stop firing at a particular location in the landmark frame, and instead start drifting in both lab and landmark frames. Alternating gray and white bars indicate laps in the landmark frame. b, Second example, from a different animal, for a session where G_final was 0.1 (same format as (a)). c-e, Trajectory of hippocampal gain, H, for three rats for all sessions where landmark control failed. The hippocampal gain generally starts near 1 and then diverges from the experimental gain trajectory (not shown) during the session.

Extended Data Figure 3:. Gain dynamics during each experiment.

Each plot represents data from a single experiment. The x-axis is the laps that the rat ran in the lab frame (on the table) and the y-axis is gain. The black scale bar in each plot indicates 10 laps. The applied experimental gain (blue) is plotted with the hippocampal gain estimate (red). The ramp rate, length of epochs and final experimental gain for each session can be observed from the curves. An asterisk indicates experiments with loss of landmark control (gain ratio greater than 1.1; see Fig. 2h). In the other plots, the blue and red curves overlap indicating control of landmarks over the place fields. Number of units that passed acceptance criteria (Methods) in each session is indicated in the bottom right hand corner of each plot.

Extended Data Figure 4:. Summary of dataset.

Each row indicates one of the 72 sessions composing the dataset during the period when the landmarks were on. In the left plot, the x-axis is laps in the lab frame. In the right plot the x-axis is experimental gain, G. The sessions are chronologically ordered (bottom to top). Sessions from different animals are separated by dashed lines. In all rats, we typically performed smaller manipulations in G first, since initial landmark failure tended to occur at larger manipulations of G. Once landmark control failed, it tended to fail more frequently. The color represents the ratio between hippocampal and experimental gains (H/G, color bar, right). Green (H/G = 1) indicates landmark control. Four of the rats (576, 637, 638, 692) experienced landmark failure (red portions of trials). Failures only happened when the G was less than one (i.e., the landmarks moved in the same direction as the rat) and generally occurred at low values of G (less than 0.5) and after rats had experienced multiple gain manipulation sessions over days. The asymmetry in landmark control between G < 1 and G > 1 is similar to a study of medial entorhinal cortex by Campbell and colleagues⁴¹. In this study, mice ran on a VR linear track controlled by a stationary treadmill, and the authors manipulated the gain factor between distance traveled on the treadmill versus the VR track. Grid cells showed asymmetric responses to increases versus decreases of the gain. Gain increases (i.e., G > 1) caused phase shifts in the spatial firing patterns but gain decreases (i.e., G < 1) caused changes in the spatial scales. These results were elegantly explained by a model of how grid cells respond to conflicts between self-motion and landmark cues. Although this paper did not address the issues of path integration gain recalibration as in the current study, its results may provide a causal explanation for the asymmetric responses of place cells to the landmark manipulations seen in the present study.

Extended Data Figure 5:. Slow drift of place fields against landmarks.

a, Example of positive drift. (top) Experimental gain, G (blue), and hippocampal gain, H (yellow), for Epochs 1–3 of a session in which G_final was 1.769. There is no H (yellow) in the first or last 6 laps due to the 12-lap sliding window. (middle) Spikes from one putative pyramidal cell (blue dots) in the lab frame. Figure format is the same as in Figure 2. (bottom) The same spikes in the landmark frame. The unit was silent for the first 12 laps but developed a strong place field in the landmark frame that slowly drifted in the same direction as the animal’s movement over the course of the session. b, Example of negative drift from a session in which the G_final was 0. In the landmark frame, the slow drift was in the direction opposite to the animal’s movement direction. Note that the unit was completely silent in Epoch 3, because the rat was not in the place field of the unit as G reached 0. c, Drift over the entire session vs. G_final. Each point represents an experimental session. Linear fits are shown for each individual rat (colored lines) and for the combined data (black line; n = 55 sessions, Pearson’s r₅₃ = 0.64, p = 1.5 × 10⁻⁷). The two example sessions of (a) and (b) are shown with the circled markers. d, Drift rate vs. G_final. Although the magnitude of drift is correlated with the final experimental gain (G_final), as shown in (c), a confound is present because the ramp duration in Epoch 2 depends on the value of G_final (e.g., for G > 1, the larger G_final is, the more laps required to ramp G up to that value). It is thus possible that the correlation between the total drift and G_final is due to the differences in Epoch 2 duration (and, in some experiments, Epoch 3 duration) rather than due to different rates of drift that depend on G. To control for the effect of trial duration, we calculated drift rate by dividing the total drift by the total number of laps in the landmark frame over which the drift was computed. Linear fits are shown for each individual rat (colored lines) and for the combined data (black line; n = 55 sessions, Pearson’s r₅₃ = 0.54, p = 1.9 × 10⁻⁵). The two example sessions of (a) and (b) are shown with the circled markers. These results show that the drift rate was related to the value of G_final.

Extended Data Figure 6:. Dynamics of recalibration.

a-e. The complete hippocampal gain (H) dynamics for all 5 rats for trials that exhibited landmark control. (The gain dynamics for Rat 692 is also shown in the main text, Fig. 3e.) In the left panels for each rat (color), H is plotted as a function of laps run in the lab frame. Sessions are aligned to the instant when the landmarks were turned off (denoted as lap 0). In the presence of landmarks, (before lap 0), the hippocampal gain tracked the experimental gain profiles during a given session (not shown). After the landmarks turned off, the traces largely maintained their recalibrated gain, while also showing some variable drift across experiments. Note that for each rat, for experiments in which G = 1 (i.e., the landmarks did not move), the value of H was close to 1 when the landmarks were extinguished. The right panels for each rat show the gain trajectories of all the units in the dataset. The gray scale represents the number of active cells with gains falling in a given bin (bin size is 5° for laps axis and 0.01 for gain axis). These graphs demonstrate the high degree of coherence of the hippocampal population, as almost all cells shared the same gain with minimal deviation. The light-colored lines that occasionally deviate from the main trajectories arise from the small number of cells with poor spatial tuning or from cells that remapped. In the latter case, because our spectral gain analysis used a window of 12 laps, these remapped cells continued to show artefactual values for the limited number of laps that fall in this window but during which the cell was silent. As can be seen, these exceptions had negligible influence on the median population gain values. f, Sustained recalibration. Comparison of G_final (x-axis) and H computed using laps 13–24 (i.e., the value of H at lap 18) after the landmarks were turned off (y-axis). Sessions for each rat are plotted in different colors, along with the perfect recalibration line (dashed line, black) and a linear fit (solid line, black; n = 27 sessions, Pearson’s r₂₅ = 0.85, p = 2.04 × 10⁻⁸). The number of data points is lower than in Fig. 3c because some experiments ended prior to lap 24. g. Histogram of coherence scores (same format as Fig. 2g) for units firing during Epoch 4 (landmarks off). The shape of the histogram is very similar to Fig. 2g. Almost all units had a coherence score below 0.1, indicating that the place fields acted as a coherent population in sessions with (blue) and without (pink) landmark control in Epochs 1–3, even after landmarks were turned off. Units with coherence score above 0.1 (range 0.11 – 0.41) were combined in a single bin (17/336 units).

Extended Data Figure 7:. Path integration gain recalibration is also demonstrated by hippocampal interneurons.

a, (top) Experimental gain, G (black) and hippocampal gain, H (yellow) for Epochs 1–4 of a session where the G_final was 1.769. H was computed as usual from putative pyramidal cells (Methods, Estimation of Hippocampal Gain). In Epoch 4, landmarks are off and hence there is no G. (middle) Spatiotemporal rate map of one putative interneuron in the lab frame. Due to the high firing rate of interneurons, rate maps are more illustrative than the spike plots used in place cell examples. Each horizontal bin represents a lap in the lab frame, similar to the alternating gray and white vertical bands in the place cell examples (e.g. Fig. 2 a,c,e). Each vertical bin spans 3° in the lab frame. (bottom) Rate map of the same unit in the landmark frame. Each horizontal bin represents a lap in landmark frame, and each vertical band spans 3° in landmark frame. Note that the firing pattern is preserved across laps until Epoch 4, when the landmarks turn off. b, Example of putative interneuron in a session where G_final was 0.846. Same format as (a). c, Histogram of coherence score between interneurons and putative pyramidal cells, as in Fig. 2g. The score for each putative interneuron is computed as the mean value of | 1 – I / H | over the entire session, where I is the spectral gain estimated from the interneuron, and H is the hippocampal gain computed as usual from putative pyramidal cells. Units with coherence score above 0.1 (range 0.15–0.24) were combined in a single bin. d, H estimated using the first 12 laps after landmarks were turned off, using the median of estimates from putative pyramidal cells compared to the median of estimates from putative interneurons. There are only 5 data points since these are the subset of sessions in Fig. 3c with simultaneously recorded putative interneurons and place cells.

Extended Data Figure 8:. Illustration of spectral decoding scheme.

In the dome, as visual landmarks are presented and moved at an experimental gain G, the rat encounters a particular landmark every 1/G laps (the spatial period). If the place fields fire at the same location in the landmark reference frame, the cell’s firing rate exhibits a spatial frequency of G fields/lap. a, Illustration of place field firing for three values of hippocampal gain, H. b, Data from a session in which G was gradually increased from 1 to 3 (top) as in Epoch 2 of our experiments. The spectrogram of one unit is shown at the bottom, with the color denoting the power at a given position and frequency. A clear set of peaks in the spectrogram emerges at spatial frequencies corresponding to the experimental gain and at its harmonics. We use a custom algorithm to trace these peaks (Methods, Estimation of Hippocampal gain) and estimate the gain for each unit. The hippocampal gain, H, is estimated by taking the median spatial frequency across all isolated units (H_i for the i^th unit) for a given session. Note that this method does not require that cells display single, sharply tuned place fields, as it works for cells with multiple fields as well as for interneurons (Extended Data Fig. 7). c, Reproduction of Fig. 3b, along with addition panel at the bottom that represents the same spikes in the “hippocampal frame;” that is, the spikes were plotted in the frame of the landmarks as if they were rotating at the calculated gain of the place cell map (the hippocampal gain, H). The shaded vertical bars denote each lap in the hippocampal frame. Fields from all three units are horizontally aligned in this panel during all epochs, indicating that the spectral decoding technique was successful and that the place fields acted as a coherent spatial representation within the hippocampal frame. d, Reproduction of Extended Data Fig. 2a, along with additional hippocampal gain panel at bottom. In this dataset, it can be seen that even after ‘failure’ of landmark control of place fields, the fields are still coherently firing at the same hippocampal gain, which we are able to estimate using spectral decoding.

Figure 1|. Dome apparatus, experimental procedure, and sample data.

a, Semi-transparent illustration of the dome apparatus. b, Photo of the apparatus. The dome is raised to allow visualization of the interior, but it is lowered as in (a) for the experiment. c, Illustration of experimental gain G. From the same initial positions of the landmarks and rat, three gain conditions are shown, in both lab (top) and landmark (bottom) frames of reference. In each case, the rat runs 90° in the lab frame. d, Profile of gain change and epochs during a typical session. An annular ring is always projected at the top of the dome (as shown in (a)) for illumination purposes, and is not turned off even in Epoch 4. e, Representative firing rate maps for five different units from five separate gain manipulation sessions, shown in the lab frame (top, middle rows) and landmark frame (bottom row) during Epoch 3 (constant experimental gain). Plots in the top row are color scaled to their own individual maximum firing rates; middle and bottom row plots are color scaled to the maximum firing rate of the bottom plot of each pair.

Figure 2 |. Control of place fields by landmarks.

a, (top) Profile of experimental gain, G, for Epochs 1–3 of a session where G_final was 0. (middle) Colored dots show the location of the rat in the lab frame (y axis) as a function of cumulative distance traveled on the track (x axis) when spikes from 3 units (red, blue, yellow) were recorded. Alternate gray and white bars indicate laps in this frame. (bottom) The same spikes in the landmark frame. Alternate gray and white bars indicate laps in this frame. The yellow unit fired weakly during the first 8 laps, became stronger on laps 9–10, and maintained the strong field in the landmark frame throughout the remainder of the session. During the last landmark-frame lap, the unit fired in a field that spanned ~1080° (3 laps) in the lab frame (middle). b, Rate maps of the red unit in lab and landmark frames for Epoch 2 of the trial shown in (a). The firing rate is low and diffusely distributed (on average) in the lab frame, whereas there is a well-defined place field in the landmark frame. c, Epochs 1–3 of a session where the G_final was 2 (same format as (a)). In Epoch 3, all three units maintain normal spatial firing in the landmark reference frame, but they have 3 fields/lap, separated by 120°, in the lab frame. d, Rate maps of the red unit for Epoch 3 of the trial shown in (c). e, Epochs 1–3 of a session where the G_final was 0.5. Remapping occurred near the transition between Epoch 2 and Epoch 3, as the previously silent red unit became active and maintained a stable place field in the landmark frame. In the lab frame, however, the unit fired every other lap, (i.e., it was active on the gray laps and silent on the intervening white laps). f, Rate maps for the red unit for Epoch 3 of the trial shown in (e). Separate rate maps are shown for the odd- and even-numbered laps in the lab frame. g, Coherence of the population response. The n = 500 units acted as a coherent population in sessions with (blue, 411/500) and without (pink, 89/500) landmark control (see panel h). Units with coherence score above 0.1 (range 0.12 – 0.47) were combined in a single bin (29/500 units). These cells generally displayed poor spatial tuning and therefore did not admit a reliable estimate of hippocampal gain. h, Landmark control ratio. In most sessions (blue, 60/72), the landmark control ratio was ~ 1. Sessions with gain ratio above 1.1 (range 1.16 – 4.02) were combined in a single bin (pink, 12/72). i, Spatial information scores in the lab and landmark frames for each rat (sessions with n = 12, 3, 17, 15, 29 units) are significantly different (two-sided paired t-test, n = 5 rats, t₄ = 6.213, p = 0.0034). Small dots represent scores from individual units. Mean (large dots) ± s.e.m. are shown.

Figure 3 |. Recalibration of place fields by landmarks

a, Example of positive recalibration. (top) Experimental gain, G (blue) and hippocampal gain, H (yellow) for Epochs 1–3 of a session in which the G_final was 1.769. (middle) Spikes from three putative pyramidal cells (blue, red and yellow dots) in the lab frame. (bottom) The same spikes in the landmark frame. When the landmarks were turned off (dashed line, Epoch 4), H remained close to G_final, shown by the slower drift of the place fields in the landmark frame compared to the lab frame. (During Epoch 4, the landmark frame was defined assuming the gain was G_final even though landmarks were off.). Note that the traces of H (yellow) deviate from G (blue) prior to the landmarks turning off; this is an artifact of the sliding window used in the spectrogram and does not affect the conclusions (see Methods, Visualizing H). b, Example of negative recalibration. The G_final was 0.539. c, Recalibration of place fields. The x-axis is G_final and the y-axis is H computed using the first 12 laps (i.e., the value of H at lap 6) after the landmarks were turned off. Linear fits for each animal (color) and for the whole data set (black) are shown (n = 45 sessions, Pearson’s r₄₃ = 0.94, p = 3.4 × 10⁻²¹), along with the perfect recalibration line (dashed line, black). Note that the linear fit passes close to the origin, showing that H≈1 when the landmarks were extinguished after baseline control experiments. d, Stability of recalibration. Comparison of H during laps 1–12 vs. H during laps 13–24. The linear fit is shown in black. (n = 27 sessions, Pearson’s r₂₅ = 0.96, p = 1.16 × 10⁻¹⁵) e, Complete gain dynamics for one animal. For all sessions from one rat, H is plotted as a function of laps run in the lab frame. All the sessions are aligned to the instant when the landmarks were turned off (lap 0). The recalibrated H was maintained for as many as 50 laps or more.