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Recalibration of path integration in hippocampal place cells

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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 landmarks2,3 and measuring the distance and direction that the animal has travelled from previously occupied locations4,5,6,7. 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 accumulates8,9. Models of hippocampal place cells and entorhinal grid cells based on path integration treat the path-integration gain as a constant9,10,11,12,13,14, 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 system4,8,16,17,18,19, but also rapidly fine-tune the integration computation itself.

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We thank B. Nash and B. Quinlan for assistance with constructing the apparatus; M. Ferreyros, M. Breault, N. Lukish, J. Johnson, B. Vagvolgyi and D. GoodSmith for technical assistance in running experiments; and G. Rao, V. Puliyadi, C. Wang, H. Lee, R. Nickl, A. Haith and J. Bohren for discussions and technical advice. This research was supported by National Institutes of Health grants R01 MH079511 (H.T.B., J.J.K.), R21 NS095075 (N.J.C., J.J.K.), and R01 NS102537 (N.J.C., J.J.K., F.S.), a Johns Hopkins University (JHU) Discovery Award (N.J.C., J.J.K.), a JHU Science of Learning Institute Award (J.J.K., N.J.C.), a JHU Kavli NDI Postdoctoral Distinguished Fellowship (M.S.M.) and a JHU Mechanical Engineering Departmental Fellowship (R.P.J.).

Author information

Author notes

  1. These authors contributed equally: Ravikrishnan P. Jayakumar, Manu S. Madhav

  2. These authors jointly supervised this work: Noah J. Cowan, James J. Knierim


  1. Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA

    • Ravikrishnan P. Jayakumar
    •  & Noah J. Cowan
  2. Zanvyl Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore, MD, USA

    • Manu S. Madhav
    • , Francesco Savelli
    •  & James J. Knierim
  3. Department of Psychology, UCLA, Los Angeles, CA, USA

    • Hugh T. Blair
  4. Laboratory for Computational Sensing and Robotics, Johns Hopkins University, Baltimore, MD, USA

    • Noah J. Cowan
  5. Solomon H. Snyder Department of Neuroscience, Johns Hopkins University, Baltimore, MD, USA

    • James J. Knierim


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J.J.K., N.J.C. and H.T.B. conceived and all authors designed the study. J.J.K. and N.J.C. advised on all aspects of the experiments and analysis. F.S. made key contributions to the analysis and interpretation of the data and provided supervision over data acquisition and analysis. R.P.J. and M.S.M. designed and constructed the apparatus, performed experiments and analysed the data. R.P.J., M.S.M., N.J.C. and J.J.K. wrote the paper, and F.S. and H.T.B. provided critical feedback.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Manu S. Madhav.

Extended data figures and tables

  1. Extended Data Fig. 1 Representative histology.

    Coronal slices from the five rats used in this study. Arrows point to tetrode tracks at 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 rat (576), the histology was inconclusive owing to poor fixation and slice quality; however, we determined that the tetrodes were correctly placed in CA1 by the mediolateral placement of the bundle, tracks in the few sections that we could analyse, and features in the EEG signals observed during recording (for example, sharp waves and ripples). In one rat (638), two of the most medial tetrodes (not shown) appeared to record from the fasciola cinereum, rather than CA1.

  2. Extended Data Fig. 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 in which Gfinal was 0.231. Note that the two curves overlap until about lap 40, when they start to diverge. Middle, spikes from three putative pyramidal cells (coloured dots) in the laboratory frame. Alternate grey and white bars indicate laps in the laboratory 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 laboratory and landmark frames. Alternate grey and white bars indicate laps in the landmark frame. b, Second example, from a different rat, for a session in which Gfinal was 0.1 (same format as a). ce, Trajectory of hippocampal gain, H, for three rats for all sessions in which landmark control failed. The hippocampal gain generally starts near to one, and then diverges from the experimental gain trajectory (not shown) during the session.

  3. Extended Data Fig. 3 Gain dynamics during each session.

    Each plot represents data from a single session during epochs 1–3 (landmarks on). The x axis is the laps that the rat ran in the laboratory frame (on the table) and the y axis is gain. The black scale bar in each plot indicates 10 laps. The applied experimental gain G (blue) is plotted with the hippocampal gain estimate H (orange). The ramp rate, length of epochs and final experimental gain for each session can be observed from the curves. Asterisks indicate sessions with loss of landmark control (mean 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. The number of units that passed the acceptance criteria (Methods) in each session is indicated in the bottom right-hand corner of each plot.

  4. Extended Data Fig. 4 Summary of dataset.

    Each row indicates 1 of the 72 sessions comprising the dataset during the period in which the landmarks were on. In the left plot, the x axis is laps in the laboratory frame. In the right plot, the x axis is the experimental gain, G. The sessions are chronologically ordered (bottom to top). Sessions from different rats are separated by dashed lines. In all rats, we typically performed smaller manipulations in G first, as initial landmark failure tended to occur at larger manipulations of G. Once landmark control failed, it tended to fail more frequently. The colour represents the ratio between hippocampal and experimental gains (H/G, colour bar, right). Green (H/G = 1) indicates landmark control. Four of the rats (576, 637, 638 and 692) experienced landmark failure (red portions of sessions). Failures happened only when G was less than one (that is, 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 several gain-manipulation sessions over days. The asymmetry in landmark control between G < 1 and G > 1 is similar to a study of medial entorhinal cortex40. In that study, mice ran on a virtual-reality linear track controlled by a stationary treadmill, and the gain factor was manipulated between the distance travelled on the treadmill versus the virtual-reality track. Grid cells showed asymmetric responses to increases compared with decreases of the gain. Gain increases (G > 1) caused phase shifts in the spatial firing patterns, but gain decreases (G < 1) caused changes in the spatial scales. These results were explained by a model of how grid cells respond to conflicts between self-motion and landmark cues. Although the study did not address the issues of path-integration gain recalibration, as in our current work, its results may provide a causal explanation for the asymmetric responses of place cells to the landmark manipulations seen in the present study.

  5. Extended Data Fig. 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 Gfinal was 1.769. There is no H (yellow) in the first or last 6 laps owing to the 12-lap sliding window. Middle, spikes from one putative pyramidal cell (blue dots) in the laboratory frame. Figure format is the same as in Fig. 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, which slowly drifted in the same direction as the movement of the rat over the course of the session. b, Example of negative drift from a session in which Gfinal was 0. In the landmark frame, the slow drift was in the direction opposite to the direction of movement of the rat. 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 plotted against Gfinal. Each point represents an experimental session. Linear fits are shown for each individual rat (coloured 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 marked with a circle. d, Drift rate against Gfinal. Although the magnitude of drift is correlated with the final experimental gain (Gfinal), as shown in c, a confound is present because the ramp duration in epoch 2 depends on the value of Gfinal (for example, for G > 1, the larger the value of Gfinal, the more laps are required to ramp G up to that value). It is thus possible that the correlation between the total drift and Gfinal is due to the differences in duration of epoch 2 (and, in some sessions, epoch 3) rather than due to different rates of drift that depend on G. To control for the effect of session 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 (coloured 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 marked with circles. These results show that the drift rate was related to the value of Gfinal.

  6. Extended Data Fig. 6 Dynamics of recalibration.

    ae, The complete hippocampal gain (H) dynamics for all five rats for sessions 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 (colour), H is plotted as a function of laps run in the laboratory 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 were turned off, the traces largely maintained their recalibrated gain, while also showing some variable drift across sessions. Note that for each rat, for sessions in which G = 1 (that is, the landmarks did not move), the value of H was close to 1 when the landmarks were turned off. The right panels for each rat show the gain trajectories of all the units in the dataset. The grey 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-coloured 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 Gfinal (x axis) and H computed using laps 13–24 (that is, the value of H at lap 18) after the landmarks were turned off (y axis). Sessions for each rat are plotted in different colours, 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 sessions ended before 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 that of Fig. 2g. Almost all units had a coherence score of less than 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 the landmarks were turned off. Units with a coherence score of greater than 0.1 (range 0.11–0.41) were combined in a single bin (17/336 units).

  7. Extended Data Fig. 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 in which Gfinal was 1.769. H was computed as usual from putative pyramidal cells (see ‘Estimation of hippocampal gain’ in Methods). In epoch 4, landmarks are turned off, hence there is no G. Middle, spatiotemporal rate map of one putative interneuron in the laboratory frame. Owing 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 laboratory frame, similar to the alternating grey and white vertical bands in the place cell examples (for example, Fig. 2a, c, e). Each vertical bin spans 3° in the laboratory frame. Bottom, rate map of the same unit in the landmark frame. Each horizontal bin represents a lap in the landmark frame, and each vertical band spans 3° in the landmark frame. Note that the firing pattern is preserved across laps until epoch 4, when the landmarks turn off. b, Example of a putative interneuron in a session in which Gfinal 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, in which 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 the 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 five data points because these are the subset of sessions in Fig. 3c with simultaneously recorded putative interneurons and place cells.

  8. Extended Data Fig. 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 firing rate of the cell exhibits a spatial frequency of G fields per 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 sessions. The spectrogram of one unit is shown at the bottom, with the colour 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 (see ‘Estimation of hippocampal gain’ in Methods) and estimate the gain for each unit. The hippocampal gain, H, is estimated by taking the median spatial frequency across all isolated units (Hi for the ith 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 an additional 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 an additional panel at the bottom that represents hippocampal gain. 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.

  9. Extended Data Table 1 Results of behavioural analyses

Supplementary information

  1. Reporting Summary

  2. Video 1: Extreme control of place fields by landmarks.

    (left) Reproduction of Fig. 2a, augmented with moving time marker (vertical dashed line). (right) Overhead videos (8x speed) of the rat running in the dome apparatus as viewed with respect to two distinct frames of reference, synchronized to the time marker in the left plot. Videos show the last ~ 6.5 laps (~ 8 min in real time) of Epoch 2 (G ramps to 0). The circular object in the center is the hemispherical mirror (not visible to the rat) used to project images to the inside surface of the dome. Reflections of the three landmarks as well as the annular ring can be seen in the mirror (a small lens artifact also appears on the mirror but was not visible to the animal). Spikes from the same three putative pyramidal cells (red, blue, yellow) are shown at the angular position of the rat. For clarity, spikes only persist for about one lap in their respective frame. (right, top) Original video recorded with respect to the laboratory frame. The yellow place cell is active for ~ 4 laps (over 4 minutes). (right, bottom) Modified video, counter-rotated by the landmark manipulation angle. This results in the reflection of landmarks on the mirror appearing stationary (with a small jitter due to video timestamp resolution). The yellow place cell forms a single field subtending ~180° to 0°.

  3. Video 2: Recalibration of place fields by landmarks.

    The same format as Supplementary Video 1. (left) Reproduction of Fig. 3a. (right) Videos show approximately the last 4 laps of Epoch 3 (landmarks on) and the first 8 laps of Epoch 4 (landmarks off). (right, top) The place cells do not fire in consistent locations in the laboratory frame. (right, bottom) In the landmark frame, place cells fire in consistent locations during Epoch 3 and then drift slowly in the absence of landmarks during Epoch 4, because the hippocampal gain, H, is close to (but not identical to) the final experimental gain, Gfinal. (During Epoch 4, landmarks are off but the video is counter-rotated as if the gain were Gfinal.).

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