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Linking hippocampal multiplexed tuning, Hebbian plasticity and navigation

Abstract

Three major pillars of hippocampal function are spatial navigation1, Hebbian synaptic plasticity2 and spatial selectivity3. The hippocampus is also implicated in episodic memory4, but the precise link between these four functions is missing. Here we report the multiplexed selectivity of dorsal CA1 neurons while rats performed a virtual navigation task using only distal visual cues5, similar to the standard water maze test of spatial memory1. Neural responses primarily encoded path distance from the start point and the head angle of rats, with a weak allocentric spatial component similar to that in primates but substantially weaker than in rodents in the real world. Often, the same cells multiplexed and encoded path distance, angle and allocentric position in a sequence, thus encoding a journey-specific episode. The strength of neural activity and tuning strongly correlated with performance, with a temporal relationship indicating neural responses influencing behaviour and vice versa. Consistent with computational models of associative and causal Hebbian learning6,7, neural responses showed increasing clustering8 and became better predictors of behaviourally relevant variables, with the average neurometric curves exceeding and converging to psychometric curves. Thus, hippocampal neurons multiplex and exhibit highly plastic, task- and experience-dependent tuning to path-centric and allocentric variables to form episodic sequences supporting navigation.

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Fig. 1: Good performance but impaired spatial selectivity in a VNT.
Fig. 2: Allocentric, path-centric and angular tuning.
Fig. 3: Tuning is correlated with behaviour.
Fig. 4: Increased neural clustering correlated with improved behaviour within a session.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

All analyses were performed using custom-written code in MATLAB version 9.5 (R2018b). Codes necessary to reproduce the figures in this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank C. Vuong, D. Aharon and B. Willers for help with initial development of the experimental paradigm and early data collection; N. Agarwal and F. Quezada for help with training and behaviour; A. Kees and P. Ravassard for surgical assistance; and K. Choudhary for data management support. This work was supported by grants to M.R.M. from the W.M. Keck Foundation, AT&T, NSF 1550678 and NIH 1U01MH115746 to M.R.M. Some results presented in this manuscript were presented in abstract form at the annual Society for Neuroscience conference in 2015 (632.16), 2016 (263.03), 2017 (523.11), 2018 (508.06) and 2019 (083.85).

Author information

Authors and Affiliations

Authors

Contributions

J.D.C., L.A. and M.R.M. designed the experiments. J.J.M. and M.R.M. designed the analyses. J.D.C. and L.A. performed the electrophysiology experiments. B.P. performed the NMDAR block experiments. J.J.M. performed all analyses with input from M.R.M. J.J.M and M.R.M. wrote the manuscript with input from J.D.C. and L.A.

Corresponding authors

Correspondence to Jason J. Moore or Mayank R. Mehta.

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The authors declare no competing interests.

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Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Rats use a place navigation strategy to solve the task.

a, Performance, measured by rewards/meter, consistently improved across subsequent sessions in different session blocks (p = 0.02, two-sided Wilcoxon sign-rank test on difference between % Improvement across consecutive days without a gap, n = 27 differences). Thin gray lines indicate individual session blocks, with the thick black line indicating the mean (n = 12 session blocks). b, Top, left, individual trials (thin colored lines) and mean path from each start position (thick black lines) for a single behavioral session with 4 start positions. Paths are color coded based on start position. Right, all mean paths rotated to begin at the same point and heading, illustrating that rats take unique paths from each start position. Paths are color coded to match the colors in the left panel. Bottom, same as top but for a different behavioral session with 8 start positions. c, The path correlation (see Methods) was significantly smaller (p = 1.9 × 10−7, one-sided Wilcoxon sign-rank test) across start positions (0.58, [0.53, 0.63]) compared to within start positions (0.81, [0.77, 0.84], n = 34 sessions for all statistics). Values are reported as median and 95% confidence interval of the median here and in d. d, As in c, the across start position correlation was smaller than the within start position correlation for each individual rat in the study. Rat 1: Across (0.58, [0.51, 0.68]) vs Within (0.88, [0.80, 0.89]), p = 2.4 × 10−4, n = 12 sessions). Rat 2: Across (0.53, [0.44, 0.63]) vs Within (0.82, [0.74, 0.85]), p = 2.4 × 10−4, n = 12 sessions). Rat 3: Across (0.56, [0.50, 0.69]) vs Within (0.76, [0.73, 0.84]), p = 1.6 × 10−2, n = 6 sessions). Rat 4: Across (0.61, [0.47, 0.66]) vs Within (0.78, [0.73, 0.81]), p = 0.06, n = 4 sessions). One-sided Wilcoxon sign-rank test used throughout.

Extended Data Fig. 2 Further behavioral quantification.

a, The percentage of time rats spent in the goal-containing northeast (NE) quadrant (36, [33, 39]%) was significantly greater than chance (p = 2.8x10−4, two-sided Wilcoxon sign-rank test), and greater than all other quadrants (NW: 20, [19, 22]%; SE: 26, [23, 28]%; SW: 17, [16, 18]%). b, Left: The median performance was 0.43, [0.38, 0.47] reward/meter; Middle: The median trial distance was 230, [210, 260] cm; Right: The median trial time was 10, [9.5, 11] s of movement. c, Quadrant occupancy as in a, split between 4-start sessions and 8-start sessions, exhibiting similar characteristics. d, Behavioral measures from b, split between 4-start sessions and 8-start sessions. No significant differences exist between the conditions in any measure. Rewards/meter: 4-start (0.46, [0.34, 0.49]), 8-start (0.40, [0.35, 0.46]), p = 0.35. Trial Distance: 4-start (220, [205, 267]), 8-start (252, [217, 297]), p = 0.30. Trial Time: 4-start (9.75, [8.47, 12.0]), 8-start (10.5, [9.9, 11.7]), p = 0.27. e, Left, occupancy index (Supplementary Information) as a function of radial distance from the goal location. p = 1.3x10−12, 34 sessions; one-way repeated-measures ANOVA. Right, population average, showing rats spend more time near the goal than expected by chance. Lines and shading indicate the median and 95% confidence interval of the median, color coded as in c. f, Left, speed index (Supplementary Information) as a function of radial distance from the goal location. p = 2.0x10−9, 34 sessions; one-way repeated-measures ANOVA. Right, population average, showing rats run slower near the goal than expected by chance. Color conventions are as in e. n = 34 sessions for all combined statistics; n = 20 sessions for 4-start statistics; n = 14 for 8-start statistics. Values are reported as median and 95% confidence interval of the median.

Extended Data Fig. 3 NMDAR antagonist impairs virtual navigation task performance.

a, Top, black lines, trajectories from 6 rats injected with saline, on the first day in a new environment. The goal heading index (GHI, Supplementary Information) for each rat is indicated above. Bottom, green lines, full trajectories during a probe trial (see Methods) immediately following the session above, demonstrating rats preferentially spent time near the learned reward site (open black circles). The large green dot indicates the starting position for the probe trial. Scale is as in Fig. 1. b, Top, red lines, trajectories from 6 rats injected with the NMDA antagonist (R)-CPPene (see Methods). Bottom, purple lines, trajectories from a probe trial immediately following the sessions in red. c, GHI is strongly positively correlated with rewards/meter (R = 0.89, p = 1.08x10−12, two-sided t test, n = 34 sessions). d, Top, there was no significant difference (p = 1, two-sided Wilcoxon sign-rank test) in rewards/meter between the saline (SAL, black, 0.19, [0.14, 0.24], n = 6 rats) and CPP (red, 0.22, [0.15, 0.25], n = 6 rats) conditions. Bottom, trial length was not significantly different between the two conditions (p = 0.41, two-sided Wilcoxon rank-sum test; SAL: 3.7 [3.3, 4.1] m, n = 282 trials; CPP: 3.8, [3.1, 5.1] m, n = 69 trials). e, Top, rats traveled less distance overall in the CPP sessions (64, [15, 105] m, n = 6 rats) compared to SAL sessions (260, [150, 300] m, n = 6 rats; p = 0.03, two-sided Wilcoxon sign-rank test). Bottom, rats traveled less distance in the CPP probe trials (1.5, [0.12, 3.6] m, n = 6 rats) compared to SAL probe trials (9.6, [4.9, 12] m, n = 6 rats; p = 0.03, two-sided Wilcoxon sign-rank test). f, Top, rats spent more time moving in the SAL sessions compared to CPP sessions (p = 2.9x10−13, 2-way ANOVA with Saline/CPP group as a categorical variable and time (19 bins) as a continuous variable). Bottom, rats spent less time moving in the CPP probe trials compared to the SAL probe trials (p = 1.7x10−3, 2-way ANOVA with Saline/CPP group as a categorical variable and time (12 bins) as a continuous variable). g, GHI was significantly greater than 0 in the SAL full session (0.11, [0.09, 0.28], n = 6 rats, p = 0.02, Right-tailed (one-sided) Wilcoxon sign-rank test throughout this panel) and SAL probe trials (0.08, [0.002, 0.14], n = 6 rats, p = 0.03), as well as the CPP full session (0.10, [0.05, 0.17], n = 6 rats, p = 0.02), indicating movement directed towards the reward zone. Goal heading index in the CPP probe trials was not significantly greater than 0 (−0.19, [−0.33, 0.09], n = 4 rats, p = 0.88), indicating equivalent time spent moving towards or away from the reward zone. 2 sessions were excluded due to insufficient movement.

Extended Data Fig. 4 Additional examples of spatial tuning in 4- and 8-start navigation tasks using the binning method.

a, Example units as in Fig. 1b–c. b, Example units as in a but for sessions with 8 start positions rather than 4.

Extended Data Fig. 5 Differences between binning and GLM-derived maps; quantification of stability of GLM results for space, distance, and angle tuning.

a, 4 example units demonstrating the differences between binned (top) and GLM (bottom) maps. b, Sparsity of spatial, distance, and angular maps using the binning method versus the sparsity using the GLM. For allocentric space and episodic distance, but not allocentric angle, the binning method estimated larger sparsity on average than the GLM (Space: p = 7.3 × 10−29; Distance: p = 7.4 × 10−3; Angle: p = 0.06; n = 384 units, two-sided Wilcoxon sign-rank test for all). c, Top, example rate maps for two units from the first (top row) and second (middle row) halves of a session. Bottom, the stability of tuned spatial rate maps (0.25, [0.14, 0.40], n = 111 units) was significantly higher than both the stability of untuned maps (0.14, [0.08, 0.23], n = 273 units; p = 0.02, two-sided Wilcoxon rank-sum test here and throughout the figure) and the stability expected from random shuffles of first and second half maps (−0.00, [−0.06, 0.08], n = 384 units; p = 3.7 × 10−7). Untuned maps were also more stable than chance (p = 5.2 × 10−4). d, Example path distance rate maps for two units from the first and second halves of a session. Bottom, the stability of tuned path distance maps (0.38, [0.30, 0.44], n = 181 units) was significantly higher than the stability of untuned maps (0.10, [0.03, 0.20], n = 203 units; p = 5.1 × 10−8) and of shuffled controls (−0.02, [−0.10, 0.03], n = 384 units; p = 1.8 × 10−19). Untuned distance maps were also more stable than chance (p = 3.2 × 10−3). e, Example angle rate maps for two units from the first and second halves of a session. Bottom, the stability of tuned path angle maps (0.37, [0.28, 0.43], n = 155 units) was significantly higher than the stability of untuned maps (0.09, [0.05, 0.17], n = 229 units; p = 1.9 × 10−8) and of shuffled controls (0.02, [−0.04, 0.05], n = 384 units; p = 3.4 × 10−17). Untuned distance maps were also more stable than chance (p = 1.7 × 10−3). No adjustments were made for multiple comparisons in c–e.

Extended Data Fig. 6 Distance coding cells show similar selectivity across start positions.

a, Spikes as a function of rat’s position, for two different cells (top and bottom) are color coded based on the start position. b, Spikes as a function of the distance traveled, with trials from different start positions grouped together. The maps look qualitatively similar from all four start positions. The variations in firing rates could occur due to other variables, e.g. direction selectivity. c, Hence, we used the GLM method (see Methods) using data from all the trials. Spikes are shown as a function of the path distance and time elapsed. The GLM estimate of firing rate as a function of distance alone is shown by thick line.

Extended Data Fig. 7 Examples of path distance tuning for longer distances in 4- and 8-start navigation tasks; additional properties of path distance tuning.

a, Example units as in Fig. 2b. b, Example units as in a but for sessions with 8 start positions rather than 4. c, The distance sparsity of units in 4-start sessions (0.13, [0.12, 0.14], n = 183 units) was slightly but significantly greater (p = 0.03, two-sided Wilcoxon rank-sum test) than the distance sparsity in 8-start sessions (0.11, [0.09, 0.13], n = 181 units). d, The effect in c was not present when controlling for the total number of spikes (p = 0.43, two-way ANOVA, see Methods). e, The distribution of occupancy times was skewed toward earlier distances, with a center of mass at 115 cm. f, Left, sample distance tuning curve (black) overlaid with the sum of two fitted Gaussians (green). Right, the individual Gaussians that were fitted. g, The median goodness of fit (correlation coefficient between the original and fitted curve) was quite high (0.97, [0.96, 0.98], n = 181 units), with no unit having a fit less than 0.89. h, Distribution of the number of significant peaks in distance maps. 50% of units had more than one peaks, with a mean of 1.7, [1.5, 1.8] peaks. Error bars represent the 95% confidence interval of the mean obtained from a binomial distribution using the Matlab function binofit(). i, The peak index (peak amplitude of a fitted Gaussian divided by constant offset) of distance curves (2.2, [2.0, 2.4], n = 300 peaks) was significantly higher (p = 2.1× 10−69, two-sided Wilcoxon rank-sum test) than for shuffled data (0.63, [0.57, 0.68], n = 463 peaks). j, The width of fitted Gaussian components (width at half-max; 20, [18, 21] cm, n = 300 peaks) was slightly but significantly smaller (p = 0.03, two-sided Wilcoxon rank-sum test) than for shuffled data (22, [21, 23] cm, n = 463 peaks). Details of the fitting procedure and quantification of field properties are available in the Supplementary Information.

Extended Data Fig. 8 Path distance tuning is not easily explained by selectivity to time or distance to the goal.

a, Path distance (top row) and path time (bottom row) rate maps for three sample cells. sd and st represent the sparsity of rate maps for distance and time, respectively. Column 1 depicts a cell that is well-tuned in both the distance and time domains. Column 2 shows a cell that is better tuned in the distance domain. Column 3 shows a cell that is better tuned in the time domain. b, Rate maps in a are overlaid in the bottom row for ease of comparison. Distance between 0 and 200 cm and time between 0 and 10 s are normalized from 0 to 1 for visualization. c, Left, sparsity of Path Time maps versus sparsity of Path Distance maps. Right, sparsity index (defined as (sd – st)/(sd + st)) was slightly but significantly greater than 0 (0.03, [0.02 0.05], n = 384 cells; p = 1.5x10−6, two-sided Wilcoxon sign-rank test). d, Path distance (top row) and goal distance (bottom row) rate maps for three sample cells. sd and sg represent the sparsity of rate maps for path distance and goal distance, respectively. Column 1 depicts a cell that is well-tuned in both the frames of reference. Column 2 shows a cell that is better tuned in the path distance frame. Column 3 shows a cell that is better tuned in the goal distance domain. e, Rate maps in d are overlaid in the bottom row for ease of comparison. Distance between 0 and 200 cm and time between −200 and 0 cm are normalized from 0 to 1 for visualization. f, Left, sparsity of Goal Distance maps versus sparsity of Path Distance maps. Right, sparsity index (defined as (sd – sg)/(sd + sg)) was significantly greater than 0 (0.27, [0.23 0.31], n = 384 cells; p = 7.8x10−37, two-sided Wilcoxon sign-rank test).

Extended Data Fig. 9 Examples of angular tuning in 4- and 8-start navigation tasks; additional properties of angular tuning.

a, Example units as in Fig. 2c. b, Example units as in a but for sessions with 8 start positions rather than 4. c, The angular sparsity of units in 4-start sessions (0.10, [0.09, 0.12], n = 155 units) was not significantly different (p = 0.77, two-sided Wilcoxon rank-sum test) than the angular sparsity in 8-start sessions (0.11, [0.09, 0.12], n = 155 units). d, There was no significant difference when controlling for the total number of spikes (p = 0.06, two-way ANOVA, see Methods). e, The distribution of occupancy times was skewed toward the north-east direction, with a mean vector pointing towards 56°. f, Left, sample angle tuning curve (black) overlaid with the sum of four fitted Von Mises curves (red). Right, the individual Von Mises curves that were fitted. g, The median goodness of fit (correlation coefficient between the original and fitted curve) was quite high (0.98, [0.97, 0.98], n = 155 units). h, Distribution of the number of significant peaks in angle maps. 83% of units had more than one peak, with a mean of 2.7, [2.5, 2.8] peaks. Error bars represent the 95% confidence interval of the mean obtained from the Matlab function binofit(). i, The peak index (peak amplitude of a fitted Von Mises curve divided by constant offset; 1.8, [1.7, 2.0], n = 411 peaks) was significantly higher (p = 2.1× 10−35, two-sided Wilcoxon rank-sum test) than for shuffled data (0.77 [0.72, 0.84], n = 476 peaks). j, The width of fitted Von Mises curves (width at half-max; 47, [46, 49]°, n = 411 peaks) was not significantly different (p = 0.70, two-sided Wilcoxon rank-sum test) than for shuffled data (45, [44, 48]°, n = 476 peaks). Details of the fitting procedure and quantification of field properties are available in the Supplementary Information.

Extended Data Fig. 10 Episodic relationship between space, distance, and angle selectivity.

a, Sparsity for rate maps in allocentric space (left), path distance (middle), and allocentric angle (right) versus the center distance coordinate (see Methods) for each cell. Significantly tuned cells are marked with large, colored dots and cells that are not significantly tuned are marked with small, black dots. b, The percentage of cells significantly tuned as a function of their center distance coordinate for space (blue), distance (green), and angle (red). The combined plot at the far right is the same as Fig. 2h. c, Cross-correlations between the curves in b, overlaid with shuffled control cross-correlations, demonstrate that the relative ordering of parameter tuning – Distance, then Space, then Angle – is greater than expected by chance. Dotted black lines indicate the median and 95% range of the cross-correlation of the curves in b constructed from shuffled data (see Methods). Cross-correlation peaks above this range (Left, cyan, 11.25 cm indicating Distance leads Space; Middle, magenta, −150 cm indicating Space leads Angle; Right, orange, −161.3 cm indicating Distance leads Angle) indicate statistical significance at the p < 0.05 level.

Extended Data Fig. 11 Additional measures of performance correlate with neural tuning; speed does not correlate with performance.

a, Same values as in Fig. 3c plotted as a function of Trial Latency (see Methods). Correlation values and p-values are shown above each figure. Rw and pw represent the correlation value and p-value for the weighted best fit line. For unweighted fits, p-values are from a two-sided t test for each panel, with n = 34 sessions. For weighted fits, p-values are calculated through a resampling procedure (see Methods). b, Same as a, but plotted as a function of Trial Distance (see Methods). c, Same as a, but plotted as a function of within-start path correlation (Extended Data Fig. 1b-c, see Methods). d, Same as a, but plotted as a function of goal heading index (see Methods). e, Including sessions from all rats, the median speed in a session was not significantly correlated with behavioral performance as measured by rewards/meter, Trial Latency, Trial Distance, Path Correlation, or Goal Heading Index. Correlation values and p-values are shown above each figure. p-values are from a two-sided t test for each panel, with n = 34 sessions.

Extended Data Fig. 12 Experience-dependent changes in behavior, neural activation, and shifts in single unit path distance tuning.

a, Trial latency (time spent running) decreased as a function of trial number (Effect of trial number on Trial Latency: p = 5.0 × 10−5, 34 sessions; one-way repeated-measures ANOVA). The thick line is the median, and the thin lines are the 95% confidence interval of the median. b, Mean speed did not significantly change as a function of trial number (Effect of trial number on Mean Speed: p = 0.44, 34 sessions; one-way repeated-measures ANOVA). The thick line is the median, and the thin lines are the 95% confidence interval of the median. c, The fraction of total cells active (rate in a 3-trial boxcar average > 0.2 Hz) increased with experience (correlation coefficient R = 0.94, p = 2.7 × 10−25, n = 52 trials, two-sided t test). d, Averaged across the ensemble, the firing rates were higher in later trials than early trials (Figure 4b). This was quantified on a cell-by-cell basis by computing the rate modulation index for each cell (see Methods), which was centered at 0.11, [0.08, 0.15], and significantly greater than 0 (p = 1.8x10−13, two-sided Wilcoxon sign-rank test, n = 384 units). e, Eight example cells with distance tuning curves exhibiting shifting with experience. Curves are estimated from the GLM using data only from trials 1–26 (light green) or 27–52 (dark green). The cells in the top three rows demonstrate backwards, or anticipatory, shifting. The cells in the bottom row demonstrate forwards shifting. f, Cross-correlation plots, sorted by the experiential shift (distance lag of the peak in the cross-correlation) of peak correlation, for all cells significantly tuned for distance but not angle, (n = 88; 91 cells met this criteria, but 3 were excluded for having insufficient spiking in one of the two halves). g, The median experiential shift (−7.5, [−15, 0] cm) was significantly different from 0 (p = 0.014, two-sided Wilcoxon sign-rank test).

Extended Data Fig. 13 Within-session clustering and forward movement of spatial, distance, and angle maps and their relationship with psychometric curves.

a, Left, distributions of peaks of allocentric spatial rate maps (top, blue) and spatial occupancy (bottom, gray) in early trials, showing dispersed, fairly uniform distributions. Right, distributions of spatial peaks (top) and spatial occupancy (bottom) in later trials, showing clear clustering near the goal location. b, The allocentric goal distance (see Methods) significantly decreased with increasing trial number (Neurons: R = −0.63, p = 1.5 × 10−3, two-sided t test, n = 22 trial blocks (every other trial from trial 5 to 47) here and for all other tests in this panel; Behavior: R = −0.64, p = 1.2 × 10−3, two-sided t test, n = 22 trial blocks), and the sparsity of these distributions increased with trial number (Neurons: R = 0.67, p = 5.7 × 10−4, two-sided t test, n = 22 trial blocks; Behavior: R = 0.63, p = 1.8 × 10−3, two-sided t test, n = 22 trial blocks). c, The center of the distribution of path-distance tuning curve peaks and behavior both moved closer to the trial beginning with increasing trial number (Neurons: R = −0.91, p = 2.8 × 10−9, two-sided t test; Behavior: R = −0.69, p = 3.9 × 10−4), and the sparsity of these distributions increased with trial number (Neurons: R = 0.89, p = 2.6 × 10−8; Behavior: R = 0.89, p = 4.4 × 10−8). d, The angle goal distance (see Methods) for angular tuning curve peaks and behavior decreased with increasing trial number (Neurons: R = −0.86, p = 3.4 × 10−7, two-sided t test, n = 22 trial blocks (every other trial from trial 5 to 47) here and for all other tests in this panel; Behavior: R = −0.55, p = 7.6 × 10−3); the sparsity of these distributions increased with trial number (Neurons: R = 0.67, p = 7.1 × 10−4; Behavior: R = 0.65, p = 1.0 × 10−3).

Extended Data Fig. 14 Temporal relationship between neural firing properties and behavior, split into high- and low-performing sessions.

a, Top, performance increased with trial number. This was true when including all cells (colored dots, same data as Fig. 4a, right), cells from sessions with high performance (top 50% of sessions, gray dots, “High”), or cells from sessions with low performance (bottom 50% of sessions, black dots, “Low’). Solid lines are exponential fits to the data. Middle, the firing rate of active cells increased with trial number. Bottom, cross-correlation of the population firing rate with performance, for all sessions, high-performance sessions, and low-performance sessions. For all data and high-performance sessions, the lag of the peak correlation is near 0, indicating a co-evolution of performance with firing rate. In low-performance sessions, there is a distinct asymmetry, indicating that neural changes precede behavioral changes. Dotted lines indicate the 99% range of shuffled cross-correlations. The marked point is the approximate center of this asymmetry, at −5 trials, and is above the chance line, indicating statistical significance at the p < 0.01 level. b, Top, as in Extended Data Fig. 13c, the center of the distribution of path-distance occupancy shifted towards the trial beginning with experience within a session. The effect is more pronounced for sessions with high performance. Middle, same as above but for the distribution of path-distance tuning curve peaks. Bottom, cross-correlation of neural and behavioral experience plots. c, Same as b but for angle goal distance. d, Same as b-c but for allocentric goal distance.

Extended Data Fig. 15 Population vector decoding of path distance and allocentric angle.

a, Decoded distance versus true distance for trials 1–15 (left) and trials 16–30 (right). b, Path-distance population vector overlap (Supplementary Information) between entire session activity and activity in trials 1–15 (left) or between trials 1–15 and trials 16–30 (right). Lines and dots mark the smoothed peak correlation on the right-hand plot. Black lines indicate predictive shifts and gray lines indicate postdictive shifts, with a mean value of 15 cm. c, Decoded angle versus true angle for trials 1–15 (left) and trials 16–30 (right). d, Same as b but for angle. The best decoded angles span 0–90°. Right, experiential shift in angle representation was modest and varied as a function of angle (mean −3.2°), which could be due to different turning behavior at specific angles or different turning biases across sessions.

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Moore, J.J., Cushman, J.D., Acharya, L. et al. Linking hippocampal multiplexed tuning, Hebbian plasticity and navigation. Nature 599, 442–448 (2021). https://doi.org/10.1038/s41586-021-03989-z

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