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A prefrontal–thalamo–hippocampal circuit for goal-directed spatial navigation



Spatial navigation requires information about the relationship between current and future positions. The activity of hippocampal neurons appears to reflect such a relationship, representing not only instantaneous position but also the path towards a goal location. However, how the hippocampus obtains information about goal direction is poorly understood. Here we report a prefrontal–thalamic neural circuit that is required for hippocampal representation of routes or trajectories through the environment. Trajectory-dependent firing was observed in medial prefrontal cortex, the nucleus reuniens of the thalamus, and the CA1 region of the hippocampus in rats. Lesioning or optogenetic silencing of the nucleus reuniens substantially reduced trajectory-dependent CA1 firing. Trajectory-dependent activity was almost absent in CA3, which does not receive nucleus reuniens input. The data suggest that projections from medial prefrontal cortex, via the nucleus reuniens, are crucial for representation of the future path during goal-directed behaviour and point to the thalamus as a key node in networks for long-range communication between cortical regions involved in navigation.

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Figure 1: Trajectory-dependent firing in CA1 but not CA3.
Figure 2: Trajectory-dependent firing in NR.
Figure 3: Trajectory-dependent firing in mPFC.
Figure 4: Loss of trajectory-dependent firing in CA1 after NR inactivation.
Figure 5: Prospective coding.


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We thank A. M. Amundsgård, K. Haugen, K. Jenssen, E. Kråkvik and H. Waade for technical assistance, M. Andresen, E. Hårstad and G. Jakobsen for taking care of animals, J. Ye and J. Wu for help with immunostaining of brain sections, K. Deisseroth for providing eNpHR3.0 plasmids, and A. Treves and A. Tsao and other members of the Moser laboratory for discussion. This work was supported by two Advanced Investigator grants from the European Research Council (‘CIRCUIT’, Grant Agreement no. 232608; ‘ENSEMBLE’, Grant Agreement no. 268598), the Kavli Foundation, the Centre of Excellence scheme of the Research Council of Norway (Centre for the Biology of Memory and Centre for Neural Computation).

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Authors and Affiliations



H.T.I., E.I.M. and M.-B.M. designed the experiment. S.-J.Z. made all viral constructs. M.P.W. advised on location of electrodes and lesions, H.T.I. performed all experiments and analyses. H.T.I., E.I.M. and M.-B.M. wrote the manuscript after discussion among all authors. M.-B.M. and E.I.M. supervised and coordinated the project.

Corresponding authors

Correspondence to Hiroshi T. Ito or May-Britt Moser.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Nissl-stained coronal sections showing tetrode positions in each animal with recordings in CA1, CA3 or NR.

Positions of tetrode tracks are indicated by red circles. Rat number, recording region and type of electrode assembly are indicated above each section.

Extended Data Figure 2 The influence of rate variability on sorting of high-rate and low-rate trajectories, trajectory coding in CA1 and CA3, and spatial properties of neurons in mPFC, NR and CA1.

a, Demonstration of the influence of rate variability on sorting of high-rate and low-rate trajectories in Figs 1d, f, 2d, 3d and 4d. For each cell, the rate variability (s.d.) within the trajectory in which the cell exhibited a higher peak firing rate was estimated. Gaussian noise with the estimated s.d. was then added to the original rate data. The figure shows two sets of data with the addition of independent Gaussian random noise, sorted into high-rate and low-rate trajectories as in Fig. 1d. The colour-code difference between high-rate and low-rate trajectories reflects the rate variability within the same trajectory. These plots are substantially different from the original plots for CA1 (Fig. 1d), NR (Fig. 2d) and mPFC (Fig. 3d) but are similar to the plots for CA3 (Fig. 1f) and CA1 with NR lesions (Fig. 4d), indicating that colour-code differences on the latter plots can be largely accounted by the rate variability within the same trajectory. b, Box plot showing CA1–CA3 difference in change of peak rate (left) but not field position (right) in the continuous alternation task. *P < 0.05. c, Distribution of spatial information across cells in CA1, NR, and mPFC (frequency histogram and box plot; *P < 0.05). Spatial information per spike was significantly higher in CA1 neurons than in NR or mPFC neurons (CA1, 1.46 ± 0.09; NR, 0.048 ± 0.009; mPFC, 0.134 ± 0.012 bits per spike (mean ± s.e.m.); CA1 versus NR, P < 0.001, D = 0.98; CA1 versus mPFC, P < 0.001, D = 0.93, Kolmogorov–Smirnov test). Spatial information per spike was also higher in mPFC than in NR (D = 0.36, P < 0.001, Kolmogorov–Smirnov test) but this difference was not significant when measured in bits per second (D = 0.07, P = 0.19), indicating that the difference per spike is largely due to higher firing rates in NR (NR, 7.83 ± 1.27 Hz, mPFC, 4.86 ± 0.39 Hz (mean ± s.e.m.)). The total number of neurons analysed was 71 in CA1, 61 in NR, and 164 in mPFC.

Extended Data Figure 3 Tetrode positions and localization of trajectory-dependent cells in mPFC.

a, Positions of tetrode tracks are indicated with red circles. Rat numbers are indicated. b, Spike waveform widths (peak-to-trough time) and mean spike rates on the stem (both trajectories combined) were plotted for each cell in mPFC. Trajectory-dependent cells are indicated in red and trajectory-independent cells in blue. No significant difference was observed in spike widths of the two cell types (D = 0.071, P = 0.802, Kolmogorov–Smirnov test) but the mean spike rates of trajectory-dependent cells were weakly—but significantly—higher than those of trajectory-independent cells (trajectory-dependent cells, 8.10 Hz; trajectory-independent cells, 5.87 Hz; D = 0.172 P = 0.016, Kolmogorov–Smirnov test). c, Percentage of trajectory-dependent cells in superficial versus deep layers of mPFC and in prelimbic versus dorsal anterior cingulate areas. The percentage of trajectory-dependent neurons was slightly larger in the dorsal anterior cingulate area than in the prelimbic area (45.3% versus 33.2%, z = 2.26, P = 0.024, binomial test). There was no significant difference between superficial and deep layers (32.0% versus 41.0%, z = 1.54, P = 0.125).

Extended Data Figure 4 Nissl-stained coronal sections showing tetrode positions in CA1 of animals and the extent of their NR lesions.

Positions of tetrode tracks in CA1 are indicated by red circles. Right sections show outlines of the lesioned areas (orange) and NR (black dashed line) at different anterior–posterior levels. Note that all lesions are bilateral. Percentage of NR lesions (lesioned NR area/total NR area): #15465, 73%; #16214, 68%; #16249, 85%; #16337, 70%. Percentage of lesioned areas specific to NR (lesioned NR area/total lesioned area): #15465, 71%; #16214, 80%; #16249, 73%; #16337, 80%.

Extended Data Figure 5 Effect of removal of NR input on behaviour, spike rates and local field potentials in CA1.

a, Left, behavioural performance (percentage of correct trials) on the continuous alternation task in control animals and animals with NR lesions. No significant difference was observed (χ21 = 1.76, P = 0.184; Kruskal–Wallis test). Right, number of days required for animals to reach behavioural criterion (correct trials >90%; t14 = 0.236, P = 0.817). b, No significant difference was observed between control and NR-lesioned animals in mean running speed on the stem (t19 = 0.403, P = 0.692). c, The mean spectral power of the local field potentials recorded in the CA1 pyramidal layer was not different between control and lesioned animals. The plots show mean values (solid lines) with 95% confidence intervals (shaded areas). d, Left, change in field position across alternating trajectories for CA1 place cells recorded in control animals and animals with NR lesions. Right, box plots showing difference in change of peak rate between CA1 in control animals and CA1 in animals with NR lesions (top; D = 0.346 P < 0.001, Kolmogorov–Smirnov test). There was no corresponding change in field position (bottom; D = 0.083, P = 0.982 Kolmogorov–Smirnov test). *P < 0.05. e, Behavioural performance did not change during laser stimulation in NR in eNpHR-expressing animals (χ22 = 2.77, P = 0.250; Friedman test). f, Running speed on the stem did not change significantly during laser application (F2,28 = 0.89, P = 0.423, repeated-measures ANOVA). g, Mean firing rates of place cells on the stem (both trajectories combined) did not change significantly during laser application but were significantly reduced after termination of the stimulation (F2,28 = 6.52, P = 0.002, repeated-measures ANOVA; before versus during: t49 = 1.651, P = 0.105, during versus after: t49 = 2.137, P = 0.038, post hoc paired t-test). The lack of a consistent reduction in CA1 mean firing rate during light application probably reflects the fact that excitatory inputs from NR to CA1 terminate not only on pyramidal cells but also on local inhibitory neurons44. h, Spectral power of local field potentials in the CA1 pyramidal layer was not significantly changed by laser application in NR (before/during laser application, mean ± s.e.m. μV2 Hz−1 in a decibel scale): delta (1–4 Hz): 37.3 ± 0.92/37.6 ± 0.99; theta (6–11 Hz): 41.8 ± 1.08/41.4 ± 1.18: slow gamma (25–50 Hz) 31.6 ± 0.41/31.7 ± 0.42; fast gamma (60–90 Hz): 26.1 ± 0.53/26.2 ± 0.53). The plot shows mean values (solid lines) and 95% confidence intervals (shaded areas). i, Left, field position shift between alternating trajectories (frequency histograms and box plots). Right, box plots showing difference in change of peak rate (top; F2,98 = 12.02, P < 0.001, repeated-measures ANOVA), but not field position (bottom; F2,98 = 0.02, P = 0.983). Before laser stimulation, the rate change between left and right laps among place cells that expressed significant trajectory-dependent firing was 52.0 ± 5.1% (mean ± s.e.m.). During stimulation, the rate change dropped to 38.6 ± 4.4% (t33 = 4.04 P < 0.001; paired t-test, two-tailed). The effect recovered to baseline levels after the laser application was terminated (55.0 ± 3.9%; t33 = 4.81, P < 0.001; paired t-test).

Extended Data Figure 6 Nissl-stained coronal sections showing positions of tetrodes and optic fibres in optogenetic experiments.

The figure is organized into six blocks, one for each of six animals. Five-digit animal numbers are indicated above each block. Top two rows of each block, positions of tetrode tracks (red circles) in CA1 of each animal. Bottom left, position of optic fibre above NR (red rectangular outline). NR is indicated by a black dashed triangle. The tip of the fibre was placed near the midline to silence cells at both sides of the midline. The bottom right panels of each block show spike rates for two representative units on the tetrodes attached to the optic fibre (>750 μm from the tip of the fibre). The two panels show mean values (solid line) and 95% confidence intervals (shaded areas) of spike rate, with spike rasters at the top. The 532 nm laser was applied for 5 s (0–5 s on the x axis). A significant reduction of spike rate was observed during laser application for all units in this figure (P < 0.05, t-test). Unlike the ibotenic-acid lesion, which destroyed 68–85% of the NR, the laser light probably reached only a small portion of the nucleus. The total volume of NR is roughly 2 mm3 (1 mm of width, 1 mm of height, and 2 mm of length). Supposing that the tip of the optic fibre was located 250 μm above NR, that the laser light suppressed activity up to 1 mm below the fibre tip (optic fibre 0.39 NA, core size Ø 400 μm), and that all cells within this region were inactivated, the estimated proportion of NR affected by the laser light would be 36% at the most. The tetrodes attached to the optic fibre were positioned approximately 750 μm below the fibre tip, near the distance limit of laser light for activation of halorhodopsin. At this depth, the intensity of the laser was probably not sufficient to activate halorhodopsin maximally. The sub-maximal activation probably accounts for the relatively slow time course of NR silencing (sometimes > 1 s). Another contributing factor may be that thalamic neurons express T-type calcium channels, which are de-inactivated by hyperpolarization, making the neurons more excitable27. This excitation may retard the suppression of NR activity.

Extended Data Figure 7 Trajectory coding in CA1, CA3 and CA1 of NR-lesioned animals, and influence of behavioural variables on the decoding analysis.

a, Decoding of succeeding trajectory using peak firing rates of CA1 or CA3 place cells with firing fields on the stem as inputs to a linear classifier. Only trials with correct choices are included. Decoding performance was estimated from randomly selected cell groups in the entire data set across animals and plotted as a function of number of neurons in the sample. The plot shows mean (solid lines) ± s.e.m. (shaded areas). Significant differences between CA1 versus CA3 or CA1 versus CA1 with NR lesions are indicated by dashed lines at the top (P < 0.05). To estimate the decoding performance for a specific number of cells, the desired number of cells was randomly selected from the entire data set across all animals. As the total trial number of runs on left- or right-run trajectories was often different across the recording sessions from which the cell group was taken, we randomly subsampled the trials to equalize the total trial number across sessions. This subsampling procedure was performed ten times, decoding performance was acquired for each, and the average was taken as an estimate of the decoding performance of the cell group. Then, a different cell group with the same number of cells was randomly selected and the same procedure was performed. The procedure was repeated 1,000 times to acquire a statistical distribution of decoding performance for the given number of cells (bootstrap resampling method). P values were estimated from the bootstrap distributions. The peak firing rates of approximately 15 CA1 place cells on the stem provided sufficient information to indicate a correct succeeding trajectory with over 90% accuracy (96.6 ± 4.3% with a total of 30 cells, mean ± s.e.m.). The decoding accuracy was significantly lower when CA3 cells or CA1 cells from NR-lesioned animals were used as inputs to the classifier (decoding performance with 30 cells: CA3, 69.9 ± 7.0%; NR-lesioned, 76.9 ± 7.6%). These results suggest that, for correct choices, the subsequent trajectory can be read out reliably from the collective firing of place cell ensembles in CA1 of animals with intact NR–CA1 connections. b, Left, decoding of correct subsequent trajectory using firing rates of CA1 place cells from NR-lesioned animals as inputs to the classifier. Trials with correct choices and error trials are shown separately (number of trials analysed for animals with NR lesions: correct, 467; error, 23; cell number per session, 7.5 ± 0.9 (mean ± s.e.m.)). Symbols as in Fig. 5a. We also estimated the decoding performance using peak firing rates on the stem (without binning). In the CA1 of lesioned animals, the decoding performance was not significantly different between correct trials and error trials (67.2 ± 2.2% versus 69.6 ± 9.8%; mean ± s.e.m.). In CA1 of control animals, performance was 80.5 ± 1.2% on correct trials and 56.0 ± 10.1% on error trials (interaction term in a logistic regression analysis with task performance (correct versus incorrect) and manipulation (control versus NR lesion) as coefficients, Z = 2.08, P = 0.038; post hoc binomial test for correct versus incorrect trials: NR lesion, Z = 0.232, P = 0.816; control, Z = 3.03, P = 0.002). Right, retrospective and prospective components estimated from spike rates of CA1 cells in animals with NR lesions. Symbols as in Fig. 5c. NR lesions specifically disrupted the prospective component of the trajectory representation (50.6 ± 4.9% successful decoding of succeeding path on the last half of the stem, compared to 59.5 ± 4.7% in intact animals; chance level 50%), supporting the idea that the mPFC–NR–CA1 circuit is necessary for the hippocampus to access to the information about intended actions. The retrospective component was still decodable (60.1 ± 4.9% successful decoding of retrospective paths on the last half of the stem, compared to 63.5 ± 4.8% in intact animals), suggesting that CA1 cells with residual trajectory dependence after NR lesions exclusively represent the animal’s trajectory on the preceding trial. c, d, Differences in decoding performance are not caused by differences in running speed, head direction or lateral position. c, Differences in running speed, head direction, and lateral position between left- and right-turn trajectories were assessed across all recording sessions used for the decoding analysis. No significant differences in any of these behavioural variables were observed (P > 0.05, t-test with Bonferroni correction for multiple comparisons of six bins). The plot shows mean ± s.e.m. Standard errors were estimated for each recording session. d, While we did not observe any significant difference in any of the above behavioural variables, we still observed small systematic trends, as shown in c. To exclude the possibility that these small trends have an influence on the decoding performance45 we generated, for each variable, a subsampled data set by excluding iteratively the trial with the largest deviation until we obtained nearly the same mean value for the respective behavioural variable on left- and right-turn trajectories. The decoding performance was calculated from this subsampled data set and the result was compared to the one from the original data set. No significant difference in decoding performance was observed between the groups, suggesting that the small and non-significant differences of behavioural variables do not account for the differences in firing on left and right trials and the decoding that results from these differences.

Extended Data Figure 8 Firing rates in NR and mPFC fail to distinguish between discrete environments.

We have shown that CA1 cells encode intended trajectories by differences in firing rate rather than firing position. A similar rate-based coding scheme has been observed in place cells of freely foraging animals trained to distinguish between open-field environments differing in colour or shape but not location (with similar rate differences following changes in colour or shape)22,24. Based on this similarity, we asked whether activity in mPFC and NR accounts for rate differences also between discontinuous environments. We recorded simultaneously 51 place cells from CA1 and 49 cells from NR during free running in a pair of differently coloured square boxes located at the same place in the room (three rats). A total of 176 cells were recorded from mPFC in a different set of animals (two rats). a, Colour-coded rate maps for a representative sample of simultaneously recorded cells in CA1 and NR on consecutive trials of free foraging in the square enclosure. Cartoons on top indicate the sequence of trials with different box colours (black–white–white–black). Boxes were always in the same location. Note strong rate remapping (change in firing rate but not firing location) in CA1 but no rate code in NR. b, Colour-coded rate maps for cells in mPFC. Symbols as in a. Note lack of change in firing rate. c, Top, change in peak firing rate between trials with similar (blue) or different (red) colour configuration. Bottom, spatial correlation between trials. The rate change between the two environments was significant in CA1 (same versus different colour, peak rate change t100 = 6.40, P < 0.001) but not in NR (t96 = 0.875, P = 0.38) or mPFC (t350 = 0.924, P = 0.36). Taken together, these results suggest that changes in the distribution of firing rate in CA1 can have multiple sources. While mPFC–NR inputs may be necessary for trajectory selection, the change in rate distribution between discrete environments may depend on other hippocampal inputs, such as those from the lateral entorhinal cortex46. In the foraging task, the firing rates of the mPFC and NR neurons are modulated by subsequent direction of movement, mirroring their trajectory-dependent firing in the alternation task (Extended Data Fig. 9), but because trajectory directions are variable in this task, trajectory-dependent activity is likely to be cancelled out in time-averaged rate maps. The colour-reversal task should be sufficiently sensitive to detect influences of discrete stimuli, considering that mPFC cells do respond to such changes under other conditions47.

Extended Data Figure 9 Activity of neurons in mPFC and NR correlates significantly with movement direction in the continuous alternation task and the open field environment.

a, Spike-rate maps based on the animal’s self-movement were generated by previously published procedures48. In brief, position and head direction data were smoothed with a 25-sample quadratic local regression (loess) fit. Changes in the animal’s position and heading were calculated between the start and end of a sliding 100 ms time window to generate movement vectors. Movement vectors in each map were binned at 4 cm s−1 × 4 cm s−1. The self-motion rate map was generated by dividing the sum of spike-triggered movement vectors by the total number of movement vectors at each bin, which was smoothed by a 2D Gaussian filter with a bandwidth at 1.5 bin. To understand the temporal relationship between spike timing and the animal’s prospective or retrospective motion, spike-triggered movement vectors were generated from movement vectors that were systematically time-shifted relative to spike time, from one second before to one second after the spike event. Top, colour-coded rate maps for a representative mPFC cell which was tuned to left forward movement in the open field environment. Bottom, colour-coded rate maps for a representative NR cell that was tuned to right forward movement. b, Self-movement information in spikes was estimated using the following equation:

where λi is the mean firing rate in the i-th bin, λ is the overall mean firing rate and pi is the probability of the animal being in the i-th bin (occupancy in the i-th bin/total recording time). Shaded areas indicate the range of the values (mean ± s.e.m.) obtained from a shuffled data set generated by shifting spike timings either +2 s or −2 s across the session, which will disrupt spike-triggered movement information but maintain spike number and spike patterns. The time periods when spikes provide significant information about self-centred movement direction compared to the results from the shuffled data set are indicated by dashed lines at the top (P < 0.05, t-test). c, Self-movement rate-map stability within a recording session. The behavioural session (10 min) was divided into first and last halves and Spearman’s correlation between self-movement maps generated from each half was calculated. Significant map stability was observed around the spike time both in mPFC and NR (compared to the shuffled data set, P < 0.05, t-test), indicating that spikes provide reliable information about self-movement. d, Two representative examples of mPFC cells recorded both in the alternation task and in the open field. While these cells expressed a similar trend of preferred self-movement direction across the tasks, they exhibited stronger self-movement tuning in the alternation task than in the open field exploration.

Extended Data Figure 10 Conjunctive coding of position and trajectory increases representational dimensionality in CA1.

Trajectory-dependent coding is not necessary for performance in the continuous version of the alternation task because animals with complete hippocampal lesions are unimpaired in this task21, as were the animals with lesions of the NR input to the hippocampus in the present study. The continuous alternation task may thus be too simple for decision behaviour to be affected by lesions of the NR–CA1 system. To examine how trajectory-dependent firing might contribute to navigation behaviour, we estimated the representational advantage of encoding space with trajectory-dependent place cells instead of separate cell populations for trajectory and location. It has been suggested that nonlinear integration of multimodal information in individual neurons enhances the capacity of downstream neurons to classify combinations of features of high-dimensional information35. Similarly, we hypothesized here that a key advantage of trajectory-dependent place cells in CA1 is the enhancement of the classification capacity for position–trajectory combinations in efferent neurons, an advantage that may not be evident in an alternation task with only a single choice point. a, Example of a task that requires discrimination of multiple position–trajectory combinations. For successful performance, animals choose a right-turn path at the first choice point in A and then a left-turn path at the next choice point in B. b, To perform the task in a, the brain might use cells that represent correct combinations of movement direction and position on the trajectory. An example cell might be active when the animal plans a right path at position A as well as a left path at position B, but not otherwise. c, Suppose that cells with activity on the stem can be categorized into three classes: trajectory-dependent non-place cells, trajectory-independent place cells, and trajectory-dependent place cells. The neural activity in b cannot be generated from any linear combination of the two former classes (trajectory-dependent non-place cells and trajectory-independent place cells), as shown in the following argument. Suppose that the activity patterns of trajectory-dependent non-place cells, either right turn or left turn, can be expressed by the following activity matrices, with each row representing future trajectory, right or left, and each column showing position, that is, A or B:

Similarly, activity of trajectory-independent place cells, with firing fields on either position A or B, can be expressed as follows:The activity matrix of a downstream neuron driven by a linear combination of the above four types of neurons can be expressed as follows:For the downstream neuron to express the desired activity in b, the following conditions are required:where θ is the threshold of activity. However, summation of (1) and (4) gives , whereas summation of (2) and (3) gives , resulting in a contradiction. Thus, neurons with pure selectivity alone cannot generate the desired activity. To achieve the activity in b, neurons with nonlinear mixed selectivity, namely trajectory-dependent place cells, are required (also see ref. 35). d, To estimate the number of implementable patterns in the recorded CA1 neurons, firing rates of neurons at each of 12 behavioural states (six stem positions with two future trajectory directions) were analysed. In addition to the recorded activity, we extended the data using a resampling procedure35. Resampling was performed by cyclic permutation of firing rates across stem positions. Supposing that the original activity of the recorded neurons is represented by sequential numbers of six stem positions as (1 2 3 4 5 6), five sets of new activity were generated by exchanging activity across stem positions, resulting in (2 3 4 5 6 1), (3 4 5 6 1 2), (4 5 6 1 2 3), (5 6 1 2 3 4) and (6 1 2 3 4 5). Resampling not only increased the number of neurons for analysis, but also minimized spatial bias of ensemble representations across stem positions. Following resampling, decoding performance was calculated for all binary combinations of 12 states (212 = 4,096 patterns), using a linear classifier with firing rates in each behavioural state as inputs, as in Fig. 5. e, The number of implementable patterns was determined for neurons in CA1, CA3, and CA1 from animals with NR lesions, and from CA1 of NR-lesioned animals combined with NR cells from intact animals. For the latter group, the total number of cells was doubled after combining the same number of cells from two populations, as indicated on the x axis with a different colour. A binary pattern was considered as implementable if the decoding performance was better than 99%. For each sample size, cells were randomly selected five times to estimate the standard deviation of the decoding performance. Plots indicate mean ± s.d. Regardless of the size of the cell sample, the analysis showed a significantly larger number of implementable patterns for CA1 than for the other groups, including the combination of trajectory-dependent cells in NR and non-trajectory-dependent place cells in CA1, suggesting that integration of NR inputs in CA1 place cells is a key step to achieve high-dimensional representations. The results point to trajectory-dependent place cells and the mPFC–NR–CA1 circuit as possible elements of the neural circuit for discrimination of complex position–trajectory combinations, such as the one illustrated in a. Combinatorial coding provides a computational basis for efferent neurons to perform addition or subtraction among vectors in different coordinate systems49,50,51, such as the allocentric reference frame imposed by spatial cells in the entorhinal cortex52 and the egocentric trajectory frame dependent on projections from mPFC through NR. Such vector operations may be essential for the network to estimate a future allocentric position, which is one of the key steps of route planning during goal-directed navigation.

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Ito, H., Zhang, SJ., Witter, M. et al. A prefrontal–thalamo–hippocampal circuit for goal-directed spatial navigation. Nature 522, 50–55 (2015).

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