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Vector trace cells in the subiculum of the hippocampal formation

Abstract

Successfully navigating in physical or semantic space requires a neural representation of allocentric (map-based) vectors to boundaries, objects and goals. Cognitive processes such as path-planning and imagination entail the recall of vector representations, but evidence of neuron-level memory for allocentric vectors has been lacking. Here, we describe a novel neuron type, vector trace cell (VTC), whose firing generates a new vector field when a cue is encountered and a ‘trace’ version of that field for hours after cue removal. VTCs are concentrated in subiculum, distal to CA1. Compared to non-trace cells, VTCs fire at further distances from cues and exhibit earlier-going shifts in preferred theta phase in response to newly introduced cues, which demonstrates a theta-linked neural substrate for memory encoding. VTCs suggest a vector-based model of computing spatial relationships between an agent and multiple spatial objects, or between different objects, freed from the constraints of direct perception of those objects.

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Fig. 1: Vector trace responses to a range of cues.
Fig. 2: Vector field properties.
Fig. 3: Rotation of room cues and intra-box cues show that trace fields do not reflect responses to local odor cues.
Fig. 4: Hours-long persistence of trace fields in VTCs after cue removal.
Fig. 5: VTCs were common in the distal subiculum, but rare in the proximal subiculum.
Fig. 6: Earlier-going theta phase shift in encoding is greater in VTCs than in non-trace cells.

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Data availability

Data are available upon reasonable request from the authors.

Code availability

Key custom Matlab code, including that for defining trace and overlap scores and constructing vector-rate maps, will be made publicly available at https://github.com/WillsCacucciLab/VectorTraceCode.

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Acknowledgements

We thank E. Stanton, A. Long and S. Thurlbeck for technical assistance. We thank N. Burgess and D. Bush for helpful comments on an earlier version of this manuscript. We acknowledge funding from the BBSRC (BB/M008975/1 to C.L. and co-investigator T.J.W.; BB/T014768/1 to C.L. & co-investigator S.P.), the Royal Society (UF100746 to T.J.W.), the MRC (MR/N026012/1 to T.J.W.) and start-up funds from CIMEC, Trento, Italy (to S.A.L.).

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Authors

Contributions

S.P. and C.L. conceptualized and designed the study. S.P. performed the experiments. S.P., T.J.W. and C.L. analyzed the data and wrote the manuscript. S.A.L. contributed to conceptualization, experimental design and training. J.D. contributed to training, surgery and histology. C.L., S.P., T.J.W. and S.A.L. contributed to funding acquisition. All the authors discussed the results and contributed to the manuscript.

Corresponding authors

Correspondence to Steven Poulter, Thomas J. Wills or Colin Lever.

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The authors declare no competing interests.

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Peer review information Nature Neuroscience thanks Michael Hasselmo and the other, anonymous, reviewer(s) 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

Extended Data Fig. 1 Co-recorded Vector Trace cells and Non-trace cells.

Firing rate maps of simultaneously-recorded Vector Trace cells (VTC) and Non-trace cells in three rats. Conventions as in Fig. 1. Each row illustrates firing rate maps for one cell (peak-rate bin (Hz) top-left). Left column: Pre-cue trial. Left-middle column: Cue trial, where each cell forms a new firing field when the cue (white space) is introduced. Right-middle column: Post-cue trial. In VTCs (top row for each rat), following cue removal, the cue-responsive firing field persists. In contrast, in Non-trace cells, the cue-responsive firing field has diminished to below-threshold levels in the Post-cue trial. Right column: masks showing cue-responsive field (blue), post-cue field (yellow) and overlap between both (green). Trace (Tr) and overlap (OL) scores shown above each plot. Trace score value of non-trace cell R462_115 is 0.198, that is below Trace cell threshold of 0.20.

Extended Data Fig. 2 VTC and non-trace responses to multiple cue types.

a, Occurrence frequency of trace responses across multiple cues, in non-trace cells. In the sub-set of cells exposed to multiple different cue trials in one experimental session, the cue that evoked the strongest cue field was used to classify the cell as VTC or non-trace (see Methods). Following this, the total number of cues which evoked a significant trace response was determined for each cell. Bar graphs in (a) show the numbers of non-trace cells exposed to two cue types (left) or three cue types (right) which were determined to show 0, 1 or 2 trace responses across the entire experimental session. (Data are split into 2-cue sessions vs 3-cue sessions to facilitate statistical testing). In both the two-cue and three-cue sessions, non-trace cells were significantly biased towards exhibiting fewer trace responses than expected by chance. Red dashed lines show chance levels, calculated under the assumption that, once a cell has been classified as non-trace on one trial, there is an independent 0.29/0.71 chance of observing a trace vs non-trace response for each further cue tested. (Chance levels equivalent to overall occurrence frequency of VTCs vs Non-trace cells amongst subiculum neurons). χ2 tests were used to assess the significance of the difference between the observed frequencies and those expected under chance assumptions: χ2 stats and significance levels are shown on the bar graphs (Y axis shows sample n). Note that chance levels are zero in the categories corresponding to trace responses occurring on all tested cues: non-trace cells must not exhibit a trace response on at least one cue by definition. b, Three example non-trace cells recorded across 3 cue trials (top two rows) or 2 cue trials (bottom row), which never showed a trace response. Rectangular boxes contain each cue trial set (that is Pre-cue, Cue, Post-cue trials) for each cue that a cell was exposed to. Note that the Post-cue trial for one cue forms the Pre-cue trial for following cue, hence rate maps are repeated across cue trial sets. Cue trial sets outlined in bold red were those with the strongest cue field response, which were used for cell type classification, and contributed to the main analysis. Cartoons above each cue trial show the type of cue used. Figure conventions in (b) as per Fig. 1. c, Occurrence frequency of trace responses across multiple cues, in VTCs. Only a small number of VTCs are available to test (N=4) due to proportionally lower sampling of VTCs in multiple-cue sessions, and to the long-lasting nature of the trace response: as the Post-cue trial of one cue formed the Pre-cue trial of the following cue, trace responses to earlier cues prevented detection of cue responses to later cues. Only 4 VTCs were recorded in which cue-evoked responses can be detected across two different cue types. In these cells, more VTCs than expected by chance exhibited a trace response on both cue types. Assumptions for generation of chance levels and methods of statistical testing for (c) were as for (A). d, One example VTC recorded across 2 cue trials, which showed a trace response on both cues. Black grid delineates each cue trial set (that is Pre-cue, Cue, Post-cue trials) for each cue run on each cell. Cue trial sets outlined in bold red were those with the strongest cue field response, which were used for cell type classification, and contributed to the main analysis. Cartoons above cue trial show the type of cue used.

Extended Data Fig. 3 Spatial firing in Pre-cue trial does not explain the position of trace fields in the Post-cue trial.

a, Boxplots showing distributions of firing rate correlations across pre- and post-cue trials, restricted to those spatial bins within either the cue- or post-cue field. Boxes show 25th – 75th percentile, central line shows median. Whisker length is IQR x 1.5, data points beyond whiskers are shown as individual points. All analyses in this Figure based on n = 73 VTCs and n = 164 Non-trace cells, using two-tailed t-tests. Non-trace cells in which a post-cue field could not be defined (no elevated area of firing in post-cue compared to pre-cue trial could be detected) were excluded from this analysis. The mean correlation for both fields and both cell types are significantly greater than zero (T-test, Fisher-transformed r: VTC cue field, t72=9.5, p < 0.00001; VTC post-cue field, t72=9.7, p < 0.00001; Non-trace cue field, t163=11.0, p < 0.00001; Non-trace post-cue field, t163=15.8, p < 0.00001), indicating that some spatial structure of neuronal firing in the pre-cue trial is conserved in the Post-cue trial (despite the emergence of a trace field, in VTCs). However, for VTCs, the correlation observed is not significantly greater than the mean of a population of correlations derived from spatially-randomised Cue- and Post-cue field positions (see Methods; T-test Fisher-transformed r versus mean of shuffled population: VTC cue field, t72=1.14, p = 0.26; VTC Post-cue field, t72=1.65, p = 0.10), demonstrating that the Cue- and Post-cue fields are not areas of enhanced similarity between the Pre- and Post-cue fields, compared to the remainder of the rate map (excluding the Wall field). Gray dashed lines show medians of spatially-randomised r populations. For non-trace cells, correlations were significantly lower than the mean of the spatially randomized population within the cue field (t163 = 3.0, p = 0.003), but significantly higher than the spatially randomized population in the post-cue field (t163=8.33, p < 0.00001). b, Histograms showing the distributions underlying the box plots in (A). Colored bars show distributions of within-field correlations, grey dashed lines show the cell- and field type-matched distributions of spatially randomized field correlations.

Extended Data Fig. 4 Analysis of wall vectors. Angular tunings between wall-field and cue-field vectors were similarly stable across VTCs and non-trace cells; VTCs’ distance tunings showed more variance and were longer than those of non-trace cells; distance tunings were longer for cue fields than wall fields in both cell types, but this was more pronounced in VTCs.

a, Rate maps and vector plots for three representative VTCs, and three representative non-trace cells. Conventions as Fig. 1a,b for first four columns. Conventions as Fig. 2a,b for columns of vector plots: wall field vector in Pre-cue trial (5th column); cue field vector in Cue trial (6th column); and trace field (cue) vector in the Post-cue trial (7th column). Distance tuning scale is 0–60cm in all vector plots. b, Scatterplots of angular tunings showing VTCs (left, n=64) and non-trace cells (right, n=132) showed stable angular tuning for wall-field vector in Pre-cue trial vs Cue-field vector in Cue trial. The overall mean angular difference between the wall-field and the cue field was 8.2 ± 4.4° (mean absolute angular difference: 26.2 ± 3.3°) for VTCs, and 0.9 ± 3.9° (mean absolute angular difference: 32.5 ± 3.0°) for Non-trace cells, with no difference between the cell types (Watson-Williams F1,194 = 1.32, p = 0.25; Welch t194 = 1.416, p = 0.16). For VTCs, the overall mean angular difference between the Pre-cue wall-field and the Post-cue trace field was similarly minimal at 4.1 ± 4.4° (mean absolute angular difference: 28.3 ± 2.9°). Thus, as expected, angular tunings were stable across wall fields and cue fields. The inter-trial absolute difference values involving the wall field show somewhat larger error than those in VTCs between the cue field and its trace field (19.5 ± 2.7°, see Fig. 2e & main text), because square-walled environments are suboptimal for estimating angular orientation of vector fields67. c, Histograms of distance tunings for VTCs (left) and Non-trace cells (right) for wall-field vector in Pre-cue trial. Exactly as for cue field vectors’ distance tunings (main text, Fig. 2c), VTCs’ distance tunings in their wall-field vectors showed a much wider variance than those of non-trace cells (F test variance ratio = 2.46, p < 0.001) and were longer than those of non-trace cells (Inset compares mean ± s.e.m. values: VTCs n=64: 14.1 ± 1.0 cm; Non-trace n=132: 11.2 ± 0.4 cm; Welch t194 = 2.605: p = 0.011). d, Scatterplots of distance tunings for VTCs (left) and Non-trace cells (right) for wall-field vector in Pre-cue trial vs cue-field vector in Cue trial. Distance tunings were longer for cue field than wall field vectors in both cell types (VTCs: paired t63 = 5.04, p < 0.0001; Non-trace: paired t131 = 2.76, p = 0.007), and this lengthening effect was more pronounced in VTCs (Inset compares mean ± s.e.m. values: VTCs n=64: +4.9 ± 1.0cm; Non-trace n=132: +1.2 ± 0.4cm; Welch t194 = 3.435, p = 0.0009). All linear tests in this Figure were 2-tailed.

Extended Data Fig. 5 Preferred theta phase of firing in the distal subiculum occurs around a sixth of a theta cycle earlier than in the proximal subiculum.

a,b, Polar histograms showing distribution of individual cell phases of cue responsive cells in the wall field area in the Baseline (Pre-cue) trial in the proximal subiculum (a) and in the distal subiculum (b). Phase distribution is more concentrated in the distal subiculum, where mean preferred phase occurs a sixth-cycle earlier than in the proximal subiculum (59.4 degrees earlier: Watson-Williams F test for difference between means: F1,225 = 68.50, p < 1x10-12). c,d, Polar histograms showing distribution of individual cell phases for cells of all types (except cue-responsive cells above) in first baseline trial in the proximal subiculum (c) and in the distal subiculum (d). Similarly to cue-responsive cells, phase distribution is again more concentrated in the distal subiculum, and mean preferred phase occurs considerably earlier in the distal than proximal subiculum (53.2 degrees earlier: Watson-Williams F test for difference between means: F1,139 = 40.11, p = 3.1x10-9). Phases are divided into twenty 18-degree bins (0/360=peak;180=trough). Scale near 90-degree line (a), and zero-degree line (b,c,d) indicates number of cells in a given phase bin. Key: µ is mean phase (red line, red font text), r is length of Rayleigh vector (also indicated by length of red mean phase line, from centre to outer circumference), k is Von Mises’ k (indexing phase concentration). Grey curved caps depict +/- 95% confidence limits. All phases are referenced to theta recorded from distal subiculum.

Extended Data Fig. 6 Preferred theta phase of firing shifts markedly earlier during cue-related encoding in both vector trace cells and non-trace cells.

Polar histograms showing distribution of individual cell phases in the cue field area whose mean phases (red lines, red-font text) and 95% confidence limits (grey curved caps at perimeter) are shown in Fig. 6, for each of the two cell types: (a to b) trace cells, (e to f) non-trace cells, from Pre-cue trials (a,e), to Cue trials (c,d), to Post-cue trials (b,f). Preferred theta phase of firing is very stable across Pre-cue and Post-cue trials in both cell types. Notably, against this background of strong phase stability, preferred theta phase of firing is markedly earlier in both cell types during Encoding trials (Cue Trial: c,d) than during Baseline (Pre-cue Trial: a,e) and Retrieval (Post-cue Trial: b,f) trials (all Cue-vs-Pre-cue & Cue-vs-Post-cue F values >19.25, all p values < 1.82 x 10-5). Within-cell earlier shift in Encoding was greater in vector trace cells than non-trace cells (main text; Fig. 6) There were no within-trial, across-cell-type, absolute-phase differences (Watson-Williams F tests: Pre-cue trial: F1,150 = 0.55, p = 0.46; Cue-trial: F1,180 = 2.81, p = 0.10; Post-cue trial: F1,160 = 0.69, p = 0.41). Phases are divided into twenty 18-degree bins (0/360:peak,180:trough). Vertical scale near zero-degree line indicates number of cells in a given phase bin. Key: µ is mean phase (red line, red font text), r is length of Rayleigh vector (also indicated by length of red mean phase line, from centre to outer circumference), k is Von Mises’ k (indexing phase concentration). Grey curved caps depict +/- 95% confidence limits.

Extended Data Fig. 7 Preferred theta phase of firing is highly stable across trials in the wall field in both vector trace cells and non-trace cells.h.

Polar histograms detailing distribution of individual cell phases in the wall field area whose mean phases (red lines, red-font text) and 95% confidence limits (grey curved caps at perimeter) are shown in Fig. 6b, for each of the two cell types: (left column) trace cells, (right column) non-trace cells, from Pre-cue trials (a), to Cue trials (b), to Post-cue trials (c). Across-trial preferred theta phase of firing is very stable (Watson-Williams F tests comparing within-cell-type, across-trial, phase distributions: 2x3=6 tests; all 6 test F values < 0.083, all p values > 0.77). There were no within-trial, across-cell-type differences (Pre-cue; F1,180 = 1.70, p = 0.19; Cue: F1,179 = 2.31, p = 0.13; Post-cue: F1,182 = 2.79, p = 0.10). Phases are divided into twenty 18-degree bins (0/360=peak; 180=trough). Vertical scale near zero-degree line indicates number of cells in a given phase bin. Key: µ is mean phase (red line, red font text), r is length of Rayleigh vector (also indicated by length of red mean phase line, from centre to outer circumference), k is Von Mises’ k (indexing phase concentration). Grey curved caps depict +/- 95% confidence limits.

Extended Data Fig. 8 Earlier-going shift in theta phase preference in the cue field is larger in vector trace cells than non-trace cells.

Polar histograms detailing distribution of phase difference data summarized in Fig. 6b for Baseline-Encoding comparisons (a,b) and Retrieval-Encoding comparisons (c,d) for VTCs (left column) and non-trace cells (right column). Differences are expressed as Precue-minus-Cue trial (Baseline-Encoding) and Postcue-minus-Cue trial (Retrieval-Encoding). The earlier-going phase shift in the cue field was larger in distal VTCs than distal non-trace cells, both for the baseline-vs-encoding comparison (a): Precue-Cue: Watson-Williams F1,146 = 5.72, p = 0.018), and the retrieval-vs-encoding comparison (c): Postcue-Cue: Watson-Williams F1,157 = 4.29, p = 0.04). In contrast, the baseline-vs-encoding (b) and retrieval-vs-encoding differences (D) in the wall field were similarly concentrated near zero for both VTCs and non-trace cells (Precue-Cue (B): Watson-Williams F1,174 = 0.17, p = 0.68; Postcue-Cue (d): Watson-Williams F1,178 = 0.01, p = 0.92). Note appreciably higher concentrations of phase (indexed by Von Mises’ k) around the zero-difference values in wall fields than cue fields in both cell types, indicative of stability of theta phase in the wall field. Phases are divided into twenty 18-degree bins (0/360=peak; 180=trough). Vertical scale near 180-degree line indicates number of cells in a given phase bin. Key: µ is mean phase (red line, red font text), r is length of Rayleigh vector (also indicated by length of red mean phase line, from centre to outer circumference), k is Von Mises’ k (indexing phase concentration). Grey curved caps depict +/- 95% confidence limits.

Extended Data Fig. 9 Examples of simultaneously-recorded vector trace cell pairs, demonstrating phase changes are specific to cue-driven firing, and not linked to one region in the recording arena.

a,b, Simultaneously-recorded pairs of vector trace cells in two rats. Columns left to right: rate maps for each cell across trials (Pre-cue, Cue, Post-cue), field masks (Cue and Post-cue), and preferred (mean) theta phase of firing in Encoding and Retrieval trials (‘Theta phase in cue field region’). These examples show that the same cue (A: 4.5cm high brick array; B: 50cm high wall) elicits, in simultaneously-recorded cells, trace fields occupying different areas of the box, far from each other. VTC firing at earlier theta phase is specifically linked to the cue-driven firing field for each cell, and, across cells, is dissociated from the rat’s position.

Extended Data Fig. 10 Firing rates in VTC and non-trace cells in distal subiculum can be dissociated from phase.

Boxplots showing distributions of mean neuronal firing rates in the cue field (a) and wall field (b), in both VTCs and Non-trace cells in distal subiculum. Boxes show 25th – 75th percentile, central line shows median. Whisker length is IQR x 1.5, data points beyond whiskers are shown as individual points. One possible account of changes in preferred phase (for example following cue insertion), is that these may reflect high-rate and low-rate regimes of firing respectively, under models of theta phase precession in which higher depolarisation drives earlier phase of firing68,69 butsee,70. Here we show that, by contrast, phase and firing rate can be dissociated, in particular in the Post-cue trial. Consistent with our cell-type classifications, VTC firing rates were significantly greater than Non-trace cell firing rates in the cue field area in the Post-cue trial (A: 2-way mixed ANOVA cue field firing rates: Trial*Cell type; F2,284 = 8.1, p < 0.001; Post hoc Simple Main Effects VTC vs Non-trace: Pre, p = 0.63; Cue, p = 0.137; Post, p < 0.001. N Cells = 56 VTCs, 88 Non-trace cells. Cells were filtered as for phase analyses: cells without theta modulation [Rayleigh p>0.01] or <50 spikes in cue field were excluded). By contrast, there was no difference in the preferred phase of VTC and Non-trace cells, in any trial, including the Post-cue trial (see Fig. 6, Extended Data Fig. 6, Watson-Williams F tests: Pre-cue trial: F1,150 = 0.55, p = 0.46; Cue-trial: F1,180 = 2.81, p = 0.10; Post-cue trial: F1,160 = 0.69, p = 0.41). There is therefore no significant difference between VTCs and Non-trace firing rate in the cue trial which could explain the greater earlier-ghoing phase shift. Furthermore, there is a strong dissociation between phase and rate in the Post-cue trial, whereby VTC rates are significantly higher than Non-trace cell rates, but preferred phase is strongly similar for the two classes of neuron. We note that, even in Non-trace cells, firing rates in the cue field increase between the Pre- and Post-cue trials (Simple Main Effects, p = 0.005), possibly due to imperfect classification of VTC versus Non-trace cells, or due to some residual memory-based firing occurring even in non-trace cells. In the wall field (b), VTCs showed significantly greater firing rates overall (2-way mixed ANOVA wall field firing rates: Trial; F2,352 = 6.9, p = 0.001), but no cell-type specific changes in firing across trials (Trial*Cell type; F2,352 = 0.65, p = 0.52. N Cells = 66 VTCs, 112 non-trace cells. Cells were filtered as for phase analyses: cells without theta modulation [Rayleigh p>0.01] or <50 spikes in wall field were excluded). All linear tests in this Figure were 2-tailed.

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Poulter, S., Lee, S.A., Dachtler, J. et al. Vector trace cells in the subiculum of the hippocampal formation. Nat Neurosci 24, 266–275 (2021). https://doi.org/10.1038/s41593-020-00761-w

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