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Moving bar of light evokes vectorial spatial selectivity in the immobile rat hippocampus


Visual cortical neurons encode the position and motion direction of specific stimuli retrospectively, without any locomotion or task demand1. The hippocampus, which is a part of the visual system, is hypothesized to require self-motion or a cognitive task to generate allocentric spatial selectivity that is scalar, abstract2,3 and prospective4,5,6,7. Here we measured rodent hippocampal selectivity to a moving bar of light in a body-fixed rat to bridge these seeming disparities. About 70% of dorsal CA1 neurons showed stable activity modulation as a function of the angular position of the bar, independent of behaviour and rewards. One-third of tuned cells also encoded the direction of revolution. In other experiments, neurons encoded the distance of the bar, with preference for approaching motion. Collectively, these demonstrate visually evoked vectorial selectivity (VEVS). Unlike place cells, VEVS was retrospective. Changes in the visual stimulus or its predictability did not cause remapping but only caused gradual changes. Most VEVS-tuned neurons behaved like place cells during spatial exploration and the two selectivities were correlated. Thus, VEVS could form the basic building block of hippocampal activity. When combined with self-motion, reward or multisensory stimuli8, it can generate the complexity of prospective representations including allocentric space9, time10,11 and episodes12.

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Fig. 1: Hippocampal response to a revolving bar of light.
Fig. 2: Directionality, stability and ensemble decoding of aVEVS.
Fig. 3: aVEVS is retrospective and changes gradually with stimulus pattern, colour, motion predictability and time.
Fig. 4: aVEVS cells are place cells and stimulus distance-encoding cells.

Data availability

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

Code availability

All analyses were performed using custom-written code in MATLAB version R2016a. Codes necessary to reproduce the figures in this study are available from the corresponding authors upon reasonable request.


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We thank K. Delao, C. Polizu and S. Samant for help with data collection; V. Yuan, S. Ryklansky, A. Chorbajian and W. Zhu for help with single-unit clustering; and D. Dixit. This work was supported by grants to M.R.M. from the W.M. Keck Foundation, AT&T, NSF 1550678 and NIH 1U01MH115746.

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Authors and Affiliations



M.R.M. and C.S.P. designed the experiments. S.D., C.S.P., R.R., C.V., T.T., A.H. and K.C. performed the experiments. C.S.P. developed the stimuli and performed the analyses with input from M.R.M. M.R.M. and C.S.P. wrote the manuscript with critical input from S.D. and other authors.

Corresponding author

Correspondence to Mayank R. Mehta.

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Extended data figures and tables

Extended Data Fig. 1 Relationship between different properties of aVEVS.

a, (top) aVEVS quantified by z-scored sparsity is significantly correlated (r = 0.82, p < 10−150) with, but significantly greater than the z-scored direction selectivity index (DSI) (41% z > 2 for sparsity vs 31% for DSI, KS-test p = 9.3 x 10−10). (Bottom) Cumulative histogram (cdf) of z-scored metric of sparsity and DSI. b, Similar as a, (1- (circular variance)) is significantly correlated (r = 0.84, p < 10−150) but significantly weaker (33% z > 2 for (1- circular variance)) than sparsity. (KS-test p = 7 x 10−6). c, Similar to a coherence is significantly correlated (r = 0.89 p < 10−150) but significantly weaker (26% z > 2 for coherence KS-test p = 6.3 x 10−16) than sparsity. d, Similar to a, but mutual information is significantly correlated (r = 0.47 p = 8.6 x 10−132) but significantly smaller than sparsity (37% z > 2 for mutual information, KS-test p = 7.2 x 10−5).

Extended Data Fig. 2 Unimodality of aVEVS.

Majority of (a) uni-directional as well as (b) bi-directional tuning curves were unimodal with only one significant peak (top row), whereas (c) untuned responses did not have significant peaks, as expected. Both tuned responses were used for the bi-directional cells, and only the tuned response was used for the uni-directional cells. Significant troughs, i.e. off-responses were not found for unidirectional or bidirectional cells (bottom row). Significance of a peak (or trough) was determined with the spike train shuffling analysis, similar to that performed to compute the z-scored sparsity. A peak (trough) was determined to be significant if it was larger (smaller) than the median value of peaks (troughs) in all shuffles and had a height of at least 20% of the range of firing rate variation in the shuffle data. These criteria resulted in zero significant peaks for some tuned responses.

Extended Data Fig. 3 Trial-to-trial variability of mean vector angle but not mean firing rate determines aVEVS tuning.

For each cell, in each trial, we computed the mean firing rate (MFR), mean vector length (MVL) and mean vector angle (MVA) of aVEVS (see Methods). To enable comparison across metrics, this analysis was restricted to responsive trials (firing rate above 0.5 Hz) where MVL and MVA could be meaningfully computed. Qualitatively similar results were obtained when this restriction was removed. a, Trial to trial fluctuations of firing rate was qualitatively similar between tuned (maroon) and untuned (gray) cells (KS-test p = 0.25). b, The variability was not significantly correlated with the degree of aVEVS tuning (Pearson partial correlation, after factoring out mean firing rate, p = 0.85). c, d, The variance of MVL (see Methods) was significantly greater for untuned cells (KS-test p = 0.01) than tuned cells (c) and was inversely related to aVEVS tuning strength (r = −0.19, p = 7.3 x 10−10) (d). e, The circular standard deviation of MVA, which signifies the instability of aVEVS tuning from trial to trial, was significantly (p = 1.3 x 10−72) smaller (11%) for tuned than untuned cells and (f) strongly anti-correlated with aVEVS (r = −0.77 p = 7.4 x 10−192). g, This standard deviation of MVA was inversely correlated with MVL for tuned (r =  −0.15 p = 0.004), and for untuned cells (r =  −0.12 p = 0.003). h, It was also positively correlated with the preferred angle of tuning (r = 0.18 p = 3.5 x 10−4), with lower variability for cells tuned to the front angles (0o) than behind (±180o). Standard deviation of MVA was uncorrelated with preferred angle of tuning for untuned cells (r = 0.02, p = 0.67). All correlations were computed as Pearson correlation coefficients.

Extended Data Fig. 4 Continuity of stability and sparsity measures and example cells.

a, across all neurons, the z-scored sparsity, i.e., degree of tuning, and stability varied continuously, with no clear boundary between tuned and untuned neurons. b, Same distribution as a, with color-coding of stable and tuned responses separated. c, Detailed breakdown of aVEVS properties that had significant sparsity (i.e., tuned) or significant stability and whether these were observed in both directions (e.g., bidirectional stable) or only one direction (e.g. unidirectional tuned). If unidirectional, whether CW or CCW direction was significant. Nearly all cells that were significantly tuned in a given direction were also stable in that direction. d, For clarity, the CCW (blue) and CW (red) trials are stacked separately in all raster plot figures, even though these alternated every four trials. First five examples are of bi-directionally tuned cells (green y-axis); next four examples are of uni-directionally tuned cells (orange-yellow y-axis). e, These cells did not have significant sparsity (z < 2) in either direction but had significant stability.

Extended Data Fig. 5 Firing rate differences between CW and CCW revolution direction.

a, Percentage of tuned responses as a function of the absolute preferred angle, for bidirectional and unidirectional populations are significantly different from each other (KS-test p = 0.04). b, Firing rate modulation index for uni-directional cells inside preferred zone was significantly different from zero (t-test, p = 4.1 x 10−35), but not outside (p = 0.35). c, Correlation coefficient of CCW and CW responses for different populations of cells, (KS-test green, bidirectional, p = 3.3 x 10−27, orange, unidirectional p = 7.0 x 10−27, lavender, untuned stable, p = 4.4 x 10−4). Dashed curves indicate respective shuffles. d, Firing rate of unidirectional cells in tuned versus untuned directions shows significantly higher (KS-test p =  7.9 x 10−9) firing rates in the tuned direction. e, Same as d, for bidirectional cells showing higher firing rate (KS-test, p = 2.4 x 10−18) in the revolution direction with better tuning. f, Cumulative histogram of ratio between firing rate in untuned to tuned direction was less than one for 67% of cells. g, Same as f, but for bidirectional cells (other/better since both directions are tuned) showing 65% of firing rate ratios were less than one. h, To remove the contribution of firing rate to sparsity, the strength of tuning (z-score sparsity) difference was computed with spike thinning procedures (similar to Extended Data Fig. 6; see Methods) ensuring equal firing rate in both directions. The difference in tuning strength (z-scored sparsity) was not significantly correlated with firing rate ratio for unidirectional (r = −0.09 p = 0.16) as well as (i) bidirectional (r = 0.005 p = 0.95) populations. For bi-directionally tuned cells, aVEVS with higher z-scored sparsity was labeled as the “better” response, and the aVEVS with lower z-scored sparsity was called “other” response. All correlations were computed as Pearson correlation coefficients.

Extended Data Fig. 6 The relative number of bidirectional cells increases with mean firing rate, but not the fraction of tuned cells.

To remove the effect of firing rate on z-scored sparsity computation, we randomly subsampled spike trains to have a firing rate of 0.5 Hz (see Methods). a, The fraction of cells with significant sparsity, i.e., fraction tuned, increased with the firing rate for the actual data (r = 0.11 p = 2.2 x 10−6), but after spike thinning, there was no correlation (r = 0.01, p = 0.77). Thus, the true probability of being tuned was independent of the firing rate of neurons. b, Proportion of bidirectional and uni-directional tuned neurons is comparable (10% vs 13%) with and without spike thinning. c, Fraction of bi-directional cells compared to uni-directional cells increases with original firing rate, even after spike train thinning. d, Spike thinning procedure reduces the sparsity of the tuning curves, as expected, due to loss of signal. After spike thinning, sparsity was significantly correlated in both directions of revolution (r = 0.39, p = 3.8 x 10−31) and this was not due to the rate changes because sparsity was uncorrelated with firing rates (r = 0.01, p = 0.72 for CCW sparsity and firing rate, r = 0.02, p = 0.54 for CW sparsity and firing rate). All correlations were computed as Pearson correlation coefficients.

Extended Data Fig. 7 Population vector stability and decoding of visual cue angle.

a, Stability for CCW tuned responses (number of cells, n = 310). Color indicates correlation coefficient between two non-overlapping groups of trials’ population responses (see Methods). The maximum correlation values were pre-dominantly along the diagonal. Maxima along x-axis and y-axis were significantly correlated (Circular correlation coefficient r = 0.97, p < 10−150). b, Same as a but using untuned stable cells (n = 266) showed significant ensemble stability (r = 0.91, p < 10−150). c, Same as a but using untuned and unstable cells (n = 306). This was not significantly different than chance (r =  −0.16, p = 0.09). d, Same as a, using tuned cells with their spike trains circularly shifted in blocks of four trials, showed no significant stability (r = 1.1 x 10−3, p = 0.99). eh, Same as ad, but for CW data. i, Decoding CW direction shows similar results as in CCW direction (shown earlier in Fig. 2). Similar analysis as shown in Fig. 2 for the stimulus movement in CW direction. (Left) Decoding cue angle in 10 trials of CW cue movement, using all other CW trials to build a population-encoding matrix. Gray trace indices movement of visual bar, colored trace is the decoded angle. (Right) Same as left, for shuffle data. j, Same as i but using the untuned-stable cells in CW movement direction. k, Median error between stimulus angle and decoded angle over 10 instantiations of decoding 10 trials each for actual and cell ID shuffle data. Green dashed line indicates width of the visual cue; black dashed line indicates median error expected by chance.

Extended Data Fig. 8 Retrospective coding of aVEVS cells versus prospective coding in place cells.

a, (Top) A bidirectional cell responds with a latency after the stimulus goes past the angular position of the bar of light depicted by the green stripped bar. (Bottom) Population overlap is above the 45o line, indicating retrospective response. b, Same as a but for a prospective response, where the neuron responds before the stimulus arrives in the receptive field. Such prospective responses are seen in place fields during navigation in the real world, where the population overlap is maximal below the 45o line (adapted from earlier work8). Prospective coding was seen in purely visual virtual reality, but those cells encoded prospective distance, not position.

Extended Data Fig. 9 Significant retrospective aVEVS in the unidirectional and untuned stable cells but not unstable cells.

a, Stack plots of normalized population responses of cells, sorted according to the peak angle in the CCW (left). The corresponding responses of cells in the CW direction (right). b, The firing rate, averaged across the entire ensemble of bidirectional cells at −30o in the CCW direction was misaligned with the same in CW direction at the same angle (top), but better aligned with the response at −10o (bottom, vertical boxed in a), showing retrospective response. c, Same as a for uni-directional cells with CCW tuned cells (top row) and CW tuned cells (bottom row) sorted according to their aVEVS peak in the tuned direction. d, Same as in Fig. 3e for unidirectional cells. Majority (67%) of the cross correlations between CW and CCW responses had a significantly positive lag (median latency = 19.9o ± 86.1o, circular median t-test at 0o, p = 1.8 x 10−10). The larger range of latencies and weaker correlations for unidirectional cells compared to the bidirectional cells could arise because significant tuning is present in only one direction. e, Same as Fig. 3f for unidirectional cells. For all angles the population vector cross correlation coefficients had a peak at a positive lag (CW peak–CCW peak, median =  +56.2o ± 23.7o circular median t-test, p = 1.5 x 10−36), which was not significantly different from the retrospective lag in bidirectional cells (KS-test, p = 0.28). f, Average strength of tuning in CCW and CW direction is inversely related to the peak angular lag between the two aVEVS for bidirectional (Pearson’s r = −0.19 p = 0.04) as well as unidirectional cells (Pearson’s r = −0.16 p = 0.02). g, Absolute difference between strengths of tuning between CCW and CW directions was not significantly correlated with the peak angular lag in their cross correlation for bidirectional (r = 0.13 p = 0.14) or unidirectional cells (r = 0.03 p = 0.64). This analysis was restricted to cells with retrospective lags, which were in majority. h, Untuned stable cells too show significant retrospective bias, quantified using the cross correlation between the tuning curves in CCW and CW directions (median lag  = 13.6o circular median t-test at 0o,p = 0.02). i, This is not seen for the untuned unstable population (median  = 4.6o, circular median t-test at 0o,p = 0.39). j, Cross-correlations between CCW and CW tuning curves were averaged across all the bidirectional cells (green curves) for the systematic (latency for peak = 25.7o) and random (16.7o) condition and showed a similar pattern of retrospective coding. (two sample KS-Test to ascertain if the distribution of latencies was significantly different, p = 0.75). Unidirectional cells showed similar pattern for systematic (19.7o) and random (31.8o) conditions, but correlations were weaker than bidirectional cells. k, Cumulative distributions show that under systematic and random conditions comparable number of cells had positive latency (80% each) for bidirectional cells, and (67% and 68%) unidirectional cells respectively.

Extended Data Fig. 10 Photodiode experiment to measure the latency introduced by the equipment.

Instead of a rat, we placed a photodiode where the rat sat. a, b, The signal from the photodiode (purple trace) synchronized with bar position (black) was extracted (a) and cross correlation computed between the CW and CCW tuning curves of photodiode response (b). The cross correlation had maxima at a latency of −2.8o, which corresponds to a temporal lag of 38.9 ms. This was much smaller than the latency between neural spike trains (median latency 22.7o, corresponding to a temporal latency of 315.3 ms before accounting for the recording apparatus latency). For all the latency numbers reported in the main text, this small latency introduced by the recording apparatus was removed.

Extended Data Fig. 11 Additional properties of aVEVS invariance.

a, (Row 1) For same cells recorded in response to the movement of a green striped and green checkered bars of light, mean firing rates during stationary epochs (running speed< 5cm/sec), were significantly correlated (Pearson’s r = 0.48 p =  2 x 10−5). Preferred angles of aVEVS between the two stimulus patterns were also significantly correlated (circular correlation coefficient, r = 0.32 p = 5 x 10−3). Solid red dots denote preferred angles of cells tuned (sparsity (z) > 2) in both conditions; gray dots are for cells with significant tuning in one of the conditions. (Row 2) Same as a (Row 1), but for responses to changes of stimulus color, green and blue. Firing rate (r = 0.45 p = 1 x 10−4) & preferred angle (r = 0.36 p = 0.01) were correlated. (Row 3) Same as a (Row 1), but for changes to predictability of the stimulus, also called “random” vs “systematic”. Firing rate (r = 0.55 p = 2 x 10−13) & preferred angle (r = 0.27 p = 0.01) were significantly correlated between systematic and random stimuli movement. (Row 4) Same as a (Row 1), but for responses recorded across 2 days. Firing rate (r = 0.28 p = 3.2 x 10−5) & preferred angle (r = 0.22 p = 0.006) were correlated. b, Similar to Fig. 3, we computed the population remapping indices based on sparsity difference, preferred angle difference and peak value of cross correlation. The sparsity difference did not show a systematic pattern, but the other two metrics generally showed increasing remapping going from pattern (correlation = 0.68, angle difference = 30o) to color (correlation = 0.64, angle difference = 46.5o) to predictability (correlation = 0.55, angle difference = 66o) and across days (correlation = 0.63, angle difference = 66o). n indicates the number of responses measured in both conditions for each comparison, similar to Fig. 3h. Thick line – median, box – sem. c, Percentage of tuned responses in the random stimulus experiments, showing, comparable bi-directionality (10% here vs 13% for systematically moving bar). d, For same cells recorded in random and systematic stimulus experiments, the distributions of firing rates and selectivity, quantified by z-scored sparsity, were not significantly different (cyan-systematic, purple-random, KS-test for z-scored sparsity p = 0.14, for firing rate p = 0.27). e, Cross correlation between CCW and CW tuning curves showing lagged response for the majority of bidirectional cells in the random condition. f, Same as e, but for unidirectional cells. g, Cross correlation of tuning curves (for tuned cells in the random stimulus experiment) between fast- and slow-moving stimulus was calculated from the subsample of data for a particular speed in CW and CCW direction separately and stacked together after flipping the CCW data and was not significantly biased from zero (Circular median test at 0o, p = 0.56). h, Example cell showing similar aVEVS for data within 1 s of stimulus direction change (top), or an equivalent, late subsample (bottom). i, Firing rate (KS-test p = 0.73) and sparsity (KS-test p = 0.87) were not significantly different for these two subsamples of experimental recordings. j, In the randomly moving stimulus experiments, we computed a stimulus speed modulation index (see Methods). This distribution was not significantly biased away from zero. k, This modulation index was z-scored (see Methods), and only 5.2% of cells had significant firing rate modulation beyond z of ±2.

Extended Data Fig. 12 Relationship between place cells, stimulus angle (aVEVS) and distance (dVEVS) tuned cells.

a, The mean firing rates of cells was significantly correlated (Pearson’s r  = 0.43 p = 4.5 x 10−10) between the aVEVS and place cell (spatial exploration) experiments. b, Majority of cells active during the aVEVS experiments were also active during random foraging in real world. c, Almost all of the aVEVS cells were also spatially selective during spatial exploration. d, Between the approaching and receding directions, the mean firing rates, computed when the rats were immobile, were highly correlated (Pearson’s r = 0.96 p = 4 x 10−81) and not significantly different (KS-test p = 0.99). e, Firing rates, computed when rats were stationary, during the stimulus angle and stimulus distance experiments were significantly correlated (r = 0.22 p = 0.008). f, Population vector decoding of the stimulus distance (similar to stimulus angle decoding, Fig. 2), was significantly better than chance. (KS-test p = 5.5 x 10−10 for approaching and p = 4.7 x 10−9 for receding data). Approaching stimulus decoding error (median = 194 cm) was significantly lesser than that for receding (median = 237 cm) (KS-test p = 4.2 x 10−5). These errors were 59% and 82% of the error expected from shuffled data, which was greater than that for aVEVS decoding, where the error was 33% of the shuffles, when controlling for the number of cells. g, More than twice as many cells were unidirectional tuned for approaching (coming closer) movement direction, as compared to receding (moving away). h, For bidirectional cells, location of peak firing in the approaching and receding direction shows bimodal response, with most cells preferring either the locations close to the rat, i.e., 0 cm or far away, ~500 cm. Unidirectional cells preferred locations close to the rat. i, Population vector overlap (Fig. 4j), was further quantified by comparing the values along the diagonal for actual tuning curves, with the spike train shuffles. The actual overlap was significantly above two standard deviations of the shuffles for distances close to the rat (around 0) and far away (beyond 400 cm).

Extended Data Fig. 13 Rewards and reward related licking are uncorrelated with VEVS.

a, Example cells showing aVEVS from Fig. 1, with reward times overlaid (black dots), showing random reward dispensing at all stimulus angles. b, The average rate of rewards was uncorrelated with visual stimulus angle (circular test for uniformity p = 0.99). c, Rat’s consumption of rewards, estimated by the reward tube lick rate, was measured by an infrared detector attached to the reward tube26. As expected, lick rate increased after reward delivery by ~4 fold and remained high for about five seconds (green shaded area). This duration is termed the “reward zone”. d, Lick rate inside the reward zone (green) was significantly larger than that outside (red, KS-test p =  2.3 x 10−54). Inside as well as outside reward-zone lick rates were uncorrelated with visual stimulus angle (circular test for uniformity p = 0.99 for both).

Extended Data Fig. 14 Behavioral controls of VEVS.

To ascertain whether systematic changes in behavior caused VEVS, we employed a ‘behavioral clamp’ approach and estimated tuning strength using only the subset of data where the hypothesized behavioral variable was held constant. a, Example aVEVS tuned cells maintained its tuning even if we used only the data when the rat was (b) stationary (running speed <5 cm/sec, blue, left). This was comparable to a random subsample of behavior, obtained by shuffling the indices of spikes and behavior when the animal was stationary (orange, middle) (see Methods). 38% of cells were aVEVS tuned (sparsity z > 2) when using only the stationary data which is significantly greater than chance, whereas 42% were significantly tuned in the equivalent, random subsample and this difference was significant (KS-test p = 0.02). c, Similar to b but using only the data when the rat’s head was immobile (head movement velocity <10 mm/sec). 43% and 42% of cells were significant tuned in actual behavioral clamp and equivalent subsample, and these were not significantly different (KS-test p = 0.93). d, Similar to b, but removing data within 5 s after reward dispensing, called void post-reward. 43% cells were tuned in “void post-reward” data, 43% for equivalent subsample (KS-test p = 0.56). e, Similar to d, but removing data within 5 s before reward dispensing, called void pre-reward. 39% cells were tuned for void pre-reward, 42% for equivalent subsample (KS-test p = 0.43). f, Using a subsample of data, from when the rat’s head was within the central 20 percentile of head positions (typically <10o), rat was stationary and there were no rewards in the last 5 s. This condition was called “analytical head fixation”. 28% of cells were aVEVS tuned under this behavioral clamp, which was lesser than that in an equivalent subsample (31%, KS-test p = 0.05), but significantly greater than chance. g, Tuning curves for head positions to the leftmost 20 percentile and rightmost 20 percentile were similar, with 31% and 32% cells tuned in the two conditions (KS-test p = 0.67). The preferred angles of tuning were highly correlated (circular correlation r = 0.67 p = 1.3 x 10−11) and not significantly different (circular KS-test p > 0.1). h, aVEVS tuning was recomputed in the head centric frame, by accounting for the rat’s head movements (obtained by tracking overhead LEDs attached to the cranial implant) and obtaining a relative stimulus angle, with respect to the body centric head angle. Overall tuning levels were comparable, between allocentric and this head centric estimation. First panel of h is the same as that in a since all aVEVS tuning reported earlier was in the allocentric or body centric frame. Using a subset of data when both overhead LEDs were reliably detected, 25% and 26% of cells were significantly tuned for the stimulus angle in the allocentric and egocentric frames (KS-test p = 0.9). Preferred angle of aVEVS tuning for tuned cells was highly correlated (r = 0.81 p = 1.8 x 10−15) and not significantly different between the two frames (circular KS-test p > 0.1).

Extended Data Fig. 15 GLM estimate of aVEVS tuning.

To estimates the independent contribution of stimulus angle to neural activity, while factoring out the contribution of head position and running speed, we used the generalized linear model (GLM) technique (see Methods)30. a, Tuning curves obtained by binning methods were comparable with those from GLM estimation, including for the cells used in Fig. 1 (first 2 examples in row 1 & 2). b, Sparsity levels were comparable (KS-test p = 0.07) and 40% of cells were found to be significantly tuned for stimulus angle using GLM based estimated, compared to 43% from binning in this subset of data where head and leg movements were reliably captured (cell count, n = 991). c, Preferred angle of firing between GLM and binning based estimates of aVEVS were highly correlated (circular correlation test r = 0.86 p < 10−150). d, Correlation between the aVEVS tuning curves from the two methods was significantly greater than that expected by chance, computed by randomly shuffling the pairing of cell ID across binning and GLM (KS-test p < 10−150). eh, Properties of aVEVS tuning responses based on GLM estimates were similar to those based on binning method, as shown in Fig. 1. e, Distribution of tuned cells as a function of the preferred angle (angle of maximal firing). There were more tuned cells at forward angles than behind. f, Median ± SEM z-scored sparsity and its variability (SEM, shaded area, here and subsequently) of tuned cells as a function of their preferred angle. (Pearson’s r = −0.17 p = 0.004). g, Median ± SEM full width at quarter maxima across the ensemble of tuned responses increased as a function of preferred angle of tuning. (Pearson’s r = +0.33 p < 10−150). h, CDF of firing rate modulation index within versus outside the preferred zone (see Methods) for tuned cells were significantly different (Two-sample KS test p = 2.9 x 10−37).

Extended Data Fig. 16 Simultaneously recoded cells span all angles.

16 simultaneously recorded cells showed significant aVEVS. Their preferred angles are indicated on top. Only cells selective for CCW direction shown for clarity. While the forward direction (0o) is overrepresented, these cells span all angles of the visual field including angles behind him (180o).

Extended Data Fig. 17 Simultaneously recorded cells show very weak co-fluctuation of aVEVS tuning across trials.

a, b, Two simultaneously recorded cells showing significant aVEVS in the CCW direction (a), and zoomed in for a subset of trials, showing mostly uncorrelated fluctuations in the two cells’ spiking (b). c, For the same cell-pair, mean firing rate across trials was broadly uncorrelated. Only trials with non-zero spikes were used here, and henceforth, to ensure comparison with aVEVS tuning (see below). d, Same as c but showing uncorrelated fluctuations in the depth of modulation of aVEVS response of the two cells across trials, quantified by the Mean Vector Length (MVL, see Methods). e, Same as c but showing uncorrelated fluctuation of aVEVS response across trials, quantified by Mean Vector Angles (MVA, see Methods). f, Same as c but showing largely independent fluctuations in the overall aVEVS tuning (measured by correlation between the trial-averaged aVEVS tuning curve and the aVEVS tuning curve in a given trial) for this cell-pair. The significance of co-fluctuations in cell-pairs were quantified by bootstrapping methods, by employing trial id shuffles (see Methods). CCW and CW tuning curves were treated as separate responses throughout these analyses. g, 21% (14%) of simultaneously recorded, tuned (untuned) cell-pairs showed significant (z > 2) co-fluctuation of mean firing rates across trials which provides an estimate of the non-specific effects such as running, reward consumption etc. h, Only 7% (5%) of tuned (untuned) cell pairs showed significant co-fluctuation of MVL across trials indicating little effect of nonspecific variables on the depth of aVEVS tuning. i, Similarly, only 10% (6%) of tuned (untuned) cell pairs showed significant co-fluctuation of MVA across trials. j, Only 14% (5%) of tuned (untuned) cell pairs showed significant co-fluctuation of aVEVS. Notably, the number of cell pairs showing significant co-fluctuations in any of the aVEVS tuning properties (hj) was smaller than the number of cell pairs showing significant co-fluctuation of firing rates; and there was little qualitative difference between the significantly aVEVS tuned vs untuned populations.

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Purandare, C.S., Dhingra, S., Rios, R. et al. Moving bar of light evokes vectorial spatial selectivity in the immobile rat hippocampus. Nature 602, 461–467 (2022).

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