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Speed cells in the medial entorhinal cortex



Grid cells in the medial entorhinal cortex have spatial firing fields that repeat periodically in a hexagonal pattern. When animals move, activity is translated between grid cells in accordance with the animal’s displacement in the environment. For this translation to occur, grid cells must have continuous access to information about instantaneous running speed. However, a powerful entorhinal speed signal has not been identified. Here we show that running speed is represented in the firing rate of a ubiquitous but functionally dedicated population of entorhinal neurons distinct from other cell populations of the local circuit, such as grid, head-direction and border cells. These ‘speed cells’ are characterized by a context-invariant positive, linear response to running speed, and share with grid cells a prospective bias of 50–80 ms. Our observations point to speed cells as a key component of the dynamic representation of self-location in the medial entorhinal cortex.

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Figure 1: Speed-responsive MEC cells in a linear task.
Figure 2: Entorhinal speed cells form a population of their own.
Figure 3: Invariance of the entorhinal speed code.
Figure 4: Prospective coding of entorhinal speed cells and grid cells.


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We thank A.M. Amundsgård, K. Haugen, K. Jenssen, E. Kråkvik, and H. Waade for technical assistance, R. Báldi for help with data collection in two initial experiments, J. Couey for inspiring the bottomless car, and A. Treves for discussions. The work was supported by two Advanced Investigator Grants from the European Research Council (‘CIRCUIT’, Grant Agreement No. 232608; ‘GRIDCODE’, Grant Agreement No. 338865), the European Commission’s FP7 FET Proactive programme on Neuro-Bio-Inspired Systems (Grant Agreement 600725), an FP7 collaborative project (‘SPACEBRAIN’, Grant Agreement No. 200873), the Kavli Foundation, the Louis-Jeantet Prize for Medicine, the Centre of Excellence scheme of the Research Council of Norway (Centre for the Biology of Memory and Centre for Neural Computation), and a PICT 2012-0548 Grant to E.K. from the Ministry of Science of Argentina.

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Authors and Affiliations



E.K., M.-B.M. and E.I.M. designed experiments and analyses; E.K. and J.E.C. performed the experiments; E.K. performed the analyses; E.K. and E.I.M. wrote the paper with input from all authors.

Corresponding authors

Correspondence to Emilio Kropff or Edvard I. 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 sagittal brain sections showing representative recording locations in the MEC and hippocampus.

Red dots indicate final location of tetrodes. Rat number, hemisphere (R, right; L, left) and entorhinal layers or hippocampal regions where cells were recorded are indicated. Scale bars, 1 mm.

Extended Data Figure 2 The bottomless car does not affect firing properties of grid and place cells on the linear track.

As opposed to recording from a passive rat sitting on a classical car36, the bottomless car task does not alter the spatial and temporal firing properties of grid cells (top, four cells) or place cells (bottom, four cells). Every cell was recorded under three conditions: experimenter-determined running in the bottomless car (‘car’); free foraging on the same linear track but with the bottomless car removed (‘free’); and open field. Each block of panels shows data for one cell. Left side of each panel: from top to bottom, the animal’s trajectory (black curve) and spike positions (coloured dots) for free sessions and car sessions; corresponding colour-coded rate maps, with red indicating peak rate and dark blue indicating silence; and overall firing rate across the x dimension of the track for free (grey) and car (colour) conditions. Note the similarity between spatial maps recorded in the car and the free condition. Right side of each panel: from top to bottom, colour-coded open field rate map and temporal cross-correlograms of spiking in free and car conditions. Note the similarity of the two cross-correlograms.

Extended Data Figure 3 Linear relationship between speed and firing rate in speed cells but not spatially modulated cells of the MEC or the hippocampus.

a, Scatter plot showing slope and y intercept of regression lines for each entorhinal speed cell recorded in the bottomless car (blue circles) and in the open field (grey circles). Note wide range of slopes and y intercepts. b, Identification of speed-modulated cells using analyses that do not assume linearity (see Methods). The linearity of these cells is represented by the regression of the tuning curves (red), which clusters mostly around 1 (speed cells) and marginally around −1 (anti-speed cells), in contrast with the distribution of linearity indexes of the shuffled population (grey, 100 shuffling steps, count normalized by the number of steps). This holds across experimental protocols and brain regions, as indicated. c, Spatial maps and average speed along the track of four representative anti-speed cells in the bottomless car under linear or two-speed step protocols, plotted as in Fig. 1b. d, Firing rate as a function of position, head direction (hd), and running speed for six representative anti-speed cells recorded in the MEC during free running in a square open field. Each row shows one cell. Left, colour-coded spatial rate maps. Scale bar to the right. Middle, firing rate as a function of head direction (x axis) and running speed (y axis). Firing rates in left and middle diagrams share the same colour code. Right, firing rate as a function of running speed. e, Speed modulation of firing fields in the MEC (top) and hippocampus (bottom). Left, average normalized firing profile of fields in each of the four speed groups in the bottomless car. Right, for each field, the area under the curve 1 s.d. around the average field centre is computed to obtain mean firing rate across firing fields for each speed group (mean ± s.e.m.). Statistical tests showed no significant effect of speed on the average normalized firing rate in the MEC (Kruskal–Wallis test, P = 0.12). In the hippocampus, in contrast, the same tests showed a significant trend in the modulation by speed, due exclusively to the difference between 7 and 28 cm s−1 (Kruskal–Wallis and Tukey–Kramer tests, P < 0.05). Note that similar tests on entorhinal speed cells (Fig. 1f) showed significant differences between all groups (P < 0.01). f, Average firing fields, as in e, but using position relative to field centre instead of field z score as the spatial variable (running is always from negative to positive values). This allows direct measurement of firing position as a function of running speed, connecting equation (2) with Fig. 4b. Gaussian fits are used to determine firing position, defined as the field centre for each speed category.

Extended Data Figure 4 MEC speed cells are generally not modulated by space or direction.

Examples of MEC speed cells. Three sets of data are shown for each cell. Left, colour-coded spatial rate maps. Scale bar to the right of the first map. Middle, firing rate as a function of head direction (x axis) and running speed (y axis). Same colour code as for the rate map. Maximum firing rate is indicated in the upper left corner. Right, firing rate as a function of running speed. a, Twelve representative MEC speed cells (from a total sample of 385 speed cells in 17 animals), which in general are poorly modulated by space or direction. b, Examples of speed cells that passed one additional cell-type criterion (from left to right: border, grid, head direction).

Extended Data Figure 5 MEC speed cells in a single animal.

All MEC speed cells recorded in one animal (rat 14740). For each cell we show four plots. From left to right: spatial rate maps; head-direction versus speed rate maps; spatial autocorrelograms used to calculate the gridness score; and speed tuning curves (right). Symbols for rate map, head-direction versus speed map, and tuning curve as in Extended Data Fig. 4. The spatial autocorrelogram is colour-coded from r = −1 (blue) to r = +1 (red).

Extended Data Figure 6 Speed cells form a separate cell class.

a, Observed data (purple) and 100 step-shuffled distributions (grey; count normalized by 100) of different variables used to classify cell types. The dashed lines represent the 99th percentile threshold of the shuffled distribution, with the exception of the distributions of border score and spatial information used for border cell classification, where a dual 95th percentile criterion was used. Threshold values are indicated in boxes. b, A similar comparison with shuffled data shows no signs of ‘acceleration cells’ in the MEC. The acceleration score was defined as the correlation between instantaneous firing rate and acceleration. Left, cells recorded in the open field had a distribution of acceleration score (purple) very similar to that of the shuffled population (grey bars). The number of cells exceeding the 99th percentile of the shuffled distribution (0.11) were 21 more than the average chance level (observed, 46 out of 2497; expected, 25; P = 10−4). This might be explained by the fact that out of these 46 cells, 20 were speed cells, which are as a population modulated by acceleration due to their prospective nature (Fig. 4c and equation (1)). Middle, the partial correlation between firing rate on one side and speed and acceleration on the other was computed for those speed cells with high acceleration modulation. In all cases, the partial correlation with speed was higher than the partial correlation with acceleration, with more than a twofold difference on average. Right, potential modulation by acceleration was also studied by restricting the calculation of the acceleration score to fragments of 2 s around the onsets for the highest speed change in the four-speed experiment (from 7 to 28 cm s−1), where potential ‘acceleration cells’ should exhibit a peak in their firing rate. Cells recorded in this experiment had a distribution of acceleration scores (purple) very similar to that of the shuffled distribution (grey), and only 8 out of 997 cells had a score above the 99th percentile of the shuffled distribution (0.45; expected, 10; P = 0.78). c, Tables showing the significance of population sizes and population overlaps using classification thresholds based on the 99th (top) and the 95th (bottom) percentile of the shuffled distribution. G, grid cells; HD, head-direction cells; S, speed cells; B, border cells; P, place cells; +, conjunctive cells satisfying criteria for more than one cell class. Expected chance levels are obtained from Bernoulli distributions. For single categories, the right tail P value is indicated. For overlap between categories, the left tail P value is indicated, while in the case of the overlap between head-direction and border cells, which clearly exceeds chance levels (40% of border cells are also head-direction cells), the right tail P value is added in parentheses. The mixture in the coding of speed and other behavioural variables was always smaller than the mixture between spatial and directional coding. For hippocampal data, the statistics include only cells that were active in the open field (not including sleep sessions). Note that all cell categories are defined by comparison with a shuffled distribution, that is, not by applying arbitrary thresholds. This procedure does not always define populations of significant magnitude (see b) and exhibits consistent results for the overlap of populations at the 99th and 95th percentile level. d, Scatter plots showing distributions of scores and cell-type classifications. Each dot represents a cell, with the same colour code as used in Fig. 2g. x and y axes show scores used for cell-type classification (gridness score, speed score, mean vector length head-direction score, border score, or spatial information). Dashed lines represent the classification threshold for each score. e, Scatter plot as in d showing overlap between the speed-cell and the place-cell populations in the hippocampus. In this case, speed score and spatial information were used for classification. f, Top row, pie charts showing distribution of functional cell types and their overlaps across entorhinal layers (only proportions higher than 1%). Bottom, recording across multiple days can generate an unwanted bias in the estimation of population sizes, since a single cell could be counted many times. To avoid this bias, we reduced our original data set by discarding a cell if another cell had been recorded at a distance of less than 200 μm on the same tetrode on an earlier day. In this reduced population of 608 cells, 18% were speed cells, confirming that the population size estimation is free of this kind of bias. g, Distribution for different cell categories of speed score (left) and firing rate averaged over non-silent periods (firing rate>1 Hz; right). h, The speed scores of cells in the MEC (left and middle) and hippocampus (right) were plotted against the in-field speed score of the cells, calculated only with data from the bins with a firing rate above the median. This quantity is a correction for spatially and directionally modulated cells, but has no meaning for other cells. Left, out of 16 grid cells that passed the speed cell criterion, 11 (69%) had in-field speed scores clearly below threshold, while the remaining population had similar regular and in-field scores (Mann–Whitney U-test, P = 0.31). Similarly, out of 11 border cells, 5 (45%) had very low in-field scores, and the remaining had similar regular and in-field scores (P = 0.82). Middle, a similar approach was implemented using head-direction bins instead of spatial bins. Out of 42 MEC head-direction cells with high speed score, 17 (40%) had in-field scores below threshold, while the remaining population had similar regular and in-field scores (P = 0.57). Right, different conclusions were obtained in the analysis of hippocampal place cells. Out of 19 place cells with high speed score, 6 (32%) had low in-field scores. The remaining population had in-field scores significantly higher than the corresponding regular speed scores (Mann–Whitney U-test, P < 0.02). In addition, 33 other place cells with low regular speed score had in-field speed scores higher than threshold, suggesting a stronger mixture between speed and spatial coding in the hippocampus. i, Population distribution (mean ± s.e.m.) of various quantities for all MEC cell types (S, speed; G, grid; HD, head direction; B, border).

Extended Data Figure 7 Representative examples of conjunctive grid and head-direction cells in the MEC and speed cells in the hippocampus.

Three sets of data are shown for each cell. Left, colour-coded spatial rate maps. Scale bar to the right of the first map. Middle, firing rate as a function of head direction (x axis) and running speed (y axis). Same colour code as for the rate maps. Right, firing rate as a function of running speed. a, MEC conjunctive cells do not exhibit strong modulation by speed. b, Hippocampal speed cells have characteristics that are similar to entorhinal ones.

Extended Data Figure 8 The speed code is context-invariant.

a, Colour-coded rate maps showing realignment in a grid cell recorded in rooms A and B. The sequence of recording was ABA′. In the MEC, change of room causes change in grid phase and grid orientation; in the hippocampus, this is accompanied by global remapping3. b, Speed score, tuning curve y intercept and slope in room A versus room B for 20 speed cells recorded in the room-change experiment in a (eight rats). Each dot corresponds to one cell. Values distributed around the diagonals indicate context invariance. c, Percentage change for the same quantities between trials A and B and between A and A′ (mean ± s.e.m.). In each case, the difference between the two distributions was non-significant (Wilcoxon signed rank test, speed score, P = 0.9; y intercept, P = 0.54; slope, P = 0.49). d, Reconstructed speed (purple and black) compared to actual speed in darkness (grey). Speed was decoded from the activity of three speed cells (Fig. 3f, g), with decoders trained either in the lights-on condition (black) or the lights-off condition (purple). Pearson correlation between reconstructions was 0.97. Correlation between decoded speed and actual speed was 0.45 with the ‘light on’ decoder, and 0.48 with the ‘light off’ decoder. e, All speed cells that were recorded in the open field both before and after trials in the bottomless car were selected from recordings in the MEC (top) and the hippocampus (bottom). Speed score (left), speed tuning curve y intercept (middle) and slope (right) were compared within sessions. Grey dots show the comparison between pre-open-field and post-open-field recordings (x axis and y axis, respectively). Coloured circles indicate the comparison between pre-open-field (x axis) and bottomless car (y axis) recordings. In case the speed score in the bottomless car was below threshold, an open circle was used instead of the filled coloured circle (15 out of 64 in MEC (23%) and 8 out of 16 in the hippocampus (50%)). The results indicate that, although in both areas many speed cells maintain their firing properties even across extremely different contextual and behavioural situations, MEC speed cells seem to exhibit a more universal code than hippocampal speed cells. f, Overall distribution of running speed in the open field (o.f.; grey) and in the bottomless car trials (linear speed profile; red) for rat 14566 (Fig. 3h–j). This was the rat with the largest difference in speed across behaviours (open field, 10 ± 8 cm s−1; bottomless car, 20 ± 13 cm s−1; mean ± s.d.). Yet the difference did not generate adaptation in the slope of the speed–rate tuning curve (Fig. 3f–h).

Extended Data Figure 9 Theta modulation of MEC speed cells.

a, Plots of temporal bias, as in Fig. 4a, for all MEC speed cells in the open field with weak (left) and strong (right) theta modulation as defined by the theta index (θindex; see Methods). Only the latter were prospective (discriminating threshold θindex = 0.2; see b). b, Temporal bias of speed cells classified according to location, task and theta modulation. Different measures are used: the maximum of the average correlation curve (peak of mean); and the mean (mean of peaks) and median (median of peaks) of the distribution of maxima of individual correlation curves. The anticipation of the speed cell response to the movements of the animal cannot be related to the learned prediction of the bottomless car protocol, since in all cases the leads are similar to those found in spontaneous open-field behaviour. Similar and even larger leads in neural activity over body kinematics have been described in the motor cortex of monkeys37, as well as rats38. Since the motor networks are supposed to be one of the sources of speed information feeding the hippocampal navigation systems, with prominent direct connections from secondary motor cortex to the MEC39, we cannot discard the hypothesis that the lead is simply inherited from this source. Alternatively, other simple network mechanisms such as anticipated synchronization could generate this effect locally without the involvement of predictions or learning in a cognitive sense. c, MEC speed cells ordered according to increasing theta modulation index. Colour-coded firing rate profile across the theta cycle is plotted, with each line representing a different cell. Firing rate is normalized for visualization purposes. Red arrowheads indicate the threshold (θindex = 0.2) used in a and b. The plot reveals that theta-modulated cells have a characteristic behaviour, exhibiting a ramp of activity that develops roughly along the first two-thirds of the cycle and falls to near zero during the last third. d, Representative examples of the activity of ramping (strongly modulated, top four) and flat (weakly modulated, bottom three) speed cells at different speeds (colour-coded). Rat number is indicated in the top-left corner. Note that ramps corresponding to different speeds do not run in parallel. Instead, the ramp slope increases with speed. One possible explanation for this is that the ramp represents the integration of speed (distance travelled) from the beginning of the theta cycle rather than speed itself. Note also that the ramp/silent division of the theta cycle roughly coincides with the reset/look-ahead division arising from the analysis of grid cell activity (Extended Data Fig. 10f, h). e, Normalized firing rate profile (mean ± s.d.) for four clusters resulting from applying a k-means algorithm to the data in c. The number of clusters k was set to 7, and all clusters exhibiting a ramping behaviour were merged together (similar results were obtained by applying the same procedure with k = 4 … 10). Note that most speed cells fall into the ramping (#1) or flat (#2) clusters. The sum of counts is 321, lower than the total cell number of 385, because 62 speed cells classified conjunctively as some other category were left out of this particular analysis and for two pure speed cells a simultaneous EEG recording was not available. f, Average dynamics along the theta cycle of the normalized firing rate of speed cells belonging to each of the four clusters for different running speeds (colour-coded as in c). g, First two principal components of the data. Note that the first principal component represents the ramping pattern. h, Scatter representation of the data in a across the principal components in e. Colours indicate clusters as in e. i, j, Distribution of clusters (i) and theta indexes (j) for different MEC layers. k, Plots obtained from the 25 most ramping (left) or flat (right) MEC speed cells (all trials). Each block shows the distribution of correlations between running speed and different temporal shifts of the instantaneous firing rate (left), together with a profile of normalized activity across the theta cycle for positive and negative acceleration with an absolute threshold of 50 cm s−2 (right, top) and the difference between the two curves (right, bottom; mean ± s.e.m.). Only ramping cells express pronounced prospective behaviour, as seen both by a positive temporal shift (ramping, 206 ± 22 ms, P < 0.01; flat, −23 ± 19 ms, P = 0.31; Wilcoxon signed rank tests) and by a marked difference between positive and negative acceleration curves along the ramp of activity. Friedman’s tests show a significantly higher firing rate for positive acceleration in ramping cells and for negative acceleration in flat cells (P < 0.01).

Extended Data Figure 10 Grid cells in MEC layer II express strong prospective theta-modulated spatial coding.

a, Average fields of spatially modulated MEC and CA cells in bottomless car trials, filtering for only positive (red) or only negative (black) acceleration (absolute threshold, 50 cm s−2). Recording layer (II, III or V) in the MEC or subfield in the hippocampus (CA1, CA3) is indicated in each case, and the average unfiltered field is shown in grey. Space is represented by the z score of the field and running direction is always defined from left to right. Note that fields were significantly shifted only in MEC layers II (strongly) and III (weakly), that is, not in MEC layer V or in the hippocampus (Fig. 4g). b, To rule out the possibility of a retrospective effect during negative acceleration, we restricted the analysis to the four-speed experiment. Since rats spent most of the time running at very low speed and nearly zero acceleration, the temporal bias of the average field is reduced to a minimum, and it can be used as a reliable reference. The plot shows shifted fields for different positive and negative acceleration thresholds using only data from the four-speed experiment. Acceleration threshold is colour-coded (scale bars to the right). Note that negative acceleration, regardless of its magnitude, has a very small effect on the field position, keeping the field close to the reference average field in all cases. In contrast, positive acceleration produces a prospective advance of the field that increases with acceleration threshold. c, Position of the average fields peaks in b as a function of absolute acceleration threshold when including only positive (red) or only negative (black) acceleration episodes. Note the increase in prospective shift with increasing threshold only for positive acceleration episodes. In contrast, negative acceleration produces no effect apart from a small retrospective offset. Such an offset is expected as a consequence of prospection during positive acceleration, since the average field at the lowest speed, used as a reference, should have a small, yet non-zero, prospective bias. d, Shifted fields as in b, but using only cells that could be classified as grid cells based on rotational symmetry in a complementary open field recording (using the 99th percentile of a shuffled distribution as the classification criterion). The absolute acceleration threshold was 50 cm s−2. e, Shifts that maximized the correlation between positive or negative acceleration-related fields and the reference average field shown in d (mean ± s.e.m.; *Wilcoxon signed-rank test after Holms–Bonferroni correction, P < 0.01). f, Phase map of the pool of all putative grid cells, indicating ‘look ahead’ and ‘reset’ stages over two theta cycles (see h). In the look ahead stage, the grid network engages in forward sweeps, related to phase precession proper22. In the reset stage the spatial representation suffers a sudden jump back, opposite to the running direction, and the correlation between grid cell firing phase and position is very poor. g, Similar phase maps filtering for only positive (top) or only negative (bottom) acceleration (absolute acceleration threshold, 50 cm s−2). h, Top: average firing rate along two theta cycles. The local minima, indicated with dashed lines, were used to define the frontiers between the look ahead and reset stages7,32,40,41. During the look ahead stage, phase precession proper takes place, while during the reset stage, the spatial code jumps back and remains relatively static as theta phase increases (see f). Middle, in three consecutive rows, the average dynamics of Δ along two theta cycles for different acceleration thresholds (colour-coded; from top to bottom: MEC layers II, III and V). Note that the prospective shift of grid fields increases during the reset stage and decreases during the look ahead stage. This speaks strongly against the idea that the prospective effect is a by-product of forward sweeps of different magnitude, and in favour of transient and local distortions in the representation of location. Bottom, acceleration is not strongly modulated by theta phase, as observed when computing the overall average (grey) and the average restricted to positive (red) or negative (black) acceleration. i, Frequency distribution of ratio between intrinsic firing frequency and local field potential (LFP) theta frequency in grid cells and speed cells. In grid cells (green), the mean intrinsic firing frequency is 3% higher than the theta frequency obtained from the LFP power spectrum (Mann–Whitney U-test, P = 1 × 10−21). This difference is due to phase precession. In contrast, in speed cells (grey), the mean intrinsic firing frequency is only 0.6% higher than the LFP theta frequency (P = 0.043), suggesting that a similar mechanism is not present in this population.

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Kropff, E., Carmichael, J., Moser, MB. et al. Speed cells in the medial entorhinal cortex. Nature 523, 419–424 (2015).

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