Article Figures & Data
Figures
- Figure 1.
A, Schematic of the circular-spiral track. Each loop of the track is indicated by a color. Animals made multiple inbound and outbound of the track to retrieve a single food reward located at the center or exit point of the track (brown circles). All tracks had 4 cm high walls that allowed animals to see distal cues along recording room perimeter. B, The spiking responses (red dots) and firing rate maps (occupancy normalized density plots) of four neurons that were recorded as animals ran toward the center of the spiral. These examples illustrate the forward shift of the center of mass of each repeating field during the inward journeys. The gray background indicates the position of the animal as measured from the tracking camera. C, Same as in B, but for outward journeys. D, Representative samples of histological reconstruction of electrode tracks.
- Figure 2.
Forward shift occurs during inward but not outward journeys. A, Illustration of procedure used for calculating the measure of shift. Shift was measured as the difference in radial degrees between the center of mass of pairs of adjacent subfields. A forward shift relative to the animal's running direction would be indicated as a positive difference between the centers of mass whereas a backward shift would be indicated by a negative difference. This relation holds for both inward and outward traversals. Each subfield is identified by the loop in which it was active. B, Plot of the shift between pairs of adjacent subfields (n = 158). Trials were restricted to inward traversals of the spiral. Each firing field is indicated as a point on the plot and the axes indicate the shift between loops 2 and 3 (y-axis) and 3 and 4 (x-axis). The majority of field-pairs (114/158) were in the top-right quadrant and therefore exhibited a forward shift on loops 2–3 and 3–4. The distribution of points through the four quadrants differ significantly from chance (χ2 test, p < 0.0000001). C, The shift for all adjacent fields approached 10° for inward journeys but did not differ from zero for outward journeys. Asterisk over the individual bar indicates results of testing for a difference from zero (t test, p < 0.05, Bonferroni correction, ninward = 158, noutward = 93). The horizontal bars indicate the results of a post hoc multiple-comparison test (Tukey–Kramer, p < 0.05). D, The shift between adjacent fields for each pair of adjacent loops. A significant positive shift was observed for each pair of adjacent fields during inward traversals. Asterisks over individual bars indicate whether results differed from zero (t test, p < 0.05, Bonferroni correction for four tests (n = 158). The horizontal bars indicate the results of a post hoc multiple-comparison test (Tukey–Kramer, p < 0.05). E, Same as in D but for outward journeys. No significant shift was observed on a pair of adjacent loops during outward traversals. All error bars indicate SEM.
- Figure 3.
Forward shift observed in population activity. A, Firing rate activity of 151 neurons recorded during inward traversals of the spiral track. Each loop (a 360° rotation) is indicated on the x-axis. Inward movement is from the left to the right. B, State correlation matrix generated by correlating all population states (the columns in subplot A) with states at all locations along the track (x-axis). The matrix is symmetric with respect to the diagonal. Repeating striations along the diagonal indicate that states tended to be correlated with states at 360° (one loop) intervals. The pattern of striations also suggests that the peak was offset from 360° by 6.7° (inset, green box with the diagonal indicated by the dashed line). C, D, Reconstruction of position by population state. A reconstruction analysis was performed to determine the fidelity by which populations of repeating fields encoded the current location of the animal relative to other locations ahead of or behind the rat. Template and Test field-by-location matrices similar to subplot A were created from nonoverlapping sets of trials and the similarity of population states (columns) in these matrices were compared (Pearson's r). Reconstructed position was the state/position with the largest correlation. C, Display of state correlations and the reconstructed position (black/white dots) in front of (positive) or behind (negative) the rat for the inner two loops of the spiral. Reconstructed position (black/white dots) clustered at the current location of the rat, and only 5% of reconstructed positions were outside of ±10° from the current location. D, The column mean and SEM of subplot C. Vertical red lines indicate ±360°. The peak correlation at the current location (0°) was r = 0.83, whereas values at adjacent loops peaked at ±367 (rbehind = 0.71, rahead = 0.62). Inset, Close-up of the central peak to illustrate that there was no visible asymmetry in the reconstruction.
- Figure 4.
Angular velocity and running speed change as a function of loop. On each experimental session, the average angular velocity and speed were determined for inward and outward journeys. A, Angular velocity (degrees/s) was a function of distance to the center of the spiral, being smallest on the outermost loops and largest on the innermost loops (loop 5). There was a significant positive correlation between angular velocity and loop on both inward (loops 1–5) and outward (loops 5–1) journeys (rinward = 0.94; p = 8.6672e–168, n = 370 sessions; routward = 0.81; p = 1.2998e–026, n = 110 sessions). B, A weaker but significant correlation between running speed and loop number was also observed for inward (ANOVA, p < 1e–17, n = 75 sessions) and outward journeys (ANOVA; p < 5e–16, n = 22 sessions). There was also a significant negative correlation between running speed and loop number (rinward = −0.43; p < 1e–17, n = 370; routward = −0.71; p < 6e–18, n = 110). Post hoc analysis of running speed indicated that there was no significant difference between loops 2 and 3. Together, the running on the spiral track most strongly affected angular velocity, although significant changes in running speed were also observed. C, The frequency of the hippocampal theta rhythm often increases with increasing running speed. No clear connection between theta frequency and running speed or angular velocity was observed during traversals of the spiral-shaped track. In fact, theta frequency tended to increase as rats ran inward and increase as rats ran outward (rinward = 0.36; p < 1e–12, n = 366; routward = −0.88; p < 1e–40, n = 135) despite opposite patterns of speed and angular velocity (A, B). All error bars indicate SEM.
- Figure 5.
Summary of hypotheses: the observed forward shift suggests that firing activity was not anchored in a purely allocentric reference frame (top plot) as such anchoring would predict that the fields would fire at the same angle on consecutive loops. Four potential mechanisms for the shift were explored. A, Path integration error: rats can navigate in darkness by integrating self-motion cues such as head rotation and running speed. The spiral is unique in that angular rotation gradually increases during the inward journey. The slow rate of change may cause animals to underestimate the amount of angular distance traveled and produce a forward shift. B, Local view: a shift in the firing field on the spiral could occur if neurons fired when animals spot a specific visual cue or local view. In this illustration, the cell fires at the time at which animals viewed a cue mounted on a wall outside of the maze. Contrary to our observations, however, this hypothesis predicts a backward shift, as animals would view the cue at earlier points on consecutive laps (presuming the animals look forward at an angle tangent tot the track). C, Head direction at fixed delay: a forward shift could result from neurons responding in a delayed manner to a head direction experienced in the recent past (e.g., if the neuron is receiving a delayed head-direction signal from an afferent neuron). A fixed temporal delay between the responses would allow the animal to cover more angular distance on the inner relative to the outer loops before the cell would fire. D, Step counting: in addition to path integration by integrating angular rotation and running speed (A), animals could also path integrate by “counting steps” along the spiral. Step counting would produce a forward shift if the animal worked under the assumption that the spiral was a concentric circle (green circle).
- Figure 6.
Degree of shift during traversals on concentric-circle and square tracks and in darkness. A, Schematic illustration of the squared spiral track and the spiking responses of two neurons during inward traversals on this track. B, Same as in A except for the concentric circle spiral track. The field in the upper plot did not show a clear forward shift, whereas a forward shift was observed in the field on the lower plot. C, D, Examples of responses from neurons during inward and outward journeys on the circular spiral in the dark. E, The degree of shift during successive loops of various tracks. The y-axis indicates that average shift in the center of mass of fields on adjacent loops (Fig. 2A). Data were pooled across all loops (Δ12, Δ23, Δ34, and Δ45). Positive values indicate that the fields shifted ahead of the animal on each consecutive loop. All tests for deviation from zero were performed using two-tailed t tests. All reported P values are unadjusted. Bar labels: Square, No significant shift (p = 0.33, n = 416 field-pairs from 140 neurons) was observed on the square-spiral track; Concentric, A small but significant forward shift was observed (p = 0.041, n = 179 field-pairs from 51 neurons) during inward journeys on the concentric circle track; this shift was significantly lower than the 10° shift observed on the spiral (t test, p < 0.05); Dark in, Significant forward shift (p = 0.0001, n = 38 comparisons from 11 neurons); Dark out, Fields shifted backward (p = 0.00003, n = 72 field-pairs from 39 neurons); Inward, Outward, For comparison, the magnitude of the shift present during inward and outward journeys on the circular-spiral track are also presented (identical to plot in Fig. 2C).
- Figure 7.
Analysis of the relationship between running speed and the forward shift. Trials were divided in to fast and slow trials according to running speed and firing fields were generated for these two groups. The centers of mass of these fields were compared. The histogram plots the distribution of differences of the field centers in between fast and slow trials (COMFAST–COMSLOW). No significant effect of running speed was observed (p = 0.32, t test, n = 628 fields). Analysis was restricted to fields on loops 2–4.
- Figure 8.
Step counting. One way that shift could develop is if self-motion signals from the motor system were used to integrate distance traveled along the spiral track. If animals were capable of estimating the circumference of the track at each location (shaded circular area in inset), then this strategy could provide an estimate regarding when animals would complete a 360° rotation. Running on the spiral-shaped track would induce an error in this estimate as the radius of the spiral gradually decreases, thus the estimated circumference would overestimate the distance required to return to the original heading (dashed line). The magnitude of this error was estimated by first determining the circumference of a circle at each point on the spiral and then projecting this distance onto the trajectory taken by animals along the spiral. This projection resulted in a large angular shift that increased exponentially during inward traversals. Most notable was the fact that this estimate of shift was far greater than the 10–15° shift observed on the spiral. Furthermore, the observed shift did not increase exponentially in the manner indicated by the step-counting estimate. This suggests that the forward shift was not a first-order function of integrating steps.
- Figure 9.
A, Illustration of how a forward field shift during inward journeys could result from a delayed response of neurons to a head angle experienced in the recent past. The dashed line indicates the angle at which a neuron in a structure upstream of the hippocampus may be tuned. If there is a delay in the response of hippocampal neurons to such a cell (e.g., due to transmission or processing delays), then the angular response measured in the hippocampus would appear to shift forward as animals would cover more angular distance per unit time on the inner as opposed to the outer loops. If neurons with forward shifting fields are responding to previously experienced head angles, then measures of tuning quality such as the peak and width of the tuning response to head angle should become optimal for a point in time in the past. To examine this hypothesis, the peak and width of the firing fields were examined after time shifting the spike trains by varying temporal offsets (10 ms increments). The best tuning response should be indicated as the offset with the highest peak and most narrow width. The analysis was restricted to individual firing fields recorded during inward journeys on laps 2–4 of the spiral (n = 391 fields, 110 neurons). B, The peak of the tuning curve calculated at different temporal offsets. Thick lines indicate median values of the peak heights at each offset (rescaled to the range of −1 to 1; y-axis). Thin lines indicate the notch confidence interval [±1.58 IQR/sqrt(n)], whereas the dashed lines indicate the 15.9 and 84.1 percentiles (spanning 68.2% of the data). Asterisks indicate median values that differed significantly from the median at an offset of zero (p < 0.05, rank sum test). No significant shift from a zero offset was observed in the peak. C, The same analysis was performed on the width of the tuning curves (width was quantified as the SD). As with the peak, no clear offset in the minimum of the tuning width was observed. As with peaks, widths were rescaled to range from −1 to 1. D, The offset associated with the maximal peak height and minimum width (SD) was computed for each field. These means of these values were not different from zero (t test, Ppeak > 0.75, PSD > 0.67, n = 391, error bars = SEM).
