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1Department of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania; and 2Division of Neural Systems, Memory, and Aging, University of Arizona, Tucson, Arizona
Submitted 7 February 2005; accepted in final form 4 June 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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), although their activity can also reflect nonspatial variables (Eichenbaum 1996; Markus et al. 1995; Oler and Markus 2000). Typically, when the rat enters a new environment, place cell populations instantly "remap," exhibiting firing fields whose relationships to one another are essentially uncorrelated with those recorded in previously visited environments (Muller and Kubie 1987). The new ensemble activity patterns stabilize over a period of 10–20 min, presumably as a result of synaptic learning throughout the hippocampal formation (Wilson and McNaughton 1993). Because CA1 activity patterns are sparse and relatively orthogonal, multiple maps can coexist in the synaptic weight matrix without catastrophic interference (Marr 1971; Samsonovich and McNaughton 1997; Treves and Rolls 1991), and can be recalled later when the rat reenters the corresponding environment.
This account is complicated by the phenomenon of partial remapping. Skaggs and McNaughton (1998) reported that when rats traveled between two visually identical boxes with matching orientations (Fig. 1A, same orientation), the activity patterns of CA1 place cells differed across boxes, but overlapped substantially more than would have occurred by chance. This partially remapped state appeared to be stable: recording over 10 days, Skaggs and McNaughton found that although the distribution of correlations of firing fields across the two boxes varied from day to day, possibly reflecting statistical sampling error, there was no discernable trend toward increased or decreased correlation.
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), which has both linear and angular components. Likewise, hippocampal activity may be updated in part by a path-integration mechanism (for reviews see McNaughton et al. 1996; Redish 1999), although there is some evidence that in the absence of visual, tactile, and olfactory cues, path integration alone is insufficient to maintain rotational alignment of place fields with the environment (Save et al. 2000). An idiothetic direction sense maintained by angular path integration has been identified with a head direction cell network in postsubiculum, anterior thalamus, and other areas (Sharp et al. 2001; Taube 1995, 1998; Taube et al. 1990a,b). The Skaggs and McNaughton experiment was designed to assess the relative roles of linear path integration and visual landmarks on place field distributions. It appears that sensory cues largely override the linear path integrator's influence when visiting two identical environments. Because the cues had identical allocentric bearings in the two boxes, there was no discordance between sensory cues and the rat's internal sense of direction as the animal traveled from one box to the other.
In the present experiment, to assess the effects of discordance between angular path integration and visual landmarks on place field maps, the extent of remapping between boxes was compared under two conditions. In the same-orientation condition, patterned after Skaggs and McNaughton (1998), the boxes were oriented identically and connected by a corridor. In the opposite-orientation condition, the boxes were abutted by rotating them by 90° in opposite directions, so that their orientations differed by 180° (Fig. 1A, opposite orientation). Three rats experienced both trial types on each of two consecutive days, permitting a direct comparison of place cells' responses under each condition. On the third day the rats ran two trials in the opposite-orientation condition to assess the consistency of their remapping behavior.
Some of the results from this experiment have been reported previously in preliminary form (VanRhoads et al. 2004).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Three male FBNF1 rats (Harlan Sprague Dawley), age 9–13 mo, were used in this experiment. The apparatus consisted of two identical boxes similar to those in the Skaggs and McNaughton (1998) experiment. The boxes were 60 x 60 x 60 cm in size, with a trapezoidal doorway in one wall whose width progressed from 15 cm at the bottom to 33 cm at the top. (The opening was wider at the top to permit free travel of the recording cable.) In the same-orientation condition, the boxes were placed side by side with identical orientations, such that the prominent features of each box (a light and a doorway) faced the same direction. The doorway panels of each box were connected to one another by a 15-cm-wide hallway, as shown in Fig. 1A, same orientation. An attempt was made to keep the rats' visual experiences in the two boxes as nearly identical as possible. The room lights were kept off. Distally, black curtains devoid of cues encircled the boxes. To obscure any overhead distal cues, a single dim light (0.9 W) surrounded by a semitransparent shade was fixed in each box near the top of the inner wall opposite the box doorway. These lights were adjusted so that they were similarly bright in each box and cast similar faint shadows on the box walls and floor. The boxes were placed such that the commutator-to-headstage cable fell in the exact center of the entire two-box/hallway apparatus. To prevent the rat from experiencing disparate angular force on his head and neck from the tug of this cable in the two boxes, a triangular dowel-rod guide track was attached to the top of each box near the doorway. A fresh, large sheet of brown packaging paper was placed under the entire two-box/hallway structure at the beginning of each recording session, to prevent scent markings or other rat-produced floor cues from accumulating. The boxes, hallway, and all exposed nuts and bolts were painted a uniform dark gray to minimize spurious reflections in the tracker data. The positions of the boxes were outlined in tape on the recording room floor to ensure consistent alignment.
Recording
Rats were implanted and recordings made using the procedures described in Skaggs and McNaughton (1998). Neuronal spike signals from the dorsal CA1 pyramidal layer were amplified by a factor of 1,000 to 5,000, band-pass–filtered between 600 Hz and 6 kHz, and transmitted to a Cheetah Data Acquisition system (Neuralynx). Signals crossing a minimal threshold, set just above background noise levels, were digitized at 32 kHz and sampled for a duration of 1 ms, beginning 0.25 ms before the spike peak. A cluster of light-emitting diodes was mounted on the headstage to allow position tracking by means of a video camera that was placed directly above the experimental apparatus and recorded with a sampling frequency of 60 Hz.
Unit isolation
Putative single neurons were isolated based on the relative action potential amplitudes and principal components from the four tetrode channels (Gray et al. 1995; McNaughton et al. 1983; Mizumori et al. 1989; Recce and O'Keefe 1989; Wilson and McNaughton 1994), by means of a semiautomatic clustering algorithm (BBClust, author: P Lipa). The resulting classification was corrected and refined manually with dedicated software (MClust, author: AD Redish), resulting in a spike train time series for each of the discriminated cells. Only single neurons satisfying standard criteria (e.g., Skaggs and McNaughton 1998) for hippocampal pyramidal cells were included.
Protocol
Rats underwent 19 to 26 recording sessions, one per day. Each session was composed of five epochs: Sleep 1 (about 30 min), Forage 1 (16–20 min), Sleep 2 (about 40 min), Forage 2 (16–20 min), and Sleep 3 (about 30 min). On odd-numbered days Box 1 was installed in position A for the first foraging epoch, then moved to position B for the second epoch. On even-numbered days the opposite was done. The swapping of boxes between epochs was done to help distinguish box-specific associations from location-specific associations.
The intervening Sleep 2 epoch allowed the rat to rest from foraging, and provided time for the box locations to be exchanged and other changes to be made to the apparatus, such as installing or removing the connecting corridor. The brown paper covering the floor was also replaced during Sleep 2.
Rats were not intentionally disoriented during this experiment. At the start of each day's session, they were transported from the colony room to the recording room along the most direct route possible. The rats were carried in a flowerpot lined with a towel. On reaching the recording room, they were deposited in another towel-lined flowerpot sitting on a cinderblock 6–12 in. away from the midpoint of the two-box apparatus. While in this flowerpot, the headstage was attached and the Sleep 1 epoch began. At the beginning of a foraging epoch, the rat was gently grasped by the experimenter, lifted from the flower pot, and deposited in box A as close to the doorway as possible, facing the center of the box. At the conclusion of a foraging epoch the rat was gently grasped with one or two hands, removed from box B, and placed back in the flowerpot to begin the next sleep epoch.
The rat's task during the two foraging epochs was always the same: to search for small chocolate pellets, one box at a time. Each epoch consisted of four 4.5-min box visits, starting in box A, moving to box B, then back to box A, and finally back to box B. During each visit, the rat was restricted to that box by a closed door. At the end of 4.5 min, the door would open and the rat would exit the box, run down the hallway, enter the other box, and resume foraging as the door closed behind it. In the opposite-orientation condition the boxes were separated by a single door, which was raised when it was time for the rat to travel to the other box. The door was then reversed before being lowered, so that the same side always faced the rat.
Rats were food deprived to promote foraging. They were offered water to drink from a 1-ml syringe at the beginning of Sleep 2. Small balls of slightly moist rat food were also sprinkled in the boxes in addition to the chocolate pellets.
For the first 16–23 days, the rats became familiar with the two-box environment and experienced a series of manipulations in the same-orientation configuration. These included, in order: turning the lights off after the start of a trial (3–4 days), introducing a white cue card into one box to visually differentiate it from the other box (4 days; this proved ineffective), placing a white towel on the floor of one box (4 days), and starting the rat in Box B instead of Box A (at most 1 day). The data from these manipulations are not presented here. Starting on day 17, 24, or 18 (for rats 1, 2, and 3, respectively), place cells were recorded as the rat experienced the 3-day sequence of conditions shown in Fig. 1B. For commonality across rats, this sequence is referred to as days D1–D3. Day D1 was a rat's first exposure to the opposite-orientation condition.
Place field calculation
For analysis purposes, each of the two foraging epochs was subdivided into four visits: first visit to box A, first visit to box B, second visit to box A, and second visit to box B. This yielded a total of eight box-visits per day, for each of which a 16 x 16 pixel spatial firing rate map, or place field, was calculated.
To facilitate further analyses, each place field was smoothed by fitting it to a two-dimensional cubic B-spline (De Boor 2001) with five segments along each axis. The spline, which is a nonparametric regression model of the firing rate map, was then used as the estimate of the cell's true spatial firing rate in that visit. The 16 x 16 pixel maps for each box visit in Figs. 3–5 and 10 are the result of this smoothing process.
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The analysis began by finding the pyramidal cells with spatially selective firing fields. The inclusion of interneurons, which fire throughout the environment and have no discernable place fields, would have skewed the measure of remapping. For each smoothed place field, of which there were eight per cell (one per box visit), the spatial information content (SIC) was calculated according to the method of Skaggs et al. (1993). To be included in the analysis, a cell's SIC value had to pass two tests in two successive visits to the same box. For example, if the cell passed the tests in visits SA1 and SA2, or OB1 and OB2 (see Fig. 1B for visit notation), it would be included.
The first test, called Imin, was an absolute measure of spatial information content: the SIC value had to be 
0.15 bits/spike. This low threshold excluded only the interneurons. Interneuron firing can have some weak spatial correlation, but because of the high spike rate the number of bits per individual spike is low.
The second test was a visit-specific statistical measure: a place field's SIC value in a given visit was compared with a distribution of SIC values for 250 "randomized" fields computed from the same spike sequence, but with randomized position data. To generate these data, the rat's actual position data were reversed in time and then divided into 10-s windows. These windows were then randomly shuffled, resulting in a new temporal sequence of positions. After each shuffle, a spatial firing rate map was constructed. The SIC values for these 250 randomized maps formed a distribution of expected values under the null hypothesis that the cell was not spatially selective. The critical value I95% for the visit was set at the 95th percentile of this SIC distribution. A cell passed the test in a given visit if the SIC of its unshuffled firing rate map exceeded this critical I95% value. This test should classify fields as spatially selective with a type I error of 
5%.
Whereas the Imin test measures a cell's intensity of firing rate variation across spatial locations, the I95% test measures a cell's consistency of firing rate within spatial locations. The I95% test therefore disqualifies two types of cells: those with unreliable fields whose firing rates are not strongly correlated with space, and those with low firing rates, for which the sample of spikes is too small to substantiate consistent spatially selective firing. In the extreme case of a cell with only a few spikes, those spikes could be from a single burst that occurred on one pass through the putative place field. In that case, shuffling the position data in 10-s windows will maintain the high SIC value, causing the cell to fail the I95% test because shuffled sequences have information content comparable to the original.
Table 1 shows that for each epoch, the number of cells that satisfied both the Imin and I95% tests was almost always less than the number that satisfied each test individually. Thus the tests are somewhat independent. If they are effective at selecting legitimate place cells, those cells should show a high degree of correlation between successive visits to the same box, illustrated in Fig. 2. In Fig. 2A, cells that failed the I95% test (95% shaded area) have substantially lower correlations between SA1 and SA2 visits than those that passed the test (5% unshaded area). The correlation between two smoothed place fields were found by calculating the pixelwise correlation coefficient of the fields, excluding undersampled pixels. In Fig. 2B, excluded cells may occasionally have high correlation values because they are interneurons that fire nearly everywhere, but they fail the Imin test because their SIC values are <0.15 bits/spike. The dashed lines in both figures mark the threshold for statistical significance of SA1 x SA2 correlations, calculated by comparing the distribution of correlations across two visits to the same box with that for the Complete Remapping distribution, described below.
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Our goal is to assess whether the hippocampus as a whole remapped between various pairs of visits, such as successive visits to the same box, or between box A and box B, or between same-orientation and opposite-orientation conditions. Because the cells' spatial firing patterns are not perfectly correlated even across visits to the same box (note the distribution of points along the x-axes in the plots in Figs. 6–9), and because random changes in individual cells might be observed even when the hippocampus as a whole does not remap, it is necessary to construct statistical tests to formally assess the degree of correlation observed between visits. Given any two visits, one can measure the correlation of place cell firing fields between those visits for all the cells in the population, yielding a distribution of correlation values. Analyses of variance can then test whether this distribution is statistically different from other distributions of interest. A total of eight salient distributions were identified, summarized in Table 2.
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The SA x SB distribution consisted of correlations between the first box A visit and the first box B visit, with one exception: the second visits had to be used for the first day of rat 1, resulting from the aforementioned recording problem in SA1.
The OA1 x OA2 distribution consisted of correlations between successive box A visits in the opposite-orientation configuration.
The SA x OA distribution contained correlations between fields from the temporally closest visits to box A in each configuration, i.e., between SA2 and OA1 on day 1, and between OA2 and SA1 on day 2. Because the boxes in the opposite-orientation configuration were rotated 90° in the room frame with respect to the boxes in the same-orientation configuration, fields from the opposite-orientation configuration were first rotated 90° before correlations were calculated. However, cells recorded during the second day for rat 1 showed a stronger correlation without rotation, and therefore were not rotated before calculating the correlations reported here.
The OX2 x OX3 distribution, where X could be either A or B, contained correlations between fields in the same box during the second visit of the first foraging epoch and the first visit of the second foraging epoch on day 3. This distribution measured consistency of fields across the intervening Sleep 2 period.
The OA x OB Before Remap distribution contained correlations between boxes A and B in the opposite-orientation configuration before remapping was observed. The onset of remapping varied across rats; because rat 1's fields remapped on first entry to box B in the opposite-orientation configuration (see RESULTS section), it was excluded from this group. Fields in box B were rotated 180° before correlations were calculated.
The OA x OB After Remap distribution contained correlations between boxes A and B in the opposite-orientation configuration after remapping had been observed. Fields in box B were rotated by 180° before correlations were calculated for the first 2 days of recording, but were not rotated on the third day.
The Complete Remapping distribution modeled the expected distribution of correlations between place fields when the hippocampus remapped completely. To estimate this distribution, cells' box A firing fields were correlated with the box B firing fields of other cells, on different tetrodes, within the same dataset. Because some cells had fields in only one box, this estimate includes cases where a cell remaps by gaining or losing a field between boxes.
Once again, these eight groups are distributions of correlations between two place fields for a cell. When computing these distributions, if neither field was spatially selective (SIC value failed to exceed I95% and Imin), that correlation was excluded from the distribution because the cell was considered uninformative about the similarity of representations in the two environments.
For the bulk of the analysis, correlations were measured by calculating the Pearson r correlation coefficient. This requires first normalizing each place field by its variance. A drawback of this approach is that if a cell remaps by changing only its firing rate and not the shape of its firing field, the correlation between normalized fields will be high and no remapping will be detected. Such "rate remapping" has been reported by Lever et al. (2002a) and Hayman et al. (2003). Therefore to test for systematic rate differences across conditions, we also computed a second set of eight distributions using the following difference metric in place of the Pearson r correlation
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P-HMM reconstruction
By averaging over several minutes, rate maps provide a robust estimate of place cells' overall spatial firing patterns, which permits the discovery of heterogeneous behavior within the cell population, such as varying degrees of partial remapping. We also performed a complementary analysis, population reconstruction, which assumes homogeneity within the population to reconstruct a variable of interest, such as the animal's location, from the activity of many cells within a small window of time.
Our population reconstruction analysis used three box visits during which the same cells were recorded: two Reference visits, one from each box, between which remapping was observed, and a Test visit which could be from either box. The Test visit was divided into time windows of 250 ms and, for each window, t, a spike count vector Nt(1...C) was created containing the number of spikes recorded from each cell, 1 c C. The results of the analysis then indicated whether the spike count vector during each Test time window was more likely to have been generated by the box A or box B map, or whether the cells were inactive.
A Poisson hidden Markov model (P-HMM) was constructed from the rate maps of each pair of Reference visits to provide a model of the expected distribution of spike count vectors in either box. The P-HMM used three states: Box A, Box B, and Quiescent. The state transition probabilities were weighted strongly in favor of remaining in the same state (P = 0.97), which was intended to reflect the idea that transitioning between maps occurs much less frequently than traveling within a map. Transitions from a state to either of the other two states had a probability of 0.015. The P-HMMs were defined to output spike count vectors of length C.
It was assumed that spikes from a place cell occurred according to a Poisson distribution whose mean depended on the rat's location, and that place cells were conditionally independent of each other, given the hippocampal map and the rat's location. These assumptions were used in the Bayesian reconstruction methods in Zhang et al. (1998), the statistical machinery they develop being similar to the present approach.
Based on these assumptions, each element of the P-HMM's output vector was Poisson distributed and independent of the other elements. Specifically, for a given time window t, the distribution of spike counts for element c was modeled as
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The Quiescent state was associated with rate maps whose values were all zero, representing a state in which no cells were active. This proved to be an important inclusion in the P-HMMs because during the beginning of a visit cells sometimes showed little activity. When only a handful of cells were recorded, this could be interpreted as representing the activity patterns of the "wrong" box.
The reconstruction process was based on the supposition that a P-HMM was the generative model of the spike count vectors recorded in the Test visit. The Viterbi algorithm (Forney 1973), the standard algorithm for inferring an HMM's sequence of "hidden" states from a sequence of its outputs, was used to infer from the observed spike counts the most likely sequence of active hippocampal maps.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Eight distributions of place field correlation coefficients were computed from the 160 place cells as described in ANOVA groups in METHODS and Table 2. Two of these distributions, the No Remapping and the artificially constructed Complete Remapping distributions, were included as baseline measures of what the distribution of place field correlation coefficients should be in the extreme cases of no or complete remapping. The other six distributions were compared with each other and with these two baseline distributions to assess the extent to which remapping occurred under various conditions.
Remapping occurred in the opposite-orientation configuration
All eight distributions listed in Table 2 were analyzed together using a Kruskal–Wallis nonparametric ANOVA, which showed significant differences among them (
72 = 1291.3; P << 0.001). Post hoc comparisons revealed no significant differences among the first six (P > 0.5), including the No Remapping distribution, suggesting that the same hippocampal map was being recalled in each of the conditions measured by these distributions. Post hoc comparisons also revealed significant differences (P << 0.001) between these first six distributions and the last two (the OA x OB After Remap distribution and the artificially constructed Complete Remapping distribution), There were no significant differences between the OA x OB After Remap and Complete Remapping distributions (P 
0.1). Thus remapping was observed only in the OA x OB After Remap distribution, and the degree of remapping was statistically indistinguishable from a complete remapping.
No remapping detected in the same-orientation configuration
Although Skaggs and McNaughton (1998) observed partial remapping between the two boxes in the same-orientation configuration, there was no evidence for remapping between boxes in the corresponding condition in this study, including those visits subsequent to opposite-orientation sessions. The median correlation values of the same box (SA1 x SA2) and different box (SA x SB) distributions were both 0.71. Post hoc comparisons between same box and different box correlations revealed no significant difference (P > 0.5).
A Kruskal–Wallis nonparametric ANOVA revealed no significant differences among the six sets of fields (3 rats x 2 days) that constituted the SA1 x SA2 group, our prototypical No Remapping group (52 = 4.8; P 0.44). Similarly, no significant differences among the six sets of fields that constituted the SA x SB group were observed (52 = 9.25; P 0.1). A visual comparison of SA fields to SB fields in Figs. 3–5 confirms that cells behaved similarly in the two boxes. Figure 6 compares the correlations in the same box (SA1 x SA2) distribution with the different box (SA x SB) distribution. Cells tend to cluster near the 45° line, meaning that their correlations between boxes are similar to their correlations between visits to the same box.
Same-orientation box A fields were maintained in the opposite-orientation condition
For all three rats, the box A fields in the opposite-orientation condition were isomorphic to those in the same-orientation condition. For each visit, we found the best fitting rotation from among 0, 90, 180, or 270°, and then computed the correlation. The best-fitting rotation was 90° in all but one case. The median correlation between fields in the temporally closest same-orientation and opposite-orientation box A visits (SA x OA) was 0.61. Post hoc comparisons showed no significant difference between this distribution and the same-box distributions from either configuration (SA1 x SA2 and OA1 x OA2, P > 0.5).
A Kruskal–Wallis nonparametric ANOVA revealed significant differences among the six sets of correlations that constituted the SA x OA distribution (3 rats x 2 days; r52 = 16.0; P < 0.01). The rat 1, day 2 set had the lowest median correlation of the six (0.49), and post hoc comparisons showed that the rat 1, day 2 SA x OA correlations were significantly lower than the rat 2, day 2 set (P < 0.05).
To understand to what extent these differences were attributable simply to differences in overall place field stability among recording sessions, each SA x OA distribution was compared with the corresponding SA1 x SA2 distribution using Kolmogorov–Smirnov tests. Only during the second day of rat 1 was there a significant difference (D25,25 = 0.54, P < 0.002), suggesting that variations in SA x OA correlations were indeed linked to varying place field stability. Even for the rat 1, day 2 set, the SA x OA group median of 0.49 suggests at most a partial remapping between configurations.
The second day in rat 1 was different from the others in that, despite the rotation of box A by 90° between the opposite-orientation and same-orientation configurations, the place fields did not rotate. Figure 7A compares the within-configuration box A correlations to the between-configuration box A correlations for each rat and each day. Except for this second day in rat 1, cells that showed consistent fields in box A between visits in the opposite-orientation configuration also showed consistent fields across configurations when rotated by 90°. Figure 7B shows the within-configuration versus between-configuration plots for rat 1, day 2 for the four possible rotations of the fields consistent with the shape of the box walls. Only the 0° rotation shows a strong positive correlation.
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Overall, box A place fields were as stable between visits in the opposite-orientation configuration as in the same-orientation configuration. The OA1 x OA2 median correlation was 0.67, which was not significantly different from the SA x SB distribution (P > 0.5). However, a Kruskal–Wallis nonparametric ANOVA revealed significant differences between the six sets of fields that constituted the OA1 x OA2 distribution (3 rats x 2 days; 52 = 13.5; P < 0.02). The rat 1, day 2 group again had the lowest median (0.57), and post hoc comparisons showed it to be significantly lower than the median for the first day for the same rat (P < 0.05). No other differences were significant.
Box B fields eventually differed from box A in the opposite-orientation configuration
For all three rats, place cells eventually showed completely different fields between boxes A and B in the opposite-orientation configuration. However, the rats differed with respect to the visit in which box B differentiation first occurred. Rat 1's place fields remapped on first visiting box B in the opposite-orientation configuration (Fig. 3, visit OB1 day 1). Rat 2's fields remapped on its second visit to box B (Fig. 4, visit OB2 day 1). Rat 3's fields remapped on its third visit to box B (Fig. 5, visit OB1 day 2).
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A Kruskal–Wallis ANOVA was performed on the first five pairs of opposite-orientation between-box visit correlations from each rat (i.e., OA1 x OB1 on days 1 and 2, OA2 x OB2 on days 1 and 2, and OA1 x OB1 on day 3) and the No Remapping (SA1 x SA2) distributions. Significant differences were observed consistent with the previously described timing of remapping for each rat (152 = 138.0; P << 0.001). Post hoc comparisons showed the following.
RAT 1. There were no significant differences among the five visit pairs, which is consistent with the rat remapping on first exposure to the opposite-orientation condition. None of these was significantly different from any of the other "remapped" visit pairs (P > 0.5). The second visit pair of the second day yielded the largest number of cells with spatially selective fields in at least one box (24), and the between-box correlations during the second visit pair of the second day were significantly lower than the first visit pair of rat 2, which had not remapped yet (P < 0.05).
RAT 2. The first visit pair showed significantly stronger correlations than the following four (P < 0.005), which were not significantly different from the other "remapped" visit pairs (P > 0.5). This is consistent with the rat remapping on second exposure to the opposite-orientation condition.
RAT 3. Only two cells were recorded during the first two visit pairs (day 1); they both showed strong correlations between boxes. By contrast, in the third and fourth visit pairs (day 2), none of the eight cells showed even a weak correlation between boxes. Correlations in the fifth visit pair (day 3) were similarly low, but the small sample size (four cells) was not sufficient to show a statistical difference between these OA x OB pairs and the SA1 x SA2 distribution. Nonetheless, the values for the third and fourth visit pairs were significantly lower than for the first visit pair of rat 2 (P < 0.025), consistent with the rat remapping at the beginning of day 2.
The between-box correlations for the visits just before remapping in rats 2 and 3 were combined into an OA x OB Before Remap distribution (median correlation 0.67), and the between-box correlations for the visit initially showing remapping in all three rats were combined into an OA x OB After Remap distribution (median correlation 0.06). OA x OB Before Remap showed high correlation values and was not significantly different from either same-box correlation group (SA1 x SA2 or OA1 x OA2, P > 0.5). By contrast, OA x OB After Remap was significantly different from OA x OB Before Remap (P < 0.001), and not significantly different from the artificially created Complete Remapping distribution (P > 0.5).
Place fields on day D3 were stable across epochs
Figure 9 shows, for day D3, how the place fields correlated between boxes as a function of how they correlated between successive visits to box A. The correlations were measured without rotation, because two cells each recorded from rats 1 and 2 appeared to show consistent fields between boxes when not rotated (Fig. 10). The third rat showed equally low correlations for all four rotations consistent with the box shape (0, 90, 180, and 270°).
The OX2 x OX3 day 3 distribution, constituting box A and B field correlations between the second visit of the first foraging epoch and the first visit of the second foraging epoch, was not significantly different from any of the other nonremapping distributions (P > 0.5). A Kruskal–Wallis ANOVA comparing the six sets of correlations in this distribution (2 boxes x 3 rats) showed no significant differences among them (52 = 6.6; P 0.25). Thus all rats were remapping between boxes on day D3, and the maps were stable across the two opposite-orientation epochs.
No evidence of rate remapping in the absence of field remapping
The main Kruskal–Wallis ANOVA was recalculated using the same distributions in Table 2 but using a place field difference metric (Eq. 1) that is strongly sensitive to absolute rate variations. Again, significant differences were found (72 = 1268.8; P << 0.001). Post hoc comparisons again found no significant differences between the first six distributions (P > 0.5), but significant differences between these six distributions and the OA x OB After Remap distribution (P << 0.001). The median D values for the SA1 x SA2 and OA x OB Before Remap distributions were 0.37 and 0.42, respectively, whereas the median D value for the OA x OB After Remap was 0.74. The median D value of the Complete Remapping distribution (0.81) was found to be even higher than that of the OA x OB After Remap distribution (P < 0.01), although this difference is likely explained by the artificially constructed nature of the Complete Remapping distribution. Absolute firing rates are likely to vary between cells to a greater degree than between conditions for the same cell, and tetrode cell isolation techniques do not generally produce an equal sampling of spikes from all cells.
Population dynamics within a session
We analyzed the temporal dynamics of place cells during opposite-orientation box A and B visits on the day in which remapping was first observed. The purpose of the analysis was to determine to what extent place cells showed activity consistent with the same map throughout the visit (see P-HMM reconstruction in METHODS) For each rat, a Poisson hidden Markov model (P-HMM) was constructed using firing rate maps from Reference visits OA2 and OB2. These box A and box B Reference visits were used as archetypes of the firing patterns expected in each box subsequent to remapping between them. (Place field correlations indicated that place cells completely remapped between these visits.) Spike trains from two Test visits, OA1 and OB1, recorded just before the Reference visits, were then analyzed by inferring the sequence of P-HMM states (Box A, Box B, or Quiescent) most likely to have generated each spike train.
The sequences of inferred states for the Test visits of each rat are shown in Fig. 11. The top graph for each rat shows the reconstruction performed on the box A Test visit, providing a baseline indication of how well the reconstruction method was able to infer the identity of the box. The bottom graph for each rat shows the reconstruction performed on the box B Test visit. For rats 1 and 3, the box B reconstructions are consistent with the fields having remapped on entry into the box. Interestingly, the likelihood of the Quiescent state being active decreases with time in both cases (Rat 1: r = –0.28, P < 0.005; Rat 3: r = –0.22; P < 0.02), suggesting that cell firing became more robust as the visit progressed. This phenomenon is similar to that reported by Wilson and McNaughton (1993) and by Mehta et al. (1997).
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To ascertain how well the place cell firing patterns were fit by the box B state, two portions of the box visit were defined: the box B portion (t < 27 s) and the box A portion (t > 27 s). Four groups of P-HMM log observation likelihoods were then analyzed: P(Nt|Box A), 0 < t < 27 s; P(Nt|Box B), 0 < t < 27 s; P(Nt|Box A), t 27 s; and P(Nt|Box B), t 27 s). A Kruskal–Wallis ANOVA was performed on the four groups and found significant differences (32 = 226.1; P << 0.001). Post hoc comparisons revealed that groups P(Nt|Box B), 0 < t < 27 s and P(Nt|Box A), t 27 s were not significantly different, yet both groups' median correlations were significantly higher than group P(Nt|Box B), t 27 s, suggesting that the box B state was characterizing the first 27 s of population activity nearly as well as the box A state characterized the remainder of the session.
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Linear path integration could in principle have differentiated the two boxes in the same-orientation configuration, and might account for the partial remapping Skaggs and McNaughton observed (Touretzky 2004). No partial remapping, not even rate remapping, however, was observed under nearly identical conditions in the present experiment. Skaggs and McNaughton's rats were naive to the apparatus, whereas our rats had already undergone 16–23 days of trials in the same-orientation configuration. Therefore to rule out experience-dependent effects, data were examined from the rats' first 2 days of exposure to the apparatus, i.e., days 1 and 2 of the 19- to 26-day recording sequence. In these first 2 days, the between-box correlations were actually slightly stronger than the within-box, between-epoch correlations (P < 0.05), indicating that partial remapping did not occur even at the beginning of the experiment.
One seemingly minor difference is that Skaggs and McNaughton did not use a movable door to confine their rats to a single box. Instead, they provided food rewards in only one box at a time, which encouraged the rat to stay in the rewarded box until reward delivery was shifted to the other box. Another difference is that the light in the Skaggs and McNaughton experiment was dimmer and better shielded than in the present experiment. We do not know whether these differences are the critical ones underlying the difference in results.
When the rats in this experiment left box A, traveled down the corridor, entered box B, and ended up back on the box A map, did they jump to it abruptly or transition smoothly? To see whether an abrupt change in map, or position within a map, was detectable in our data, we generated sets of ensemble activity patterns for rat 2 on days D1 and D2 and rat 1 on day D2 as they traveled from box A through the corridor and into box B. (Rat 3 had too few cells to be included in this analysis.) The patterns were constructed by dividing each visit into 500-ms bins and computing the average spike rate of each cell within each bin. We then looked at a trajectory from box A through the corridor and into box B, measuring the maximum correlation at each time step between the current activity pattern and the activity pattern at the entrance to box A, which is also the expected pattern in box B because the rats were not remapping between boxes. When the rats entered box B from the corridor, we did not see any evidence that the correlation increase was sudden, as would be expected if the hippocampal representation abruptly changed from that of the corridor to that of the box A map. However, given the paucity of trajectories through the corridor, it is unlikely that such a jump would be detectable in the present data.
If the hippocampus did not abruptly jump between maps in this condition, one possible explanation is that the representation of the apparatus formed a non-Euclidean map in which the same box A doorway could be smoothly entered from either end of the straight corridor. The inability of the linear path integrator to differentiate two same-orientation boxes, even after place fields were remapping in the opposite-orientation condition, is a striking demonstration of the difference between linear and angular idiothetic information.
Opposite-orientation case
The opposite-orientation portion of the experiment tested the influence of both linear and angular path integration on place fields. All three rats eventually exhibited different maps in the two boxes when their orientations were 180° apart. For rats 2 and 3, however, this result did not emerge until the second or third box B visit, respectively.
Several experiments have shown that repeated instances of orientation discordance can weaken visual cues' control of place fields. Knierim et al. (1995) showed that repeatedly disorienting rats before placing them in a cylinder with a white cue card along the wall prevented the card from acquiring directional control of place fields. The disorientation would have caused the card to appear at a different allocentric bearing on each trial. In a subsequent experiment, Knierim et al. (1998) introduced a conflict between visual and vestibular cues by rapidly rotating the cylinder wall and floor through an angle of 135–180° while the rat remained inside. The rat's visual system would indicate no self-motion under these conditions, whereas its vestibular system would sense the rotation. Knierim et al. found that place cells could remap in this situation, and head direction cells could fail to stay aligned with the cue card.
When the rat entered box B in the present experiment, visual landmarks would indicate that the world had rotated by 180°, whereas its vestibular sense would deny that any rotation had occurred—the complement of the Knierim et al. (1998) scenario. However, if either type of discordance between visual landmarks and the rat's internal direction sense weakens the landmarks' control of place fields, it follows that repeated trips between boxes A and B in the opposite-orientation configuration should eventually lead to the abandonment of the box A map in box B.
Rat 1 seemed to be the most sensitive to orientation discordance because its cells remapped immediately on entering box B in the opposite-orientation configuration, in visit OB1 on day D1. They continued to remap during visit OB2, and again on day D2 in visits OB1 and OB2; but then, after the sleep period between epochs, when the rat was again passively transported to box A—now in the familiar side-by-side configuration—its fields maintained the same orientation relative to the room as before, rather than rotating by 90° to align with the within-box cues. (See Fig. 3, visit SA1 on day D2.) In this rat, after experiencing just two opposite-orientation epochs constituting four trips from box A to box B, the visual cues appear to have lost directional control of place cells. Jeffrey and O'Keefe (1999) previously showed that rats could learn to ignore visual cues and follow idiothetic cues when a prominent visual cue repeatedly shifted location.
Rats 2 and 3 continued to use a 90° rotation of the box A map in the same-orientation configuration. (Compare visits OA1 and OA2 with visits SA1 and SA2 on day D2, Figs. 4 and 5.) It is significant that the rats entered box A at the start of the SA1 visit by passive transport. Stackman et al. (2003) showed that rats do not integrate vestibular and optic flow cues accurately when transported passively through a 180° heading change. The 90° rotation in the present experiment may therefore have been barely noticeable. In contrast, the rats always entered box B by active locomotion, so they should have been able to maintain their angular orientation (Taube and Burton 1995). The 180° heading change required to realign the box A map with the box B landmarks would have been highly salient.
Another possible response to orientation discordance is for place fields to both remap and dissociate (follow different sets of cues), as seen in double-cue rotation tasks (Knierim 2002; Tanila et al. 1997). Dissociation was not observed in the present experiment, possibly because there were no distal cues; the room was kept dark and within-box illumination was faint. So the discordance perceivable to the rats was between visual and vestibular inputs, not between competing sets of visual cues. The outcome might have been different if the rats had access to prominent room cues. What distinguishes our result from previous discordance results, specifically the double-cue rotation experiments of Tanila et al. (1997) and Knierim (2002), is that the remapping was complete, and in two of the three rats, the remapping was delayed rather than immediate. The delay suggests that the remapping is dependent on some representation of the animal's cumulative experience (Bostock et al. 1991): it cannot be explained as a direct consequence of a sensory manipulation.
Place field "doubling" in identical boxes is consistent with the boundary vector cell model of Hartley et al. (2000) and demonstrations of field-doubling effects by Lever et al. (2002b). Because boundary vector cells are sensitive to allocentric bearings, a change in the rat's internal orientation, or failure to reset its orientation when entering a rotated version of a familiar environment, would result in place cell remapping.
Remapping versus map extension
We define two maps as distinct if there is no continuous path from a place on one map to a place on the other. If such a path exists, then the two maps are really just different regions of the same map. In topological terms, a "place" is a vector of place cell firing rates and a "map" is a collection of such vectors forming a two-dimensional manifold. Maps are distinct if the manifolds do not intersect.
The appearance of a separate box B map in the opposite orientation condition could arise in two ways. The rat could be literally remapping, i.e., jumping from the initial manifold to a separate manifold containing the box B map. Or the rat could be using a single manifold for the entire apparatus, but the portion containing the box B activity patterns might initially be unobservable because the rat jumped (or smoothly transitioned) back to the box A portion of the manifold on entering box B. In this situation, the subsequent change in box B patterns we attributed to "remapping" (jumping to a new manifold) would actually be the result of the rat's no longer resetting its position on the current manifold.
The P-HMM reconstruction for rat 2 is consistent with the notion that the rat extended the box A map into box B rather than switching to a new map. Because remapping in box B did not emerge until the second visit on day D1, we can compare firing fields of the same cells before the emergence (visit OB1) and afterward (visit OB2). Figure 11C shows that during visit OB1, the rat started out using what would later appear as the box B map. It switched to the rotated box A map after about 27 s. This is consistent with the rat initially maintaining its orientation sense during the first 27 s of the box B visit, which would be natural if the box B map were simply an extension of the existing box A map through the doorway and into additional territory.
The argument would be strengthened if place fields spanning the two boxes could be found. We did see a few such fields, but they appeared to be tied to the doorway because they did not remap when the rat adopted a separate representation for box B.
Although remapping in the opposite-orientation configuration was complete on day D2, there is a hint of partial remapping on day D3 (Fig. 10). Rat 1 had three cells and rat 2 had two cells that appeared to stay in the box A reference frame, displaying similar fields in box B despite the fact that the cues were 180° opposite. (However, cell 4 and possibly also cell 1 in Fig. 10 are exhibiting rate remapping.) The remaining cells recorded on day D3 remapped between boxes. This suggests either that the remapping on day D2 was substantial but not actually complete, or else the rats' representation for the task had begun evolving in a new direction by day D3. To date there have been no reports of two completely distinct hippocampal states becoming more similar over time, so the former hypothesis seems more likely.
In conclusion, linear and angular path integration function differently in the rat. Linear path integration appears easily overridden by visual landmarks, whereas angular path integration is more sensitive to cue discordance. In the present experiment, although repeated visits to the two boxes in the same orientation condition produced no measurable remapping, one to three visits in the opposite orientation condition prompted (nearly) complete remapping. That this remapping was both delayed and abrupt suggests a sudden failure to reset idiothetic representations, rather than a gradual adaptation of the hippocampal code.
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Address for reprint requests and other correspondence: D. S. Touretzky, Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213-3891 (E-mail: dst{at}cs.cmu.edu)
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