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Coordinated memory replay in the visual cortex and
hippocampus during sleep
Daoyun Ji & Matthew A Wilson
Sleep replay of awake experience in the cortex and hippocampus has been proposed to be involved in memory consolidation. However, whether temporally structured replay occurs in the cortex and whether the replay events in the two areas are related are unknown. Here we studied multicell spiking patterns in both the visual cortex and hippocampus during slow-wave sleep in rats. We found that spiking patterns not only in the cortex but also in the hippocampus were organized into frames, defined as periods of stepwise increase in neuronal population activity. The multicell firing sequences evoked by awake experience were replayed during these frames in both regions. Furthermore, replay events in the sensory cortex and hippocampus were coordinated to reflect the same experience. These results imply simultaneous reactivation of coherent memory traces in the cortex and hippocampus during sleep that may contribute to or reflect the result of the memory consolidation process.
The hippocampus is essential for episodic memory1,2. The dominant theory of system memory consolidation proposes that active commu- nication between the cortex and hippocampus transforms new mem- ory in the hippocampus into long-term memory stored in the cortex3,4. Recent studies have provided electrophysiological evidence for the involvement of the hippocampus and neocortex in memory processing during sleep, reflecting either active participation in the process of memory consolidation as proposed in theoretical models5,6^ or reacti- vation of consolidated memory traces. First, electroencephalogram (EEG) events between the cortex and hippocampus are correlated7–11, suggesting the two areas are engaged in active interaction during sleep. Second, cell pairs that are correlated during awake experience are also correlated during subsequent sleep within the hippocampus12–14, within the cortex^15 , and between the hippocampus and cortex^16. These pairwise correlation results and other correlation-based analy- sis^17 imply that the experience-related neuronal activity is, to some degree, reactivated during sleep. However, the reactivation in these studies lacks the specificity presumably required for episodic memory, which includes a cascade of temporally ordered events encoded by a unique sequence of activation of different neuronal populations within the cortex, within the hippocampus, or both18,19. If sleep reactivation is somehow involved in the processing of episodic memory traces, this sequential structure should be specifically replayed. Indeed, replay of specific ensemble-level patterns has been utilized in a detailed model of memory consolidation^6. Therefore, it is important to experimentally study the more specific high-order replay, in which a temporally sequential firing order across multiple cells is recaptured during sleep. Such high-order replay has been observed in the hippocampus during slow-wave sleep (SWS)20,21^ and rapid-eye-movement sleep^22. However, whether high-order replay exists in the cortex remains
unknown. More importantly, the relationship between replay events in the cortex and hippocampus has not been studied. The present study was designed to address these issues by recording spiking activity in both the visual cortex and the hippocampal CA1 area of rats during active maze-running and during natural sleep (Fig. 1). As we examined a primary sensory area that is not explicitly driven by the hippocampus, any observed replay was more likely to reflect broad cortical reactiva- tion not limited to directly hippocampus-driven activity. Four rats were trained to sleep for 1–2 hours (PRE), followed by an awake session (RUN) during which they alternated between two trajectories (leftright and rightleft) on a figure-8 maze, followed by another 1–2 hours sleep session (POST). We found that high-order replay of RUN firing patterns occurred not only in the hippocampus but also in the visual cortex during SWS, and the replays in the two areas were coordinated to represent the same coherent awake experience.
RESULTS Firing patterns during SWS in the cortex and hippocampus We first searched for spiking patterns at the population level in the visual cortex and hippocampus during SWS. In the neocortex, cells display active depolarized (up) and silent hyperpolarized (down) states in vitro23–25, in anesthetized animals and during SWS26–29. Cortical cells both within and across different cortical regions switch between up and down states synchronously9,26,27. In agreement with these previous results, we observed that cells across different layers in the visual cortex displayed synchronized stepwise increases and decreases in multiunit activity during SWS (Fig. 2a). More specifically, we observed periods of 80–300 ms during which the entire population of the recorded visual cortical cells were silent. These periods of silence were followed by increases in activity across the population lasting up to a few seconds.
Received 28 June; accepted 30 November; published online 17 December 2006; doi:10.1038/nn
The Picower Institute for Learning and Memory, RIKEN-MIT Neuroscience Research Center, Department of Brain and Cognitive Sciences and Department of Biology, Massachusetts Institute of Technology, Building 46, Room 5233, 43 Vassar Street, Cambridge, Massachusetts 02139, USA. Correspondence should be addressed to M.A.W. (mwilson@mit.edu) or D.J. (dji@mit.edu).
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We refer to these active periods as frames. We are using the term ‘frame’ rather than ‘up state’ because we identified the phenomenon by changes in multiunit activity rather than EEG rhythms or intracellular potentials, and because similar structure also exists in the hippocampus (see below) where no intrinsic up and down states have been reported. On average, cortical frames occurred at a rate 47.3 ± 2.1 min–1^ (mean ± s.e.m.) during SWS (n ¼ 20,545 during 20 sleep sessions from four rats). There was no difference in occurrence rate between PRE and POST (PRE, 44.3 ± 3.5 min–1; POST, 49.9 ± 3.3 min–1; P ¼ 0.193, t-test). The frame durations were distributed widely between 0.1 and 3 s with a mean 0.96 s and median 0.67 s, whereas the mean and median durations of the interframe silent periods were 0.17 s and 0.13 s, respectively (Fig. 2b). Cortical frames during POST had slightly shorter durations (PRE, mean 1.1 s, median 0.73 s; POST, mean 0.90 s, median 0.65 s; P ¼ 2.2 10 –15, rank-sum test) and slightly higher within-frame multiunit firing rates per tetrode (PRE, mean 54.5 Hz, median 48.3 Hz; POST, mean 58.7 Hz, median 54.1 Hz; P ¼ 1.2 10 –19, rank-sum test) than those during PRE. As shown in Figure 2a, the interframe silent periods were correlated with positive peaks of EEG K-complexes^28 in layer 5. This observation was confirmed by frame start- and end-time– triggered EEG averages (Fig. 2c). On average, the cortical frames ended about 20 ms earlier than the K-complex positive peaks, and they started about 50 ms earlier than the K-complex negative peaks. Because depth-
positive EEG events are reliably associated with down states28,29, the result imply that the interframe silent periods were produced by cortical cells’ simultaneous switch to the down state, and that frames were formed when cells rebounded to the active up state. Whereas up and down states have been observed in neocortical cells, hippocampal cells have not been reported to display such intrinsic states. Despite this, we observed that the hippocampal neuronal population also displayed during SWS synchronized periods of increased and decreased multiunit activity: that is, frame and silent periods (Fig. 2a). On average, hippocampal frames occurred at a rate of 41.7 ± 2.9 min–1^ during SWS (n ¼ 19,189 during 20 sleep sessions from four rats). There was no significant difference in occurrence rate between PRE and POST (PRE, 40.0 ± 4.1 min–1; POST, 43.5 ± 4. min–1; P ¼ 0.35, t-test). Hippocampal frames had shorter duration (mean 0.78 s, median 0.50 s, P ¼ 0, rank-sum test) than the cortical frames, and they were separated by longer interframe silent periods (mean 0.50 s, median 0.22 s, P ¼ 0, rank-sum test) (Fig. 2b). Like cortical frames, hippocampal frames during POST had slightly (and insignificantly) shorter durations (PRE, mean 0.81 s, median 0.49 s; POST, mean 0.76 s, median 0.50 s; P ¼ 0.41, rank-sum test) and slightly higher multiunit firing rates per tetrode (PRE, mean 63.0 Hz, median 58.1 Hz; POST, mean 67.6 Hz, median 61.5 Hz; P ¼ 0.040, rank-sum test) than those during PRE. Hippocampal frames were correlated with
a CA
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Figure 1 Experimental design. (a) On each recording day, there were three recording sessions: a 1–2 hour sleep session (PRE), a 20–40 minute maze- running session (RUN), and another 1–2 hour sleep session (POST) after the run. (b) During the RUN sessions, rats were trained to run an alternation task on a figure-8-shaped maze. All the visited position points during a typical RUN session are plotted to show the shape of the maze. Rats had to alternate between the red (leftright) and blue (rightleft) running trajectories to receive a reward at R or L. The arrows mark the running directions. (c) We implanted tetrodes to record CA1 cells in the hippocampus and cells in the visual cortex. Histology micrographs show two lesion spots (arrows), which mark the tetrode tip locations, in the CA1 pyramidal cell layer (‘CA1’), and two in the deep layers of the primary visual cortex V1 (‘visual’).
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Figure 2 Visual cortical and hippocampal spiking activities were organized as frames during SWS. (a) Cortical (CTX) and hippocampal (HP) frames during a 5-s SWS episode. Each tick represents a spike and each row includes all multiunit spikes recorded from one tetrode. Triangles, frame start times; circles, frame end times. Cortical EEG in layer 5 (L5, top) and hippocampal EEG within the ripple band (bottom) are displayed for the same time period. Dotted boxes mark a K-complex (top) and a ripple event (bottom). Scale bars, 1.5 mV for L5, 0.5 mV for ripple. (b) Distributions of durations of frames and interframe silent periods in the cortex and hippocampus. (c) Cortical EEG averages (mean ± s.e.m., s.e.m. represented by thickness of the curves) triggered by cortical frame start and end times. (d) Occurrence rate (mean ± s.e.m., n ¼ 20 sleep sessions) of hippocampal ripple events within hippocampal frames (F) and within interframe silent periods (S). (e) Average cross-correlogram (mean ± s.e.m., n ¼ 20 sleep sessions) between cortical and hippocampal frame start times and between their end times. Here the cortex was the reference, meaning a peak at positive time would indicate that the cortex led the hippocampus. Bin size, 10 ms.
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probability measures the significance of a match between a frame sequence and a template sequence. Unless otherwise specified, we used a threshold p o 0.05 to determine whether a sleep frame was a signi- ficant match. Such a frame is referred to as a replaying frame. Due to the discrete nature of the matching probability p (see Supplementary Methods for details), the exact cutoff threshold depended on the number of cells active in a frame and ranged between 0.028 and 0.049 (Supplementary Table 1 online). A frame with less than four active cells could not reach this threshold to be considered significant; thus, a replaying frame necessarily contained at least four active cells. For example, both the cortical and the hippocampal frames shown in Figure 4 were replaying frames. The cortical frame con- tained the sequence 0132567 with I ¼ 0.91 and p ¼ 0.0014. The hippocampal frame contained the sequence 01235 with I ¼ 1 and p ¼ 0.0083. More examples of sequence replays are shown in Supplemen- tary Figure 5 online. To compute the overall replay effect, we counted the number of replaying frames out of the total number of candidate frames, defined as those containing at least four active template cells, during SWS within last hour in PRE and within first hour in POST. In the cortex, out of 3,070 PRE and 5,808 POST candidate frames, we identified a total of 163 PRE and 366 POST replaying frames. In the hippocampus, out of 849 PRE and 1,555 POST candidate frames, we identified a total of 39 PRE and 121 POSTreplaying frames. The ratio between replaying and candidate frame numbers, averaged across all the template sequences, was significantly higher during POST than during PRE in both the cortex (PRE, 0.052 ± 0.008; POST, 0.073 ± 0.009; P ¼ 0.027, paired t-test, n ¼ 12 templates) and hippo- campus (PRE, 0.049 ± 0.011; POST, 0.080 ± 0.007; P ¼ 0.0057, n ¼ 15 templates). There- fore, in both the cortex and hippocampus, there were significantly more replaying frames during POST than PRE, indicating that the replay was experience dependent. The replay- ing ratios for every individual template sequence (trajectory) are listed in Supple- mentary Table 2 online for cortical templates and in Supplementary Table 3 online for hippocampal templates. We then investigated the properties of these replay events. First, the
ratio in POST decayed back to that of PRE after about 40 min in the cortex (ratio during first 20 min, 0.064 ± 0.011; second 20 min, 0.088 ± 0.013; third 20 min, 0.058 ± 0.009; fourth 20 min, 0.054 ± 0.012), and after about 1 h in the hippocampus (ratio during first 20 min, 0.064 ± 0.006; second 20 min, 0.089 ± 0.012; third 20 min, 0.072 ± 0.017; fourth 20 min, 0.054 ± 0.017). Second, the template sequences were compressed in these replaying events in both the cortex and hippocampus by a similar factor about 5–10 (Supplementary Fig. 6 online). Third, small differences in frame properties between PRE and POST did not contribute to the observed difference in replaying ratios (Supplementary Fig. 7 online). Fourth, there was no difference in within-frame multiunit firing rate, within- frame RUN-active-cell firing rate or frame duration between replaying and non- replaying candidate frames (Supplementary Fig. 8 online). Therefore, the replay identified by the sequence match- ing method was not biased by differences in these factors between PRE and POST frames. We then examined whether the observed numbers of replaying frames significantly deviated from those expected by chance, using two methods to evaluate the significance. First, we computed the theoretical distribution of replaying frame numbers by assuming a binomial process in which every frame independently matches a template sequence at the same probability as the cutoff threshold. This distribution is referred to as chance distribution. We compared the observed numbers of replaying frames with those expected from the chance distribution (Fig. 5a,b). For all the trajectories combined, the observed numbers in the visual cortex were statistically significant in both POST (n ¼ 366, P o 1 10 –38) and PRE (n ¼ 163, P ¼ 1.4 10 –6). In the hippocampus, the observed numbers were significant in POST (n ¼ 121, P ¼ 8.1 10 –12), but not in PRE (n ¼ 39, P ¼ 0.16). We repeated the analysis for each individual rat. In the cortex, the observed replaying frame numbers during POSTwere significant for all four rats (rat 1, P ¼ 5.0 10 –11; rat 2, P ¼ 2.8 10 –11; rat 3, P ¼ 0.00031; rat 4, P ¼ 0.0028), whereas the numbers during PRE were significant for two rats (rat 1, P ¼ 1.4 10 –5; rat 4, P ¼ 0.00041), close to being significant for another (rat 3, P ¼ 0.067) and not significant for the last (rat 2, P ¼ 0.50). In the hippocampus, the numbers for all three rats were significant in POST (rat 1, P ¼ 0.0017; rat 2, P ¼ 1.5 10 –7; rat 3, P ¼ 0.00019), but not in PRE (rat 1, P ¼ 0.17; rat 2, P ¼ 0.52; rat 3, P ¼ 0.12). The second method tested the null hypothesis that a RUN template sequence is replayed with the same probability as any of its
1 s Avg 012345
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Figure 4 Sleep frames replayed multicell firing sequences during RUN in both the visual cortex and the hippocampus. (a) Cortical firing sequence during RUN and in a POST sleep frame. Lap, firing pattern during a single running lap on the leftright trajectory. Each row represents a cell and each tick represents a spike. Avg, template firing sequence obtained by averaging over all laps on the trajectory. Each curve represents the average firing rate of a cell. Cells were assigned to numbers 0, 1, etc. and then arranged (01234567) from bottom to top according to the order of their firing peaks (vertical lines). Frame, the same cells’ firing patterns in a POST sleep frame. Triangles and circles, frame start and end times, respectively. Seq, firing sequence in the frame. Spike trains were convolved with a gaussian window and cells were ordered (0132567) according to the peaks (vertical lines) of the resulted curves. (b) Same as a, but for cells in the hippocampus on the same trajectory.
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Figure 5 Frame replays occurred significantly more often than chance in POST in both the visual cortex and hippocampus. (a) Chance (dotted line) and shuffle (solid line) distributions of the number of replaying frames that were randomly generated for the visual cortex during PRE and POST. Vertical lines, the actual observed numbers of replaying frames. (b) Same as a, but for the hippocampus.
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random shuffles. From the null hypothesis, a shuffle distribution of replaying frame number was obtained. Against this shuffle distribution, the observed numbers of replaying frames in the visual cortex were also significant (Fig. 5a,b) in both POST (P o 0.001) and PRE (P ¼ 0.009), whereas in the hippocampus the numbers were only significant in POST (P o 0.001), not in PRE (P ¼ 0.19). These analyses verify that replaying frames in POST did not arise from chance. Thus, the sequence-matching analysis demonstrates that a significant number of sleep frames replayed running-evoked firing sequences in both the visual cortex and hippocampus, providing the first direct evidence for high-order replay in the neocortex.
Interaction between cortical and hippocampal replays To study the interaction between the cortical and hippocampal replays, we next asked whether the replaying frames in the two areas were independent of each other. As we identified only a relatively small number of frames as replaying among a large number of total sleep frames (see numbers above), replaying frames were sparsely distributed during SWS. As a result, the chance that a cortical replaying frame and a hippocampal replaying frame would occur together would be very small if replaying frames in the two areas were not temporally related. We identified replaying cortical and hippocampal frame pairs that matched the same trajectory and overlapped in time (‘same-trajectory’). An example of such a pair is shown in Figure 6a. The cortical frame had a sequence 023489567 with a matching probability p ¼ 0.0063, and the overlapping hippocampal frame had a sequence 012345 with
p ¼ 0.0014. From the three rats in which both cortical and hippocampal templates were available on the same trajectory, a total of nine such pairs were observed in POST (rat 1, three; rat 2, two; rat 3, four) whereas only one was observed in PRE. As a control comparison, we also counted overlapping frame pairs in which the cortical frame replayed one trajectory while the hippocampal frame replayed the other on the same day (‘different-trajectory’). In this case, we observed only three pairs in POST and none in PRE (rat 1, zero; rat 2, two; rat 3, one). We then evaluated the significance of the observed overlapping pairs by comparing the numbers with those expected from the null hypothesis that the replaying frames in the two areas are independent. For this purpose, we applied a shuffling procedure in which replaying frames in the cortex and hippocampus were randomly and independently redis- tributed among all the candidate frames (Supplementary Fig. 9 online). We compared the actual observed numbers with distribution of the shuffling-produced overlapping pair numbers (Fig. 6b,c). The signifi- cance level (P value) was defined as the number of shuffles that yielded the same or more overlapping pairs than the actual observed pairs divided by the total number of shuffles. In the case of same-trajectory, the observed number of pairs was significant in POST (P ¼ 0.01) but not in PRE (P ¼ 0.75). For different-trajectory, the observed numbers were not significant in either POST (P ¼ 0.59) or PRE (P 4 0.99). This result indicates that frames in the visual cortex and hippocampus that replayed the same trajectories overlapped more than chance. The observed number of overlapping replaying pairs was low. However, because only a small fraction of cells that would actually be participating in replay events were recorded, many more frames could be replaying but not detected because of the limited number of cells available. To investigate how robust the overlapping effect was, we varied the matching probability (p) threshold that defines re- playing frames. As the threshold increased, we found more overlapp- ing replaying pairs in POST and the number of pairs in POST became statistically significant for a large range of p threshold in the case of same-trajectory (Fig. 6d). For example, at the more relaxed
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Figure 7 Cortical and hippocampal frames co-replayed the same running trajectory as revealed by interval analysis. (a) Time intervals between cortical and hippocampal cell pairs based on cortical replaying frames, compared with their corresponding RUN intervals on a trajectory. Solid line, linear regression between the sleep and RUN intervals. (b) Distribution of shuffling-produced correlation. Vertical line, actual observed correlation. (c) P values of the actual observed correlations based on cortical replaying frames for all trajectories. Trajectories represented by the same shape were from the same rat. Horizontal lines, significance level P ¼ 0.05. (d) Same as c, but based on hippocampal replaying frames.
Figure 6 Visual cortical and hippocampal frames that replayed the same trajectories tended to occur at the same time. (a) A cortical (CTX) and a hippocampal (HP) replaying frame that overlapped in time. Each row represents a cell and each tick represents a spike. Triangles and circles, frame start and end times, respectively. The two frames replayed the same rightleft trajectory. (b,c) Distributions of pair numbers produced by shuffling for overlapping cortical-hippocampal frame pairs that replayed the same (b) and different (c) trajectories in PRE and POST. Vertical gray lines, actual observed numbers. (d) Dependence of the significance P values of the actual observed numbers on the matching probability threshold in PRE and POST. Lines with filled triangles, same-trajectory; lines with filled circles, different- trajectory; dotted horizontal lines, significance level P ¼ 0.05.
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replaying frames; however, the robustness of high-order hippocampal replay was reduced during PRE. In contrast, PRE cortical frames showed a more robust high-order replay, indicating that in well-trained rats cortical memory traces expressed during SWS may be more likely to reflect past RUN experience than hippocampal traces are. This observation is consistent with the theoretical hypothesis that the cortex and hippocampus play complementary roles in memory formation and storage43,44, with the cortex reflecting long-term memory and the hippocampus reflecting new short-term memory. We found that the cortical and hippocampal replays were coordi- nated to match the same awake experience during SWS. The coordina- tion is likely to require active communication between the cortex and hippocampus. The observation that cortical frame onset times precede hippocampal ones (Fig. 2e) implies an initial feed-forward interaction from the cortex to hippocampus. However, it remains unclear which area is responsible for initiating individual replay events after frame onsets. Although our data revealed a trend toward hippocampal replays leading those in the neocortex (Supplementary Fig. 10 online), we were unable to definitively establish the direction of interaction. Overall, these findings are consistent with a bidirectional interaction model. First, cortical frame activation during SWS biases hippocampal activity and triggers the start of hippocampal frames through cortical- hippocampal projections^45. This could establish the context or initial conditions for subsequent replay within hippocampal frames. Sequence memories are then reactivated during ripple events that occur within hippocampal frames. The replayed sequence memories are sent back to the associational and then primary sensory cortices through hippo- campal-cortical back projections^46 , and this biases the cortical activity toward simultaneous cortical frame replay which gradually strengthens cortical-cortical synapses for long-term memory storage. In this model, the two-way interaction and memory trace transfer occur within individual hippocampal and cortical frames. Indeed, there is evidence that neuronal activity propagates among cortical layers^25 and among cortical areas26,27^ under broad synchrony of up state activation. The expression of these reactivated memory traces in sensory cortex may directly relate to the perceptual imagery experienced during sleep and dream states.
METHODS
Rats and experimental procedures. Four Long-Evans rats (5–8 months old) were trained to sleep in a sleep box and run an alternation task on a figure-8- shaped maze (Fig. 1). The daily training procedure was exactly same as in later recording days. Intra-maze cues, such as black and white stripes with different orientations and simple geometric shapes, were added to the maze floors and inner walls. The entire maze was surrounded by a black curtain without obvious distal cues except for the irregular wrinkles of the curtain. The rats were trained to alternate between two running trajectories (leftright and rightleft) to get food at two reward sites. The training and later recording protocol was approved by the Committee on Animal Care at Massachusetts Institute of Technology and followed US National Institutes of Health guidelines. After about 2–3 weeks’ training, we implanted on the rat’s skull a micro- electrode array containing 18 independently adjustable tetrodes. Six to eight tetrodes were assigned to the hippocampus (anteroposterior –3.9, mediolateral 2.2, relative to bregma) and 10–12 tetrodes aimed at primary visual cortex (anteroposterior –7.1, mediolateral 3.5). We inserted a bipolar electrode into the rat’s neck muscle to record the electromyogram (EMG). We reintroduced rats to the maze one week after the surgery and retrained them for about 10– d before the recording. Recording began once units were stable and rats ran each trajectory at least 20 times. This study only includes data taken from well- trained rats (alternation with at least 80% accuracy). Spikes from tetrodes with any of the four channels crossing a preset triggering threshold were acquired at 32 kHz. EMG and EEG signals were filtered at 0.1–475 Hz and recorded continuously at 2 kHz. Two infrared diodes were used to track the rat’s position
during a RUN session. Diode positions were sampled at 30 Hz with a resolution of approximately 0.67 cm. On some days, diodes were mounted not directly over but on one side of the rat’s head, causing one loop of the maze to appear slightly smaller than the other.
Data analysis. We used ten datasets (two or three consecutive days per rat), each of which contained at least ten RUN-active visual cortical cells and ten RUN- active hippocampal cells, in this analysis. In total, we recorded 116 cortical cells and 294 CA1 cells. Among them, 97 cortical cells (RUN mean rate Z 0.5 Hz) and 129 CA1 place cells (RUN mean rate Z 0.2 Hz and o 4 Hz) were active on the maze. Most of the cortical cells were located in the deep layers (5 or 6) in primary visual cortex (V1). A few cells were recorded from layers 4 and 3 in V and some other cells from deep layers of the visual cortical area immediately lateral to V1. Tetrode locations were identified according to ref. 47.
Sleep stage classification. EMG, hippocampal and cortical EEGs were used to classify sleep states at 1-s resolution into four stages: wake state, SWS, rapid- eye-movement sleep and an unspecified intermediate state (Supplementary Fig. 11 online). SWS was characterized as having low EMG, high hippocampal ripple, low hippocampal theta and high cortical delta power^48.
Frame definition. All multiunit spikes (not necessarily sorted single-unit spikes) from all tetrodes within the same recording area were used to determine frame boundaries (see Supplementary Fig. 12 online for details). Spikes from a recording area were combined and counted in 10 ms time bins. Spike counts were then smoothed using a gaussian window with s ¼ 30 ms. Interframe silent periods were defined as periods with spike counts below a preset threshold, and frames as periods in between. Furthermore, consecutive frames with a gap shorter than a threshold were combined.
Frame-triggered EEG and ripple detection. Broadband (0.1–475 Hz) EEGs recorded in layer 5 were used for cortical frame-triggered averages. For the hippocampus, EEGs recorded from the CA1 pyramidal cell layer were first filtered for ripple band (80–250 Hz), and then ripple power was calculated as squared EEG value at each time point. For a selected time point (start or end time) of a frame, a 5-s EEG (or EEG power) segment centered at the time was selected. All the segments triggered by all frames in consideration were then averaged to obtain the mean trace. Ripple events were detected using a threshold-crossing method on the filtered hippocampal EEG at ripple band7,30. Two thresholds were defined. If S is the standard deviation of an EEG trace, 3S was set as cross-threshold and 7S as peak-threshold. All the time points with absolute EEG values larger than the cross-threshold were identified. Time points separated by gaps smaller than 50 ms were grouped as a single event. Furthermore, only events with a peak absolute value larger than the peak- threshold were taken as ripple events and the peak time was considered to be the ripple event time. The method also determined the start and end times for every ripple event.
Frame cross-correlation. Frame start (or end) times were treated as discrete events. We first converted the events to occurrence rates with a bin size 10 ms. Given two event rates f 1 (t) and f 2 (t), where t ¼ 1,2,y,n, the cross-correlation coefficient at time lag Dt between the two events was computed as
C 12 ðDtÞ ¼
Pn t ¼ 1
ðf 1 ðtÞ f 1 Þðf 2 ðt + DtÞ f 2 Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn t ¼ 1
ðf 1 ðtÞ f 1 Þ^2
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn t ¼ 1
ðf 2 ðtÞ f 2 Þ^2
s ;
where f (^) i ¼ 1 n
Xn t ¼ 1
f (^) iðtÞ; for i ¼ 1 ; 2 :
As the correlation coefficient is normally distributed if we assume a null hypothesis that two events are independent Poisson processes^49 , we used a t-test to test the dependence between two event trains at a time lag.
Firing rate map and spatial information. Position points on the maze were binned into 2-cm 2-cm grids. A firing rate map was obtained by simply counting a cell’s spikes in a grid divided by the rat’s total occupancy time in it.
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Only position points and spikes during trajectory running were included. Spatial information was computed using one-dimensional linearized trajec- tories instead of the two-dimensional maze. The two trajectories (leftright and rightleft) were linearized separately, binned with 2-cm bins, and then com- bined. The cell’s firing rate in each bin of the two linearized trajectories was computed similarly to that of the two-dimensional maze by counting spikes divided by occupancy time. If fi, ti (i ¼ 1,2,y,n) are the firing rate and occupancy time for the ith^ bin, spatial information is given by^50
SpI ¼
Xn i¼ 1
p (^) if^ i f
log 2 f^ i f
;
where pi ¼ ti=
X i
ti
is the occupancy probability and f ¼
X
i
p (^) i f (^) i
is the mean firing rate.
Sequence matching and interval analysis. Sequence construction, sequence similarity, sequence matching probability, overall replay significance, over- lapping frame pairs and overlapping significance, and interval analysis are briefly described in the Results section. See Supplementary Methods for more details.
Note: Supplementary information is available on the Nature Neuroscience website.
ACKNOWLEDGMENTS We thank E. Miller, C. Moore, J. Fisher and F.-M. Zhou for critical readings on the manuscript, and Wilson laboratory members for technical help and suggestions and comments on the project and manuscript. Supported by grants to M.A.W. from the Brain Science Institute at the Institute of Physical and Chemical Research (RIKEN) in Japan and the US National Institutes of Health.
COMPETING INTERESTS STATEMENT The authors declare that they have no competing financial interests.
Published online at http://www.nature.com/natureneuroscience Reprints and permissions information is available online at http://npg.nature.com/ reprintsandpermissions/
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