New Experiences Enhance Coordinated Neural Activity in the Hippocampus

Increased correlations between novel arm cell pairs

Figure 2A shows example cross-correlograms (CCG’s) between the spike trains of a pair of familiar (top) and novel (bottom) arm cells. There is a clear peak near zero-lag for the pair of novel arm cells, but not for the familiar arm cells (see also Fig. S2 for more examples). This peak in the CCG translates into more near-synchronous firing of cell pairs of the sort that is required to drive Hebbian plasticity. To quantify the peaked correlation at zero-lag across the population we defined the “excess correlation” as the above-baseline correlation at zero-lag (see Methods and Fig. 2A). Excess correlation was significantly higher for novel than for familiar arm cell pairs on days 1 and 2, but not on day 3 (Fig. 2B).

Previous studies have found an increase in overall firing rate in novel environments (Nitz and McNaughton, 2004;Csicsvari et al., 2007) but as a simple firing rate increase would lead to higher correlations at all lags and would not generate a peak at zero lag, we explored other sources of the difference in excess correlation. First, we restricted the analysis to include only spikes that the two cells fired when the animal was located within the union of their place fields. Surprisingly, spiking within place fields did not account for the difference, as the distribution of excess correlation values was not different between novel and familiar arm cells, when only place field activity was included (Fig. 2C). Thus, the excess correlation was due to spiking that occurred while the animal was located outside the cells’ place fields. Next, we examined whether spiking during ripples could account for the difference in excess correlation. We detected high amplitude ripples in the LFP (see Methods) throughout the session, including periods of running and quiescence (for examples see Fig. 2D top and Fig. S3). When we excluded spiking during ripples, we found a smaller but still significant difference in excess correlation than when all spikes were included (Fig. S4). This argues that spiking within ripples contributes to the excess correlation effect but does not fully account for the difference between novel and familiar arm cells.

We then used a lower amplitude threshold to detected high frequency events (HFEs) that have the same frequency composition as ripples but are of lower amplitude (see Fig. 2D bottom and Fig. S3 for examples). We found that removing spiking during HFEs abolished the difference in excess correlation, demonstrating that HFE activity was responsible for the excess correlation difference (Fig. 2E). Spiking during HFEs was sufficiently coordinated to affect the overall correlations between spike pairs even though these events took up less than 2% of the time spent on the track (across all days and arms).

Like ripples, HFEs occurred coherently across tetrodes, and we found that there was no clear segregation between low and high amplitude HFEs (Figs. S5 and S6). While previous studies have suggested that ripples occur only during periods of quiescence (Buzsaki et al., 1983), a recent report has demonstrated that ripples also occur during running (O’Neill et al., 2006). Similarly, we found that many HFEs occurred during running (Fig. S7), and that HFEs during running contributed significantly to the excess correlation difference (Fig. S8).

Having identified HFEs as the source of the excess correlation, we examined the properties of HFEs and spiking within HFEs. We found that HFEs occurred more frequently in the novel than in the familiar arm (Fig. 3A), but were of similar duration (Fig. 3B). In addition, novel arm cells fired on average more spikes per HFEs than did familiar arm cells (Fig. 3C). Thus, the difference in excess correlation was associated with both an increased rate of HFEs and increased spiking during HFEs. We then asked whether this increase in activity associated with HFEs was restricted to the novel arm or was instead present in both novel and familiar places. We found that novel arm cells fired more spikes during HFEs than familiar arm cells even when the animal was located on the non-place-field arm (Fig. 3D). This is consistent with the observations that both novel and familiar arm cells fired significant numbers of spikes in their respective non-place field arms (Fig. S9). These spikes tended to occur either diffusely across the arms or in locations such as the food wells where animals spent large amounts of time. These spikes were therefore not associated with higher spatial firing rates characteristic of place fields. Thus, the increased activity and correlation of novel arm cell pairs is not likely to be driven by local sensory input, different behavior or greater neural network excitability associated with the novel arm but instead is present in out-of-field spiking across the environment.

Increased coordination of novel arm cells during high-frequency events

We then determined how the structure of spiking during HFEs differed between novel and familiar arm cells. For this analysis, we continue to separate neural activity in the place field and the non-place-field arm. In the two extremes, the observed increase in spiking during HFEs could result from cells firing a constant number of spikes during a larger number of HFEs or more spikes during a constant number of HFE. To address this issue we measured the activation probability as the fraction of HFEs during which a neuron fired at least one spike. Novel arm cells had a much higher activation probability than familiar arm cells on days 1 and 2 but not on day 3 (Fig. 4A). For example, on day 1 novel arm cells were about two and a half times more likely to be active during any given HFE than their familiar arm counterparts were. Novel arm cells were also active during a larger fraction of HFEs than were familiar arm cells when the animal was located in the non-place-field arm (Fig. 4B). At the same time, given that a cell was active during an HFE, the average number of spikes fired during an HFE was not significantly different between novel and familiar arm cells (Fig. 4C,D). Thus, the increased spiking rate of novel arm cells during HFEs was due to an increased probability of being active during HFEs, and was not a result of a higher number of spikes per HFE.

Given that individual novel arm cells were initially more likely to be active during HFEs, pairs of novel arm cells with overlapping place fields should be more co-active than their familiar arm counterparts. Indeed, on day 1, novel arm pairs were about six times more likely to be co-active than familiar arm cell pairs. Across the population, novel arm cell pairs were significantly more likely to be co-active than were familiar arm cell pairs on days 1, 2 and 3 (Fig. 4E,F). This result was consistent across individual animals (Fig. S10). Spiking during HFEs was also enhanced when the analysis was restricted to periods of quiescence (Fig. S11). Thus, firing in HFEs occurring during motion and during immobility were qualitatively similar, a finding that is consistent with previous observations (O’Neill et al., 2006).

The increased co-activation could be a trivial result of higher activation probability of individual cells, or it could represent increased coordination of cell assemblies above and beyond what would be expected from single neuron activity. We calculated a z-score to measure the degree of coordination, i.e., how much cell pairs were more or less co-active than expected if the two cells were independent (see Methods). We found that novel arm cell pairs were more coordinated than would be expected from their individual activity levels on days 1 and 2, but not on day 3 (Fig. 4G,H). Furthermore, if this greater co-activity carried a meaningful signal, then it should be specific to pairs of novel arm cells. We therefore analyzed mixed pairs consisting of one novel and one familiar arm cell, and found that they do not show strong co-activity (Fig. S12). We note that there were too few novel arm cells with non-overlapping place fields to analyze whether place field overlap was required for the enhancement of novel arm activity. Lastly, while some HFEs co-occur with periods of gamma oscillations, the increased coordination of novel arm cells could be seen even when those HFEs associated with high gamma power were removed, indicating that increased coordination was unlikely to be due to gamma modulation (Fig. S13).

We then examined the precision of spike timing between cell pairs during HFEs. We calculated the width of the CCG between cell pairs, measured as the root-mean-square (RMS) time lag (Fig. 5A). For this analysis, we included only spikes that occurred during HFEs (see Methods). The coordination of novel arm cell pairs was significantly more precise than that of familiar arm cell pairs on days 1 and 2, but not on day 3 (Fig. 5B). For example, on day 1 about a third of the novel arm cell pairs had a RMS time lag of < 35 ms, whereas no familiar arm cell pair was timed this precisely. We found no systematic bias in the ordering of spiking during HFEs across the population (Fig. S14), consistent with recent findings that firing sequences during ripples occur in both forward and reverse order (Diba and Buzsaki, 2007).

Spatio-temporal coordination of spatial activity

While spatial activity did not substantially contribute to the excess correlation difference between novel and familiar arm cell pairs, it is possible that novel arm cells activity showed greater temporal organization consistent with a role in driving synaptic plasticity. Our previous observation that place fields in the novel arm are initially unstable (Frank et al., 2004) makes this appear unlikely, but place field stability might not correlate with spiking coordination. Hence, we measured the coordination present in single cell and cell pair firing. In the following, we define spatial activity as a place cell’s neural activity that occurred when the animal was in motion within that cell’s place fields. To avoid confounding separate effects we excluded times during HFEs from the analysis of spatial activity, although the results hold with and without this exclusion.

We first examined the spatio-temporal coordination of single cells in the context of phase precession. We used an adaptive filtering approach (Brown et al., 2001;Brown et al., 2002;Frank et al., 2002) to estimated the position-phase response for individual cells on a moment-by-moment basis (see Methods, for an example see Supplementary Video). Such dynamic estimates are difficult to obtain with standard analysis techniques and, perhaps as a result, phase precession had been studied previously only in highly familiar environments (O’Keefe and Recce, 1993;Skaggs et al., 1996;Huxter et al., 2003;Dragoi and Buzsaki, 2006). We measured the strength of phase precession by the magnitude of the correlation between position and the theta phase angle of spiking (see Methods, Fig. 6A). As expected, the learning rates used in the adaptive filter determine the rate with which the estimated phase precession strength changes, however, we obtained the same qualitative result with a wide range of learning rates (Fig. S15). On average, phase precession in the novel arm on day 1 was weaker than in the familiar arm, but was not different on days 2 and 3 (Fig. 6B). There was, however, substantial variability across individual animals. On day 1, three out of four animals showed the same trend as the group data, but the result was significant in only one animal (Fig. S16). The phase precession difference on day 1 is not easily accounted for by differences in the theta rhythm or spike rate (Figs. S17-S19). In addition, phase precession did not differ between novel and familiar arms on days 2 and 3 even though the animals’ running speeds were significantly different (Fig. S1), corroborating previous observations that running speed does not strongly modulate phase precession (Huxter et al., 2003). In summary, it is clear that phase precession in the novel arm was not stronger than in the familiar arm.

Since phase precession only measures spiking coordination of single cells, we next examined spiking coordination between pairs of novel arm cells. As a result of phase precession, spiking of neurons with overlapping place fields is ordered within each cycle of the theta rhythm, leading to the compression of behavioral sequences within a single cycle of the theta oscillation (Fig. 7A). We quantified the fidelity of sequence compression with the sequence compression index (SCI) (Dragoi and Buzsaki, 2006), defined as the correlation coefficient between the theta timescale temporal separation of spiking and the distance between the place fields across the cell population (see Methods). While the SCI between a pair of cells depends on the strength of phase precession in the individual cells, the SCI captures coordination of the cell pair beyond that expected from phase precession alone (Dragoi and Buzsaki, 2006). The theta timescale temporal separation of spiking was determined from the CCG between pairs of cells (Fig. 7B). Familiar arm cells pairs were pooled for higher power since there were no significant differences in SCI among individual days, and between individual days and the pooled data (p > 0.24). The familiar arm SCI was 0.64 (Fig. 7C) and on no day was the novel arm SCI significantly higher than the familiar arm SCI. Instead, the novel arm SCI of 0.25 on day 1 and -0.16 on day 2 were significantly less than the familiar arm SCI (Fig. 7D,E) (z-test, p < 0.003), while on day 3 there was no significant difference (Fig. 7F) (p = 0.70). We are hesitant to interpret the lower novel arm SCI values as indicative of substantial disorganization since the SCI is quite sensitive to large deviations of only a few cell pairs. Nonetheless, on day 1 for instance, eleven out of 78 (14%) data points showed large deviations from the remaining data points. These eleven cell pairs originated from the two animals, for which we had the most data, and these pairs were recorded across seven different days. Thus, the data points with large deviations were not the result of some undetected noise in a single session. We further note that the SCI result corroborates the evidence from phase precession that spatial activity might be less organized. More importantly, we can conclude that increased coordination of novel arm cells is limited to HFEs and is not seen in spatial activity.

Stability of established representations

Remarkably, despite rapid ongoing plasticity previously established memories, i.e., the neural representation of the familiar arm, remained stable. We assessed the stability of established representations by comparing the spatial activity of familiar arm cells across days 1—3 to the spatial activity of cells that had place fields in the outer arms of the pre-training maze configuration (session 1, see Fig. 1). Spatial activity of familiar arm cells in the form of phase precession strength and sequence compression index did not exhibit significant changes due to the presence of the novel arm (Fig. 8A,B). As a final control, we verified that neural activity of familiar arm cell pairs showed excess correlation similar to place cells in the pre-training maze configuration across all three days of novel exposure (Fig. 8C). This confirms that the increased excess correlation is specific to cell assemblies representing novel locations.

Relationship between high-frequency events and ripples

We found that only by including both lower amplitude HFEs and higher amplitude HFEs that occur during running could we account for the difference in excess correlation between novel and familiar arm cell pairs. To our knowledge, this represents the first identification of a correlated neural activity pattern that is specific to HFEs. Since we did not find qualitative differences in neural activity during HFEs that were of low vs. high amplitude, or that occurred during running vs. quiescence, we suggest that these events could all, in principle, be referred to as ripples. The term “ripple” generally refers to transient, high frequency LFP events that are accompanied by strong neural activity, but there are no universally accepted criteria for separating ripples from other, lower amplitude, high frequency events. One criterion that has been proposed is the behavioral state of the animal, as ripples were thought to be absent during motion (Buzsaki et al., 1983). However, a more recent study reported that ripples frequently occur while animals are moving (O’Neill et al., 2006). Ripple-like events can also be detected using a variety of thresholds (Chrobak and Buzsaki, 1996;Csicsvari et al., 2000). Although it has been customary to use high thresholds for ripple detection (Wilson and McNaughton, 1994;Nadasdy et al., 1999;Lee and Wilson, 2002;Jackson et al., 2006;Foster and Wilson, 2006), more recently, lower thresholds have been used as well (Diba and Buzsaki, 2007). While using a lower threshold could lead to incorrect labeling of some events as ripples, it may also include a large number of events that are of the same character as higher amplitude ripples.

Consistent with the notion that ripples represent a network event that is coherent across an extended region of the hippocampus, we observed that HFEs on a given tetrode were accompanied by high frequency events on other tetrodes. In light of this view, reactivation events that have previously been observed outside of ripples detected with a high amplitude threshold (Wilson and McNaughton, 1994;Nadasdy et al., 1999;Lee and Wilson, 2002;Jackson et al., 2006;Foster and Wilson, 2006), might actually have occurred within lower amplitude HFEs. Nonetheless, we have chosen to use the term “high frequency events” to acknowledge the possibility that these events differ in some way from “true” ripples.

In contrast to our finding that novel arm cells are more active during HFEs than familiar arm cells, a recent study found that spike rates during ripples were lower in a novel environment (Csicsvari et al., 2007). However, in that study there was no task for the animal to perform and therefore, there was no relevant difference between novel and familiar. Task-relevance has been shown to affect greatly the response properties of hippocampal cell in mice (Kentros et al., 2004) and may explain the different findings in novel environments.

Coordination of Spatial Activity

Given that HFE activity of novel arm cells was more coordinated, one might have expected that spatial activity in the novel arm would be more coordinated as well. HFEs are very similar to ripples, and previous work has shown that activity in ripples tends to reflect patterns of previous spatial activity. Thus, we might expect that if activity during HFEs were more coordinated, we would also see greater coordination within spatial activity. We might also predict that spatial activity during learning should be as precisely coordinated as possible to drive spike-timing dependent synaptic plasticity more effectively. Nonetheless, we found that spatial activity was, if anything, less coordinated in the novel arm than in the familiar arm.

Overall, our results for phase precession and the sequence compression index are compatible with the 2 – 3 day time course of place field formation seen in our previous work (Frank et al., 2004). In addition, some of the measures of HFE activity were still significant on day 3 even though the place fields had stabilized by this time. These findings demonstrate another clear differentiation between HFEs and spatial activity and suggest that HFEs may play a role in memory consolidation or other interactions between the hippocampus and cortical regions that continue after CA1 representations have become stable.

Spiking coordination: origins and consequences

The generally lower coordination of spatial activity in the novel arm argues that spatial activity does not directly drive the increased coordination seen during HFEs. In addition, novel arm cell spiking during HFEs was more coordinated even when the animal was on the familiar arm. As such, some mechanism that activates and coordinates cells representing novel locations is necessary to explain our results. We speculate on such mechanisms in the following.

Based on previous findings, CA3 is the most likely source of the patterned input that drives CA1 HFEs. First, ripples are generated in area CA3 and then propagate through monosynaptic connections to area CA1 (Buzsaki, 1986;Csicsvari et al., 2000). Second, CA3 neurons are strongly reciprocally connected, while CA1 neurons are not (Amaral and Witter, 1995). Based on recent evidence that inducing LTP in CA3 can lead to ripples in slices (Behrens et al., 2005), we suggest the following mechanism for spiking during HFEs of CA1: during the initial experience, correlations among neurons representing novel locations are rapidly encoded in the recurrent CA3 network. Ripple events initiated within CA3 would tend to include neurons with recurrent synapses that recently underwent LTP, and the firing of these CA3 neurons could in turn activate their downstream CA1 targets. This intrinsic mechanism might account for the greater coordination of novel arm cells across the environment. Thus, spiking outside place fields might be particularly important in associating together cell assemblies that represent previously experienced sets of novel locations.

The temporal precision of spiking during HFEs in CA1 suggests that spiking associated with novelty is well suited to inducing synaptic plasticity in the hippocampal – cortical network. Spiking during HFEs has temporal structure similar to that used to induce LTP (Buzsaki, 1986) and ripple-like stimulation is effective in inducing plasticity a major target of CA1 outputs, the deep layers of the entorhinal cortex (Yun et al., 2002). In addition, plasticity between CA3 and CA1 requires multiple CA3 before CA1 spike pairings (Bi and Poo, 1998;Zhang et al., 1998;Wittenberg and Wang, 2006), so the repeated activation of CA1 neurons we observed could allow for plasticity at CA3 – CA1 synapses as well. A potential objection could be raised at this point: Across the population of cell pairs, we found no consistent bias in spike ordering (Fig. S14) but numerous studies have suggested that spike timing-dependent plasticity (STDP) requires a consistent bias in spike ordering for strengthening or weakening synapses (Bi and Poo, 1998;Zhang et al., 1998;Wittenberg and Wang, 2006). This apparent contradiction could be resolved in at least two ways. First, a recent study has suggested that STDP is more complex than previously appreciated and that the learning rule depends sensitively on the precise induction protocol (Wittenberg and Wang, 2006). In some cases, paired pre and post-synaptic activation leads to synaptic potentiation regardless of the spiking order. Second, while the population has no consistent spike ordering bias, individual pairs do. For some cell pairs the bias of spike order during HFEs is in the same (or opposite) direction as during spatial activity. Thus, asymmetric STDP plasticity could lead to strengthening the connections between some pairs while weakening others.

Our findings indicate that coordinated spiking during HFEs is most clearly present during a novel experience when there is much to be learned. We hypothesize that this coordination might play an important role in initial learning. Specifically, our results are compatible with that two-stage model for memory formation proposed by Buzsaki et al. (Buzsaki, 1989;Lorincz and Buzsaki, 2000): during learning, associations are first formed in the recurrent CA3 network. CA3 memory traces are then activated during ripples to drive the formation of coordinated cell assemblies in CA1, including the elimination of less well coordinated assemblies from the active population. This mechanism may have lead to the apparent improvement of phase precession and sequence compression in novel arm cell across days 1-3 that we observed. Based on our results from CA1, we hypothesize that activation of newly formed CA3 traces is more frequent and more precisely coordinated than activation of previously learned traces, allowing for more effective plasticity in CA1 and downstream regions such as the subiculum and entorhinal cortex. As an environment becomes familiar, some heretofore-unidentified process down-regulates activation, perhaps as a direct result of the formation of stable and organized representations outside the hippocampus. Synaptic plasticity induced by HFEs may also be important for establishing and maintaining reactivation of spatial activity patterns during subsequent sleep, as O’Neill et al. (2006) have suggested.

In closing, a complex picture is emerging about the special role that neural activity during ripple-like events in the hippocampus might play in learning and memory. Ripple reactivation has been suggested for some time to be involved in the consolidation of spatial memories. Our results now suggest that activity during ripple-like events might play a role in the initial formation of spatial memories as well.

Data collection and pre-processing

Details of this experiment and data collection have been reported previously (Frank et al., 2004). Briefly, four male Long-Evans rats were pre-trained to run on a T-maze for liquid chocolate rewards (Fig. 1). Animals had to run from the home arm (arm 1) to one outside arm (arm 3 or 7) and back to home; and then alternate to the other outside arm, etc. Tetrodes were then implanted (6 in hippocampal area CA1, 18 targeting the neocortex, 1 reference) according to Harvard University and National Institutes of Health guidelines. Following recovery, animals ran during two 20—25 min sessions every day separated by a 20–30 minute rest session. In the first run session, animals ran on the pre-training T-maze configuration. In the second run session, a novel arm replaced one of the familiar outer arms. After 2–3 days in one novel configuration, a different novel arm was opened. All first days of novel exposure were pooled and are referred to as “day 1”, likewise for days 2 and 3. Only stable recordings from 787 well-isolated excitatory neurons were included.

Positions were converted to distances from the end of the home arm and each direction of the trajectory (determined by head direction) was analyzed separately. Firing rates were computed (0.5 cm bins) and smoothed (Gaussian kernel, SD 2 cm). Place fields were defined as region in which the rate remained above 15% of a local peak rate of 3 Hz or more. The place field was rejected if the average velocity anywhere inside the place field fell below 2 cm/s or if the place field extended into the center of the track. Only data from outside arms were analyzed. The number of cells with place fields in the novel and familiar arm for each animal are reported in Supplementary Table S1. A single cell could contribute more than one place field when place fields were analyzed (e.g. Fig. 6), but cells with multiple fields contributed only once to any cell-based analysis.

“Time in arm” was defined as the accumulated time that animals spent within the novel or familiar arm. Periods of running were defined as times when running speed > 4 pixels/s (2.8 cm/s).

Excess correlation

CCG were computed (2 ms bins) and smoothed with a Gaussian kernel (SD 5 ms) (solid black and red lines in Fig. 2A). The excess correlation is meant to capture the correlation at zero-lag above the baseline that we would expect from the envelope of the CCG. This baseline was obtained by smoothing the CCG with a wide Gaussian kernel (SD 250 ms) (dashed black and red lines in Fig. 2A).

Detection of HFEs and ripples

LFP signals were recorded from one arbitrarily selected channel of each tetrode. A dedicated reference electrode was placed in the corpus callosum within < 1mm from the CA1 tetrodes. All neural signals were recorded relative to that reference tetrode to eliminate muscle artifacts from the recordings. On a given day, the tetrode with the largest number of isolated neurons was chosen for ripple analysis. The LFP envelope was determined by Hilbert transforming the LFP signal from that tetrode after band-pass-filtering between 150-250 Hz. Events were detected if the envelope exceeded threshold for at least 15 ms. Events included times around the triggering event during which the envelope exceeded the mean. Overlapping events were combined. A high threshold of mean + 6 SD of the envelope was used for detecting events that would meet most common definitions of ripples. HFEs were detected with a lower threshold of mean + 3 SD.

Coordinated activation during high frequency events

If neurons A and B are independently active during n_A and n_B, respectively, of N events, the expected number of events during which both neurons were active n_AB follows a hypergeometric distribution (Sheskin, 2004) with mean

and variance

To compare expected and observed number of coincident events across neuron pairs with different activity levels, we normalize the difference by the standard deviation, obtaining a z-score

Spiking precision during HFEs was measured by the RMS of the time lag in the CCG within ±100 ms. CCG were computed (2 ms bins) and included only spike pairs for which at least one spike occurred during an HFE. Only cell pairs with >10 coincident events were included in the analysis.

Dynamic analysis of theta phase precession

Theta phase angle was determined by Hilbert transformation of the band-filtered (6-10 Hz) LFP from the tetrode with highest theta power. Standard histogram approaches are not adequate for quantifying moment-by-moment changes in neural activity, particularly when the animal’s behavior is not uniform in space and time. We therefore derived an adaptive filtering algorithm (Brown et al., 2001;Brown et al., 2002;Frank et al., 2002) that estimated the changing relationship between position x_t, theta phase θ_t and firing rate λ(t). We assumed a flexible model for the instantaneous spike rate λ(t) that evolves as the neuron’s spiking changes. Two factors contribute, the position-phase response λ_S and the interspike interval (ISI) distribution λ_T such that: λ(t;q_t)= λ_S(x_t,θ_t;q_t) λ_T(τ_t;q_t). The functions λ_S and λ_T were parameterized by cardinal cubic splines, whose parameters are combined in the parameter vector q_t. These splines make it possible to capture the fine spatial and temporal structure of phase precession and the temporal structure of refractory period and bursting. The parameters of the splines functions correspond to the functional values at the control points. For the position-phase response function the control points were spaced equidistantly in position (every ~5 cm) and theta phase (every 30°). The control points of the ISI distribution were spaced unevenly (0 ms, 1 ms, 3 ms, …, 11 ms, 15 ms, 20 ms, …, 65 ms, 80 ms) to give greater emphasis to the refractory period and bursting. For ISI’s larger than 80 ms, the ISI distribution was set to 1 to avoid confounding effects of theta modulation (~125 ms). An adaptive filtering algorithm was derived for estimating the parameters q_t in timesteps of Δt = 2 ms:

The learning rates ε were 6 and 0.05 for the parameters of the spatial and temporal functions, respectively. The learning rates determine how quickly estimates of the cell’s response properties change, so we verified that our conclusions about phase precession do not differ qualitatively even if much larger or smaller learning rates were used (Fig. S15) The quality of the fit was assessed by a Kolmogorov-Smirnov test (KS) on time-rescaled interspike times (Brown et al., 2002;Frank et al., 2002). Including phase precession substantially improved the fit over the previous model that did not take phase modulation into account. For 131 of 185 cells (71%) from the first session (pre-training maze configuration) the KS statistics was within the 99%-confidence interval. In the second session (novel configuration), 104 of 191 cells (55%) were within that bound. These results indicate that the model accurately captures much of the spatio-temporal structure of place cell activity. To our knowledge, our current model is the most accurate to date for data analysis or simulation of place cell activity, since these estimated models could be used to generate data as well.

We define the strength of phase precession as the magnitude of the correlation between position and theta phase in the position-phase response λ_S(x_t,θ_t). To compute this correlation at every time step, we first convert the continuous position-phase response to a finely binned (Δx= 0.1cm, Δθ=π/20) probability distribution $p\left(x_t^i,{\theta }_t^j\right)={\lambda }_s\left(x_t^i,{\theta }_t^j\right)/\sum _{i,j}{\lambda }_s\left(x_t^i,{\theta }_t^j\right)$ and then calculate the correlation as r_t = E[(x_t − μ_x)(θ_t��μ_θ)]/(σ_xσ_θ), where E[·] is the expectation, μ_x and μ_θ are the expected values, and σ_x and σ_θ are the standard deviations of the variables. Since the correlation coefficient is defined for linear variables and theta phase angle is circular, we added a phase offset that maximized the magnitude of the correlation across the entire session to account for differences in preferred phase across neurons.

Sequence compression index

The theta-scale temporal separation of spiking was determined from the CCG’s, computed using 2 ms time bins. Only spatial activity and only cell pairs with >30 coincident events within time lags of ±100 ms were included in the analysis. The highest peak within time lags of ±100 ms was detected in the low-pass-filtered (<30 Hz) CCG (e.g., Fig. 7B). Spatial separation was determined as distance between the two centers of mass of the place fields. The correlation coefficient between temporal and spatial separation is defined as the sequence compression index (Dragoi and Buzsaki, 2006).