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1 Neuron, Volume 71 Supplemental Information Hippocampal Time Cells Bridge the Gap in Memory for Discontiguous Events Christopher J. MacDonald, Kyle Q. Lepage, Uri T. Eden, and Howard Eichenbaum Inventory of Supplemental Information 1. Figure S1 is related to pg. 5 where we discuss behavior during the delay period 2. Figure S2 is related to pg. 5 that discusses how head direction and speed related neural activity depends on time. 3. Figure S3 is related to pg. 6 of the manuscript where we discuss the distribution of STIC values across a subpopulation of neurons. 4. Figure S4 is related to pg. 9 of the manuscript where we discuss the time course of retiming. 5. Figure S5 is related to pg. 14 and the discussion of our LFP analysis. 6. Figure S6 is related to pg. 20 where we discuss isolation of pyramidal neurons. 7. Supplemental Experimental Procedures gives extensive details on the Methods we used but could not be included in the main text due to space constraints. 8. Supplemental References gives references cited only in the Supplemental Material

2 Supplemental Figures Figure S1: The movement pattern for each rat during the delay period. (a) Data from a single recording session. The grey line indicates the rat s X-Y position as a function of

3 time elapsed since the beginning of each trial s delay period (moving upward on the z- axis). The movement pattern for trials starting with object 1 is on the left while the right plot shows object 2 trials. (b-f) Movement patterns for rats are shown in the same format as in (a) but for the remaining five recording sessions.

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5 Figure S2: Head direction and speed related neural activity depend on the passage of time during the delay period. (a) The head direction (left column) and speed firing rate plots (right column) are shown for one neuron. At the top of the left column is a polar plot (e.g., Kneirim et al., 1995) in which normalized neural activity (blue line) is shown as a function of the rat s head direction (0 360 degrees) throughout the entire delay period ( 0-6 s ). Below it are six additional polar plots that show head direction activity during consecutive 1-s time segments starting from the beginning of the delay period. Similarly, the top plot in the right column shows normalized neural activity (y-axis; blue line) as a function of the rat s speed (x-axis) during the full delay period. The six plots below it are speed firing rate plots for successive 1-s time segments during the delay period. The heat plot below the left and right columns shows the neuron s activity across the whole delay period (i.e., irrespective of head direction and speed). Note that grey-shaded areas in the plots correspond to head directions (left) or speeds (right) that were observed. For the plots at the top of each column, only head directions (left) or speeds observed at least once in each of the 1-s time segments are shaded in grey. (b - l) The same format as in (a) but for 11 additional neurons. Note that all of the neurons (a-l) are from the same recording session.

6 Figure S3: The relative degree of spatial and temporal information encoded during the delay period varies across a large population of neurons that are active during the delay period. Here the frequency histogram shows the distribution of all the STIC values in neurons for which space and time contributed to activity during the delay period. Figure S4: (a-c) Each panel shows normalized activity inside a neuron s time field for each trial during the recording session. Grey lines indicate the delay length transitions. Retiming abruptly occurs more than 10 trials after the length of the delay period changes. However, the trial at which a neuron retimes varies across the population. Furthermore, once a neuron retimes, it may continue to change its firing rate in a continuous manner over the session (panel b). The neurons are the same as those shown in panels 1, 2, and 4 (left to right) of Figure 7b.

7 Figure S5: Throughout the object odor sequence, the local field potential (LFP) showed a prominent band of power within the theta range (4-12 Hz). (a) The trial-averaged time frequency spectrograms using the LFP recorded from a single tetrode during a recording session. The spectrograms are separated according to the trial period (object = left; delay = center; odor = right) as well as the object that was presented (top = object 1; bottom = object 2). For the object and odor periods, the spectral density was estimated using a single 1.2 s window of activity from each trial. The spectral density during the delay period was estimated using a 1-s window that was slid in 100 ms increments across the delay period in each trial. In all cases, the band width was 1-40 Hz and the frequency of resolution was 1 Hz. (b-f) The same format as in (a) but for five additional recording sessions.

8 Figure S6: The average waveform from a putative pyramidal neuron (blue; spike width = 0.27 ms). The average spike width of pyramidal neurons was 0.27 ms ± (range = 0.20 ms 0.60 ms) and their average firing rate across the recording session was 0.44 Hz ± 0.02 (range = Hz 2.6 Hz). Though we avoided processing putative interneurons offline (i.e., cluster cutting) and including them in our data set, we provide here an average waveform for an interneuron that we isolated (red; spike width = 0.15 ms). The average spike width of putative interneurons that were isolated was 0.18 ms ± 0.03 (range = 0.15 ms 0.21 ms) and the average firing rate was 17.8 Hz ± 2.3 (range = 15.5 Hz 20.1 Hz). Interneurons could be distinguished from pyramidal neurons off line by various features including their firing rate over the course of the recording session, their autocorrelograms, and their relatively narrow spike widths (e.g., Csicsvari et al., 1999). Spike widths were computed at 25% of maximum amplitude from spikes filtered between 154 Hz 8.8 khz. Supplemental Experimental Procedures Details of the behavioral task The task was performed in the central stem of a modifed T-maze that allowed rats to move along a track as it experienced each event sequentially during a trial. Then the rat could progress down a return arm and begin the next trial (Figure 1 in main text). Each

9 trial began with manual removal of a wooden panel that allowed access to either a rectangular block of wood with grated rails or half of a textured, green rubber ball mounted on another wood panel. The rat investigated the object for s during which it typically made several lateralized head-movements over the object. Then the object panel was removed and the rat progressed towards another wooden panel, at which point an additional blank wooden panel was placed behind the rat, confining it to an area that was 6 cm wide and 22 cm long. At the end of the delay period, the wooden panel was removed and the odor pot was placed on a small platform (7 cm 7 cm) that extended from the maze to the rat s right side. The rats never waked past the odor pots during a given trial and, per our definition, always sampled the odor. Because the wooden panel was removed manually, there was slight variability from trial to trial in terms of when the delay was marked as having ended through video scoring. For one rat, the delay period was 6.73 ± 0.41 s and 6.0 ± 0.44 s (mean ± s.d.) during its two recording sessions. For the second rat, the mean delay period was 9.97± 0.61 s and 9.86 ± 0.62 s (mean ± s.d.) during its two recording sessions. For the third and fourth rat, the delay period was 9.0 ± 0.56 s and 9.27 ± 0.71 s respectively. The odor pots were 10-cm tall, 11-cm wide (10 cm inner diameter) terra cotta pots filled with playground sand (QUIKRETE Premium Play Sand). The odor pots were kept together next to the experimenter until the end of the delay period. The sand was scented with only one of two common household spices cinnamon or basil (1% concentration by weight in sand). On go trials, the rat could dig in the sand to find a third of a Fruit Loop (Kellogs) reward buried in the center of the pot at a depth of cm. On nogo trials, the correct response was to refrain from digging and move forward on the central stem, then turn left where the rat was rewarded with two 1/3 Fruit Loops. Incorrect go and nogo responses were not rewarded. Statistical modeling of the neural spike trains Temporal modulation, independent of space and behavior In this analysis, spiking activity was modeled through a conditional intensity function that expresses the spiking probability as a multiplicatively separable function of various

10 covariates that modulate spiking activity. During the delay period, spiking activity was modeled as: λ(t) = λ time (t) λ space (t) λ speed (t) λ head angle (t) λ interactions (t) (1) Here λ time is an exponential fifth order polynomial of time relative to the start of each trial s delay period (i.e., 5 parameters see Eq. 2), λ s is a Gaussian shaped place field composed of five parameters (see Eq. 3), λ speed is an exponential second order polynomial, and λ head angle is defined in Eqn. 4 and Eqn. 5. i=1 λ(t) time = e 5 α i t i (2) i=1 λ(t) space = e 2 2 β i x(t ) i + δ j y(t ) i +λ(x(t )y(t )) j=1 (3) λ(t) head angle = e κ cos(θ (t ) θ (t ) p ) (4) λ(t) head angle = e a cos(θ (t ))+b sin(θ (t )) (5) In Eqn 2., t refers to the time elapsed starting from the beginning of the delay period and the five α s are parameters controlling the degree in which the spike rate is modulated by time during the delay period. In Eqn. 3, x(t) and y(t) refers to the x and y coordinates of the rat at time t during the delay period and x(t)y(t) is a cross-term. The terms β, δ, and λ are used to denote five total parameters specifying the degree in which each covariate modulated spiking rate. In Eqn. 4 and Eqn. 5, θ(t) are the head angles in vector form recorded at time t into the delay period, κ is the parameter that controls the degree to which the rate is modulated by the head angle, θ p is the preferred angle of spiking. The form of the model described by Eqn. (4) specifies the head angle influence on firing rate to be proportional to a von Mises distribution for a circular random variable. The a and b parameters in Eqn. 5 can be related to the modulation κ, (6)

11 For brevity, λ interactions (t) refers to all the interactions in the model as well as a constant term. However, λ interactions (t) is itself multiplicatively separable into the functions that specify the modulation of the neuron s firing rate by all second-order interactions among the rat s position, speed, head angle and velocity. We chose an exhaustive list of interaction terms so that we could explicitly account for the effect that the time covariate has on spiking probability. Eq. 1 can be expressed in a more compact form: λ(t) = e H β (7) where the term specifies the covariates described above and is a vector of parameters. The parameters for this model are estimated using maximum likelihood methods. For a small proportion of the fits we performed, the maximum likelihood of the estimates was not obtained and these cases were excluded. In practice, many of the parameters obtained by this procedure are correlated. What follows hereafter is a description of a procedure used to obtain time parameters that are independent of the other parameters in the model (e.g., McCullagh & Nelder, 1989). In this way, the temporal modulation of a neuron s firing rate can be evaluated during the delay period and is free of any confounds with other covariates specified in Eqn. 7. Note that the design matrix in Eqn. 7 can be expressed as: (8) where refers to the time part of the design matrix and refers to the columns of the design matrix associated with the remaining covariates (space, head direction, speed, and interactions). Here, is potentially confounded with. Therefore, a design matrix is needed whereby time s influence on neural activity is made orthogonal to. That is:

12 (9) In order to obtain, is projected so that it is orthogonal to : (10) The projection matrix,, which is orthogonal to the span of the columns in, is defined by: (11) where is a diagonal matrix with an estimate of the rate λ(t) in vector form down the diagonal. After obtaining, the temporal modulation is specified by λ time (t) in Eqn. 1. Importantly, the estimated firing rate (λ(t) in Eqn. 1) and time parameters using or is identical. The temporal modulation is down-weighted by their 95% confidence interval divided by 4, then averaged across trials. The down-weighting was implemented so that highly uncertain values of temporal modulation were discounted. The results of this procedure are presented in Figure 3e-h. Computing the spatiotemporal information index Due to the well-documented coding of spatial information by hippocampal neurons, an analysis was developed to compare the information encoded by time and space in single neurons. A model of neural activity was first specified as: λ o (t) = λ t o (t) λ s o (t) λ h o (t) (12) where λ o (t) is the spiking intensity for object o at time t, λ o t (t) is the modulation of the conditional intensity due to time, λ o s (t) is the modulation due to space, and λ o history (t) is the modulation due to history. We refer to Eqn. 12 as the space + time (S+T) model to highlight that it includes both space and time as covariates. λ o t is an exponential fifth

13 order polynomial in time, λ s o is a Gaussian shaped place field, and λ h o is the exponentiated sum of weighted linear combinations of past spiking increments, in 1 ms bins going back 5 ms, and in 25 ms bins thereafter going back an additional 150 ms. To compare the contribution of space and time to spiking activity, a nested modeling approach was used along with formal hypothesis testing. A space model was defined solely in terms of Λ s o (t) and Λ h o (t), and omitting Λ t o (t). That is, λ o (t) = λ s o (t) λ h o (t) (13) Similarly, a time model is defined as, λ o (t) = λ t o (t) λ h o (t) (14) In Eqn. 12, 13, and 14, we allowed the parameters to differ depending on the object presented. We fitted these models to the appropriate binned spike trains and computed the likelihood of the data for each model. Note that the space and time models (specified in Eqn. 13 and 14) are both nested within the S+T model (specified in Eqn. 12). In order to evaluate whether time provides more information to spiking than space alone, a likelihood ratio test was conducted based on the test statistic, W = -2 [ ln(γ space ) - ln(γ S+T ) ] (15) which, under the null hypothesis of no additional contribution of time, has a chi-square distribution with 5 degrees of freedom. The same approach was used to assess whether the addition of space to a model already including time increases the likelihood of the data. That is, W = -2 [ ln (Γ time ) - ln (Γ S+T ) ] (16)

14 The STIC was computed by simply computing the difference between the increase in the likelihood of the data due to space (Eqn. 13) and the increase in the likelihood of the data due to time (Eqn. 14). That is, = -2 [ ln (Γ space ) - ln (Γ S+T )] + 2 [ln (Γ time ) - ln (Γ S+T ) ] (17) This equation is simplified to become the STIC: STIC = ln (Γ time ) - ln (Γ space ) (18) A STIC value of x can be interpreted to indicate that time contributes e x more to the spiking likelihood compared to space. It is important to emphasize that correlated space and time parameters do not pose an interpretational problem for the STIC. The STIC relies on comparisons between the S+T model and its nested submodels. The submodels are formulated so that their only difference from S+T is the independent part of space or time (depending on your comparison). For example, the S+T model (Eqn. 12) and space model (Eqn. 13) differ by that part of the time covariate which isn t confounded with space. Testing for a neuron s object selectivity during different trial periods In order to test for object selectivity, a likelihood ratio test using nested models was employed. This test is carried out by fitting the S+T model (Eqn. 12) to the data obtained from all correct trials. For the null hypothesis, the model is fit using the same parameters for both objects and the likelihood of the data given the model is computed. For the alternate hypothesis, the model parameters can change depending on the object. (That is, the alternate model has double the number of parameters as the null model because there are only two objects.) A likelihood ratio statistic, W, was computed by the following equation: W = -2 [ log(γ null ) - log(γ alternate ) ] (19)

15 Here Γ refers to the likelihood of the null or alternate model that was obtained by the fitting procedure. Under the null hypothesis, the W statistic has a chi-square distribution with degrees of freedom equal to the number of additional parameters (i.e., 26) in the alternate model. In order for the neuron to be considered object-selective, we used a P < 0.05 as evidence to reject the null hypothesis. Testing for go/nogo selectivity during the odor period To determine whether a neuron differentiated between go and nogo trials during the odor period, we used the same approach as described in the previous section to determine object selectivity. However, in this case spike trains during the odor period from correct trials were further divided into go and nogo trial types and the likelihood ratio test was carried out. Population analysis Similar to Manns et al. (2007), a Mahalanobis distance measure was used to compare between the activity of the neural population observed at two different moments of the delay. The delay period was divided into N 1-s bins and only neurons that fired > 0.1 Hz during the whole delay period were used. During each of the N bins, the firing rate for all i neurons was estimated for each of the J total trials and normalized to activity from all trials and bins. The normalized firing rate of the population during bin n can be represented as an i-element long row vector in each trial j, x j. Similarly, in another bin, the population s activity can be expressed as,. In order to determine the Mahalanobis distance between a population vector observed in bin n and n+1, first the mean of the two vectors being compared is computed:

16 Finally, the covariance matrix is estimated in reference to and. The Mahalanobis distance is: D = ( - ) T -1 ( - ) Note that in this example, the distance was computed for a bin n and n+1 comparison, which we refer to as a lag 1 comparison. We computed the distance between population vectors at all possible lags and found the average D for that lag, which is shown for each recording session separately in Figure 4. This analysis was also repeated during the object and odor period, as well as the first and last 1.2 s of the delay period as shown in Figure 4b. The bin sizes used to compute the various lags in all four trial periods were 0.2 ms. Retiming comparison of firing patterns observed during different blocks of trials For all three blocks, we constructed PSTHs using 500-ms time-bins starting from the beginning of the delay period. For two rats we used only the first 9 s of data across all three blocks and for a third rat we used only the first 6 s (the third rat had a shorter delay period than the other two rats). Our method begins by computing a Kendall rank correlation coefficient between the PSTH from two blocks of interest. For example, suppose we do this for block 1 and block 2, which gives us our test value (τ B1,B2 ) that reflects the degree of similarity between the temporal patterns of activity from each block s delay period. Next, we ask whether the test value τ B1,B2 is lower than would be expected if a neuron s firing pattern was the same between block 1 and block 2. Continuing with this example, the trials from both blocks were pooled together under the null hypothesis that all of the trials from blocks 1 and 2 were derived from the same population. Following this step, all of these trials were randomly reassigned (without replacement) into one or the other block. Next, two PSTHs were made for each block containing randomly assigned trials and the Kendall rank correlation coefficient was computed to give the first resampled τ value of the empirical distribution. The random reassignment of trials to blocks 1 and 2, and subsequent calculation of the rank correlation coefficient was repeated 999 more times to obtain an empirical distribution of

17 τ under the null hypothesis. This resampling approach was taken for all comparisons of a neuron s firing pattern between all of the trial blocks (i.e., block 1 and block 2, block 1 and block 3, block 2 and block 3, etc.). In order to determine whether a neuron re-timed when transitioning to a longer delay period, we had two specific criteria. The first criteria involved asking what proportion of the τ values obtained from the appropriate empirical distribution (i.e., block 1 = block 2) exceeded the test value τ B1,B2. If the proportion was higher than 99%, then the neuron was considered to have re-timed. If a neuron did not meet the first criterion, we asked what proportion of the τ values obtained from the block 1 and block 3 empirical distribution (i.e., block 1 = block 3) exceeded the test value τ B1,B3. If this value exceeded 99% and, importantly, there was no difference between block 2 and block 3 delay period firing patterns (by using a similar approach), then the neuron was also considered to have re-timed. We found it useful to adopt this additional criterion to account for neurons whose re-timing developed slowly after the longer delay period was introduced during block 2. Furthermore, if a neuron re-timed after transitioning from block 1 to block 2 per our first criterion, we confirmed during block 3 whether it returned to same firing pattern observed during block 1. Thus we compared the test value τ B1,B3 to the empirical distribution of τ values under the null hypothesis that block 1 and block 3 were the same (i.e., p < 0.01). Finally, we asked whether a neuron that retimed in fact scaled its temporal pattern of activity to accommodate the longer delay period. For two rats, the delay period was approximately doubled from 10 to 20 s between block 1 and block 2. The PSTH from block 1 was made as described above (i.e., 9 s of time and 500-ms time-bins) but for block 2, it was made using 18 s of the delay period and with 1-s time-bins. The τ B1,rescaled B2 was computed and compared to the appropriate empirical distribution generated under the null hypothesis. For the third rat in which the delay period was approximately doubled twice during the recording session, we compared the delay period PSTH from block 1 using 500 ms time-bins and 6 s of time to the PSTH from block 3 using 1.5 s time-bins and 18 s of time. A τ B1,rescaled B3 was computed, and the resampling analysis was carried out under the null hypothesis that activity in block 1 and the rescaled block 3 was the same. Note that for our purposes, increasing the duration of the time-bin we use

18 effectively compresses a neuron s time-scale of activity. Characterizing the time-course of retiming during the recording session. For two rats, the first 10 s of the delay period from each trial was broken into 250-ms bins, spikes were placed into 250-ms bins and smoothed with a moving average of 5 bins, then normalized in reference to the mean and standard deviation of binned spikes across the session. (For the third rat with shorter delay periods, only the first 6 s were used for this procedure.) In each block of trials, bins with counts greater than the mean were identified as a neuron s time field. The average spike count during each block s firing field was computed. The firing field from the block with the highest average spike count was identified and used to recompute time field spike counts from all trials. These values are smoothed with a running median 5-trials long and are plotted in Figure S4 for three representative neurons. Using ANOVAs to assess the effect of Time on a neuron s firing rate in reference to the rat s position, head direction and speed. In order to generate spatial firing rate maps for the whole delay period, the area occupied by the rat in the delay zone throughout the delay period was divided into 1 cm by 1 cm bins. The spikes from the neuron were assigned to the appropriate X-Y bin depending on the rat s position. The total spikes within each bin across all of the trials were divided by the total time the rat spent in the bin across all trials. The values shown in the figures were smoothed using a two-dimensional Gaussian kernel (σ = 2 cm). In each video frame, the angle of the rat s head throughout the delay period was assigned to one of sixty, non-overlapping 6 bins that spanned all the way around the rat. The spikes from a neuron were placed in the appropriate bin, which depended on the direction the rat was facing. To create the head direction plots for the whole delay period, the total number of spikes were from all trials were summed and divided by the total amount of time the rat spent in a particular 6 bin. For Figure S2, the values in the polar plot were smoothed using a Gaussian kernel (σ = 12 ) and activity was normalized to the bin with the highest firing rate so that the radius of the polar plot = 1.

19 The speed firing rate plots for the whole delay period were made by first computing the difference in the X-Y position for successive frames during the delay period. This created a list of speeds throughout the delay period and for each trial. Each speed observation was assigned to one of thirty bins that spanned 0 30 cm/s. Each spike was assigned to a bin that depended on the speed of the rat. In this way, the neuron s firing rate was computed so that it was normalized by the total amount of time the rats spent at a particular speed. In Figure S2, the values in the speed firing rate plot were smoothed with a Gaussian kernel (σ = 2cm/s) wide and activity was normalized to the bin with the highest firing rate. We also divided the delay period from each trial into 1-s segments and analyzed the data from these segments independently. The number of 1-s segments used for a session varied from 6-9 because this number varied slightly across rats (see pg. 9 above). By making use of data taken only from a specific 1-s segment, we could visualize how the neural firing rate plots for each behavioral variable changes with time. The figures (Figure 5-6, Figure S2) shown from this analysis also use the same smoothing procedures as above. Note that our analysis of firing rate with respect to position, head direction and speed requires binning. As a result, for each behavioral variable the firing rate for a bin from each 1-s segment was computed on a trial-by-trial basis. These firing rates were not smoothed. Next, for a given behavioral variable we identified only those bins whose firing rate could be estimated in all of the 1-s segments. For only these bins, we obtained their trial-by-trial estimates of firing rate, which were also indexed according to the 1-s segment from which they came. (It is worth noting that in all of our recording sessions, the bins occupied by the rat during the first 1-s segment were not occupied at least once in all subsequent 1-s segments. As a result, none of the data from the first second of the delay period was used in the analysis described next.) With this trial-by-trial data, we could conduct a repeated measures analysis of variance (ANOVA) with factors time and bin to test whether time modulated neural activity. The ANOVA was run on each behavioral variable separately and a P<0.05 was considered statistically significant. Details of ANOVAs on LFPs

20 For the object and odor period, we conducted a three-factor repeated measures analysis of variance (ANOVA) to test whether trial-averaged power did not change across the 4-12 Hz band, across 100 ms (because the window size was 1.2 s and slid only 100 ms), or according to which object was presented during the trial. For the delay period, we computed the trial-averaged spectrogram using a sliding 1 s window (100 ms increments) across the delay period. Here we also used a frequency range between 4-12 Hz. A three-way ANOVA was conducted to test whether the trial-averaged power did not differ across the theta band, across the delay period or depending on which object was presented. For the ANOVA, we used a P < 0.05 as evidence to reject the null hypothesis. After conducting the ANOVA for a tetrode, the p-values that were obtained for the factor object were recorded. For a given tetrode during a trial period, we determined the proportion of active neurons (>0.1 Hz) considered object selective according to the GLM analysis. The Kendall rank correlation coefficient was computed between the tetrode s p- value and the number of object selective neurons recorded from the same tetrode. We reasoned that if object-related differences in trial-averaged theta power explained the tendency to detect object selectivity in single neurons, then lower p-values should result in a larger number of object-selective neurons. Supplemental References Knierim, J.J., Kudrimoti, H.S., and McNaughton, B.L. (1995). Place cells, head direction cells, and the learning of landmark stability. J. Neurosci. 15,