Theta oscillations represent collective dynamics of multineuronal membrane potentials of murine hippocampal pyramidal cells

Noguchi, Asako; Yamashiro, Kotaro; Matsumoto, Nobuyoshi; Ikegaya, Yuji

doi:10.1038/s42003-023-04719-z

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Published: 12 April 2023

Theta oscillations represent collective dynamics of multineuronal membrane potentials of murine hippocampal pyramidal cells

Communications Biology volume 6, Article number: 398 (2023) Cite this article

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Abstract

Theta (θ) oscillations are one of the characteristic local field potentials (LFPs) in the hippocampus that emerge during spatial navigation, exploratory sniffing, and rapid eye movement sleep. LFPs are thought to summarize multineuronal events, including synaptic currents and action potentials. However, no in vivo study to date has directly interrelated θ oscillations with the membrane potentials (Vm) of multiple neurons, and it remains unclear whether LFPs can be predicted from multineuronal Vms. Here, we simultaneously patch-clamp up to three CA1 pyramidal neurons in awake or anesthetized mice and find that the temporal evolution of the power and frequency of θ oscillations in Vms (θ_Vms) are weakly but significantly correlate with LFP θ oscillations (θ_LFP) such that a deep neural network could predict the θ_LFP waveforms based on the θ_Vm traces of three neurons. Therefore, individual neurons are loosely interdependent to ensure freedom of activity, but they partially share information to collectively produce θ_LFP.

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Introduction

Local field potentials (LFPs) are associated with various aspects of animal cognition and behavior, including attention, volition, and learning^1,2,3,4, and are also used as biomarkers of pathological states^5,6. One of the major components of LFPs in the hippocampi of humans^7,8,9 and rodents^10,11,12 is theta (θ) oscillations (3–10 Hz). θ oscillations occur mainly during active exploration, exploratory sniffing, and rapid eye movement sleep and are essential for the normal functioning of the hippocampus^12,13,14. Indeed, θ oscillations are correlated with memory performance^{15,16,17,18,19}, and reduced θ oscillations are associated with memory deficits^19,20, whereas enhanced θ oscillations facilitate cognitive function^21,22.

As a component of LFPs, θ oscillations are thought to reflect extracellular currents that arise from the collective dynamics of subthreshold membrane potentials (Vm)^23,24,25, including synaptic activity, dendritic integration, action potentials, afterpotentials, and other channel-dependent neuronal events, in a large number of neurons^26,27. However, it remains unclear how θ oscillations are associated with the Vm dynamics of multiple neurons in vivo. Previous studies have examined the relationship between LFPs and the Vm of a single pyramidal cell and reported both similarities and discrepancies^23,28,29. For example, one study with simultaneous LFP and single intracellular recordings from the hippocampi of anesthetized rabbits reported that intracellular θ oscillations (θ_Vm) occurred together with LFP θ oscillations (θ_LFP) at similar oscillation frequencies²³, suggesting that θ_Vm serve as a source of θ_LFP; however, not all neurons exhibited θ_Vm during θ_LFP states, and the amplitudes of θ_Vm were also heterogeneous across cells. Thus, it remains unclear how similar θ_Vm rhythms are exhibited in different cells during a θ_LFP period. A more recent study examined the relationships between θ_LFP and θ_Vm in head-fixed running mice²⁸, demonstrating that although θ_Vm tended to occur together with θ_LFP, these two types of oscillations often had inconsistent phases and frequencies. This inconsistency is functionally important for θ phase precession because a θ_Vm rhythm that is faster than the θ_LFP rhythm allows the neuron to fire at earlier phases of θ_LFP during spatial movement. Nonetheless, it remains unclear how the diverse θ_Vms of multiple hippocampal neurons are reflected in unidimensional θ_LFP. These questions can be answered, at least in part, by simultaneously recording the Vms of multiple neurons.

In the present study, we simultaneously recorded the Vms of up to three CA1 pyramidal cells in mice to directly compare their Vm dynamics to LFPs. We found that θ_Vm occurred intermittently, often together with θ_LFP. In some but not all LFP-cell pairs and cell‒cell pairs, θ oscillations showed similar changes in power and frequency over time. Specifically, the θ_LFP power increased when more CA1 pyramidal neurons simultaneously emitted θ_Vms. When neurons had similar θ_Vm frequencies, the θ_LFP power increased, and the θ_LFP frequency approached the average value of the neuron θ_Vm frequencies. As a result, θ_LFP was predictable from the θ_Vm dynamics of three CA1 pyramidal cells using deep learning. These findings provide fundamental insights into how LFPs are associated with multineuronal Vms in vivo, demonstrating their collective potential for predicting LFPs.

Results

Coordinated θ_LFPs across the dorsal hippocampal CA1 area

To ensure the θ_LFP-θ_Vm correlation analyses below, we first verified whether θ_LFPs were uniform within our targeted area. LFPs were simultaneously recorded from four sites in the dorsal CA1 area of the mouse hippocampus (Fig. 1a-c). The area enclosed by the four sites encompassed the area for LFP and patch-clamp recordings in the following experiments. LFPs spontaneously alternated between periods with and without θ_LFP at frequencies ranging from 3 to 10 Hz (Fig. 1d, e). The θ_LFP power was reduced after intraperitoneal administration of 50 mg/kg atropine, a muscarinic receptor antagonist (Supplementary Fig. 1). Therefore, the θ_LFP represented type 2 θ oscillations³⁰.

**Fig. 1: Synchronized θ_LFPs across the dorsal hippocampal CA1 area.**

The LFP traces were divided into a time series of 1-s segments, and the mean θ_LFP power was calculated for each segment. The time-dependent changes in the mean θ_LFP power were plotted in the space of each pair of simultaneously recorded LFP traces (Fig. 1f). The more similar the changes in the θ_LFP power of the two recording sites were, the closer the data points were to the identity line in the plot. To quantify this similarity, we calculated the correlation coefficient for each plot. For all 30 LFP pairs from 5 mice, the correlation coefficients were significant and positive (Fig. 1g), indicating that θ_LFP emerged simultaneously at all four recording sites. Considering that the recording time affects the correlation, the entire recording period was divided into 1-, 2-, 3-, 5-, 10- or 15-min time windows, and the correlation was evaluated for each time window. While the correlation increased slightly with increasing time window lengths, a significant positive correlation was observed for >90% of the entire recording period, regardless of the length of the time window (Supplementary Fig. 2, all time window lengths, P = 1.1 × 10⁻⁴, χ² = 25.6; time windows >2 min, P = 0.049, χ² = 9.6; time windows >3 min, P = 0.11, χ² = 6.11, chi-square test, n = 900, 450, 300, 180, 90, and 60 time windows for 1, 2, 3, 5, 10, and 15 min, respectively). Thus, the time changes in θ_LFP power were synchronized among the four recording sites and were minimally affected by the recording time. To examine the phase relationship between simultaneously recorded θ_LFPs, the LFP traces were bandpass filtered between 3 and 10 Hz, and the cross-correlations were computed. The time lags were calculated by referencing the θ_LFPs recorded from relatively medial or anterior locations for individual pairs so that the θ_LFP propagations along the longitudinal axis of the hippocampus^11,31 could be extracted (Fig. 1h, i). Overall, the θ_LFPs were highly synchronous between LFP pairs, regardless of their relative positions (Fig. 1h, i). The θ_LFPs recorded from medial positions significantly preceded their counterparts (Fig. 1j ML, P = 0.0023 vs. time 0, t₁₄ = −3.7, Student’s t-test, n = 15 pairs from 5 mice), while no such effects were observed between θ_LFP pairs along the anteroposterior axis (Fig. 1j AP, P = 0.095 vs. time 0, t₁₃ = 1.8, Student’s t-test, n = 14 pairs from 5 mice), which is consistent with a previous report¹¹. Therefore, θ_LFPs were synchronized across the entire hippocampal windows targeted in our study, with mediolateral propagation on a fine time scale.

Next, we divided the entire recording times into θ_LFP and non-θ_LFP periods using a threshold based on the standard deviation (SD) of the background noise against the power of the θ frequencies in the wavelet spectrogram (Supplementary Fig. 3). To determine an appropriate SD threshold, we categorized putative θ_LFP and non-θ_LFP periods using various multiples of the SD (1 SD, 2 SDs, 3 SDs, and 4 SDs) and calculated the Dice similarity coefficients to estimate the strength of synchronization of the detected θ_LFP periods between two recording sites (Supplementary Fig. 3a). The distributions of the Dice similarity coefficients were compared to their statistical chance levels obtained from 10,000 surrogate data samples in which the detected θ_LFP periods were randomly shuffled across time within each recording site. The difference in the original and surrogate data distributions was assessed according to the D value of a two-sample Kolmogorov‒Smirnov test, and the D value reached the maximum at 2 SDs (Supplementary Fig. 3b). Therefore, in the following analyses, we defined a θ period as a time period during which the θ power continued to exceed 2 SDs against the background noise.

Characteristics of Vm activity during θ_Vm and non-θ_Vm periods

To examine the θ_LFP-θ_Vm relationship, we first characterized the θ_Vm dynamics. We patch-clamped pyramidal cells in the hippocampal CA1 region of urethane-anesthetized mice (Fig. 2a). Recordings were excluded from subsequent analyses if post hoc biocytin-based visualizations, their recording sites, and/or their firing properties failed to identify the recorded neurons as CA1 pyramidal cells (Fig. 2b). As a result, we recorded Vms from 220 patch-clamped cells in a total of 112 mice. The recording periods ranged from 30 s to 2097 s (median = 180 s).

**Fig. 2: Variable θ_Vm frequencies in a CA1 pyramidal cell.**

Similar to LFPs, spontaneous Vm responses alternated between periods with and without θ oscillations (Fig. 2c); of the total recording time, ~34 ± 26% represented θ periods (mean ± SD of 220 cells, ranging from 0.84 to 95%). The frequency of θ_Vm was not unique to a given cell but varied among θ_Vm periods (Fig. 2d). Spikes from pyramidal cells were entrained to θ_Vm cycles such that the firing rates peaked at the θ_Vm phase of 0° (Fig. 2e; P < 10⁻³²³, Z = 3.7 × 10³, Rayleigh test, n = 4655 spikes from 220 cells). Analysis using a generalized linear mixed model demonstrated that the mean firing rates during θ_Vm periods increased as a function of θ_Vm power (Fig. 2f, β = 0.22, P = 8.0 × 10⁻⁹, t₁₀₃₂ = 5.8, n = 1,034 θ periods from 220 cells). The mean firing rates also increased with increasing θ_Vm frequency (Fig. 2g, β = 0.10, P = 0.035, t_1,032 = 2.1, n = 1034 θ periods from 220 cells). The firing rates and power were Z-standardized in each cell and pooled across all recorded cells.

Weakly correlated θ_LFP and θ_Vm

We next compared θ oscillations between Vm and LFPs. While recording Vm from a single CA1 pyramidal cell, we recorded LFPs from a single site in the CA1 region in the same hippocampal window (Fig. 3a–e). The θ_LFP power was not correlated with the firing rates of patch-clamped cells (Supplementary Fig. 4). To examine whether θ_Vm and θ_LFP occurred simultaneously, we plotted the time-dependent changes in the θ powers of Vm and LFPs every 100 ms (Fig. 3c, e). The correlation coefficients varied among cells; the θ_Vm power exhibited a significant positive correlation with the θ_LFP power in 66 (41%) cells out of 160 neurons, whereas the remaining 94 (59%) cells did not exhibit significant correlations (Fig. 3f). Therefore, the θ_Vm power was correlated, at least in part, with the θ_LFP power; however, this correlation was not robust. The correlation coefficients were not associated with the distances between the LFP recording sites and the patch-clamped cells (Fig. 3g, R = 0.087, P = 0.43, t-test for correlation coefficients, n = all 86 cells whose loci were confirmed post hoc), indicating that even if the cells were located near the LFP recording site or generated strong θ_Vm, their influence on θ_LFP was not necessarily large. In addition, there were no significant relationships between the correlation coefficients and the recording time length (Supplementary Fig. 5a, R = 0.11, P = 0.19, t-test for correlation coefficients, n = 160 cells), the mean θ_Vm power (Supplementary Fig. 5b, R = −0.042, P = 0.60, n = 160 cells), the mean firing rate (Supplementary Fig. 5c, R = −0.081, P = 0.31, n = 160 cells), the mean Vm (Supplementary Fig. 5d, R = −0.14, P = 0.076, n = 160 cells), and the standard deviation (SD) of Vm (Supplementary Fig. 5e, R = 0.068, P = 0.39, n = 160 cells). Furthermore, neither the cell locations along the proximodistal (Supplementary Fig. 5f, P = 0.62, one-way analysis of variance (ANOVA), n = 27, 41, 45, 11, 11 for CA1a, a/b, b, b/c, c, respectively) nor the radial (Supplementary Fig. 5g, P = 0.27, t₁₃₁ = 1.1, Student’s t-test, n = 80 and 53 cells for deep and superficial, respectively) axes were significantly related to the correlation coefficients. Therefore, the engagement of each cell with the ongoing θ_LFP might not be intrinsically predetermined but rather be flexibly modifiable.

**Fig. 3: Weak correlations between θ_LFP and θ_Vm.**

During a co-θ period when θ oscillations occurred simultaneously in Vm and LFPs, the θ_Vm frequency was positively correlated with the θ_LFP frequency (Fig. 3h, R = 0.29, P < 10⁻³²³, t-test for correlation coefficients, n = 2659 co-θ periods from 160 datasets). However, there were also many outlier data points distant from the identity line in Fig. 3h, indicating that θ_Vm and θ_LFP did not always share common frequencies. Consistent with this notion, the θ_Vm frequencies were, on average, slightly higher than the θ_LFP frequencies (P = 8.8 × 10⁻¹⁰, t_2,658 = −6.2, paired t-test, n = 2659 co-θ periods). Interestingly, the differences between θ_Vm and θ_LFP frequencies during each co-θ period decreased as the mean θ_Vm and θ_LFP powers increased (Fig. 3i, R = −0.094, P = 9.8 × 10⁻⁷, n = 2,703 co-θ periods from 160 cells). Moreover, θ_Vm and θ_LFP were not in phase. We focused on the coherent periods, during which the difference between θ_LFP and θ_Vm frequencies was <0.01 Hz, and calculated their phase differences. Considering the θ_LFP propagation along the mediolateral axis described in Fig. 1j, the phase differences were plotted separately for the datasets in which the recorded cells were located medial to LFP recording sites (Fig. 3j) or vice versa (Fig. 3k). The phase difference between θ_LFP and θ_Vm was not uniformly distributed, and the θ_Vm of the cells medial to the LFP recording sites preceded the θ_LFP by 74° on average (Fig. 3j, P = 8.1 × 10⁻⁸, Z = 16.0, Rayleigh test, n = 172 periods from 30 cells). Anatomically reversed datasets showed the opposite result, i.e., the θ_Vm recorded at lateral positions to the LFP recording sites followed the θ_LFP by 30° on average (Fig. 3k, P = 0.038, Z = 3.25, Rayleigh test, n = 46 periods from 16 cells). The phase relationship between θ_LFP and θ_Vm did not differ depending on the cell locations along the radial axis in the pyramidal cell layer (Supplementary Fig. 5h, i, P > 0.1, K = 1.8 × 10³, Kuiper test, n = 151 and 74 periods from 26 and 20 deep and superficial cells, respectively).

We repeated the same series of experiments using awake, head-fixed mice (Supplementary Fig. 6a, b, n = 22 cells from 17 mice). Neither the durations nor the frequencies of the θ_LFP differed between urethane-anesthetized and awake mice (Supplementary Fig. 6c, d), indicating that type 2 θ oscillations dominated under our experimental conditions, in which mice were forced to be immobile. The data were analyzed, as shown in Fig. 3d, revealing that 10 (40%) of the 22 cells showed significant positive correlations in θ power changes (Supplementary Fig. 6e). This ratio did not differ from that of the anesthetized mice (P = 0.71, χ² = 0.14, Pearson’s χ² test). The differences between θ_Vm and θ_LFP frequencies decreased as the mean θ_Vm and θ_LFP powers increased (Supplementary Fig. 6f, β = −0.022, P = 0.0018, t₂₅₈₇ = −3.13, n = 2589 θ periods from 22 cells).

Therefore, we concluded that θ_Vm and θ_LFP are partially correlated with each other and that the correlation strength depended on the oscillation states, such as θ power or θ frequency.

Weakly correlated θ_Vms in two CA1 pyramidal cells

The weak θ_LFP-θ_Vm coupling described above led to the inference that θ_Vms of cell pairs are coherent. We obtained simultaneous patch-clamp recordings from two CA1 pyramidal cells (Supplementary Fig. 7a) and collected 125 dual patch-clamp datasets (Vm1 and Vm2) from 82 mice. The recording periods ranged from 36 s to 2097 s (median = 150 s). We applied the same analyses as in Fig. 3 to the dual patch-clamp recording datasets. We first plotted the time changes in the θ_Vm powers of two cells (Supplementary Fig. 7b–e) and found that 80 (64%) of the 125 cell pairs showed significant positive correlations in their θ_Vm power changes (Supplementary Fig. 7c, f), whereas the remaining 45 cell pairs did not (Supplementary Fig. 7e, f). Compared with the LFP-cell pair results in Fig. 3e, the proportion of significantly correlated cell pairs was high, which might reflect the different LFP states in separate datasets. However, the proportion of cell pairs with positive correlations did not change significantly from the proportion calculated for only the datasets used in Fig. 3 (Supplementary Fig. 8a, b, P = 0.49, χ² = 0.47, chi-square test, n = 125 (all data) and 98 (data in Fig. 3 only) cell pairs, respectively). Cell pairs whose somata were physically closer had a stronger correlation (Supplementary Fig. 7g, R = −0.24, P = 0.033, n = 78 cell pairs). The θ frequencies during each co-θ period were significantly correlated between the two cells (Supplementary Fig. 7h, R = 0.25, P < 10⁻³²³, n = 2027 θ periods from 125 cell pairs), although they were not fully consistent. The differences between θ_Vm frequencies decreased as the mean θ_Vm powers of the two cells increased (Supplementary Fig. 7i, β = −0.011, P < 10⁻³²³, t_34,628 = −47.3, n = 34,630 θ periods from 125 cell pairs). Therefore, θ_Vms were correlated between adjacent cells, but again, these correlations were only partial.

Correlated θ power changes among LFPs and multiple cells

We expanded our experiments to triple patch-clamp recordings with CA1 LFP recordings (Fig. 4a, b). We collected 21 triple-patching and LFP datasets (Vm1, Vm2, Vm3, and LFP) from 15 mice. The recording periods ranged from 31 s to 900 s (median = 80 s). For the sake of simplicity, we first investigated the time-dependent changes in the θ power by focusing on the pairwise correlations between LFPs and the average value of three Vms (Fig. 4c–e). Of 21 datasets, 9 (43%) had significant positive correlations between the θ_LFP power and mean θ_Vm power (Fig. 4c, e), whereas the other 12 did not (Fig. 4d, e).

**Fig. 4: Stronger correlations of θ_LFP for more correlated θ_Vms.**

We next focused on the instantaneous θ_LFP-θ_Vm correlations. The θ_LFP power became stronger when more cells simultaneously exhibited θ_Vms (Fig. 4f, P = 0.0060, Z = 2.51, Jonckheere trend test, n = 13 datasets that included at least one period during which all recordings simultaneously exhibited θ oscillations). When all three cells simultaneously exhibited θ_Vms, the θ_LFP power was positively correlated with the squared inverse of the coefficients of variance (1/CV²) of the three θ_Vm frequencies (Fig. 4g, R = 0.17, P = 0.014, n = 206 co-θ periods from 13 datasets). This result indicates that the θ_LFP power increased when the three cells exhibited θ_Vms with more similar frequencies. Moreover, the difference between the θ_LFP frequency and the mean frequency of the three θ_Vms was negatively correlated with 1/CV² of the three θ_Vm frequencies, indicating that the θ_LFP frequency approached the mean θ_Vm frequency when the three θ_Vm frequencies were more similar (Fig. 4h, R = −0.78, P < 10⁻³²³, t₂₀₄ = 17.7, n = 206 co-θ periods from 13 datasets).

Machine learning-based prediction of LFPs

These instantaneous θ_LFP-θ_Vm correlations motivated us to hypothesize that the dynamics of θ_LFP at each moment can be estimated, at least in part, from the θ_Vms of three cells. To test this hypothesis, we sought to predict the θ_LFP waveforms from three θ_Vm waveforms using a machine learning model. Assuming that θ_Vms are associated with θ_LFP in a nonlinear manner, we employed a deep neural network (DNN) with a convolutional layer (Fig. 5a, Supplementary Fig. 9). Among the 21 triple patch-clamp recording datasets, we selected 8 datasets with recording periods >3 min to ensure sufficient sample sizes for training the DNN. In each dataset, the Vm and LFP traces were bandpass filtered between 3 and 10 Hz, divided into 10 subsets in the recording time, and further divided into 1-s segments. We trained the DNN using 1-s segments in 9 subsets of the recorded data to predict the θ_LFP waveforms during 1-s segments in the remaining subset (1/10 subsets), which were not used to train the DNN (Fig. 5b, real). For each prediction, the prediction error between the original and predicted θ_LFP traces was quantified by the root mean square error (RMSE). We also trained the DNN using randomized pseudodata, in which 1-s segments from the training period were shuffled within each cell. We then predicted the θ_LFP waveform (Fig. 5b, shuffle) and computed the RMSEs for the original θ_LFP waveform and the θ_LFP waveform predicted by the shuffled data. We repeated this procedure so that all segments in the entire recording period were targeted for prediction. The RMSEs were pooled in a cumulative plot (Fig. 5c). The prediction performance was evaluated using the D value of a two-sample Kolmogorov‒Smirnov test; in all 8 datasets, the RMSEs of the real data were significantly lower than those of the shuffled data (Fig. 5d, 3 cells). These results indicate that the DNN predicted θ_LFP waveforms based on the θ_Vm dynamics of as few as three cells with accuracy significantly higher than chance. However, the DNN significantly predicted zero or only two of the 24 datasets based on the θ_Vm dynamics of only one or two cells, respectively (Fig. 5d, 1 cell, 2 cells). The D-values of the predictions based on the θ_Vm dynamics of three cells were significantly higher than those based on the θ_Vm dynamics of fewer cells, indicating that the θ_LFP dynamics reflect the collective features of multiple θ_Vm dynamics, which needed to be collected from at least three cells. Supplementary Fig. 10 summarizes the D-values and their significance in all datasets.

**Fig. 5: Prediction of θ_LFP from θ_Vms.**

The same analysis was conducted using bandpass-filtered traces at 60–100 Hz (high gamma), 25–55 Hz (low gamma), and 0.5–1 Hz (slow oscillations). In contrast to the findings with the θ frequency band, significantly higher accuracies were obtained in only a small proportion of the datasets, regardless of the number of cells used for the prediction (Supplementary Fig. 11, high gamma: 5/24 datasets for 1 cell and 2/24 datasets for 2 cells; low gamma: 1/24 dataset for 1 cell and 2/24 datasets for 2 cells; slow oscillations, 4/24 datasets for 1 cell, 4/24 datasets for 2 cells and 2/8 datasets for 3 cells). For all three frequency bands, increases in the number of cells used for the predictions did not correspond to an increase in the prediction accuracy (Supplementary Fig. 11a, D_{1 vs. 2 cells} = 0.17, P_{1 vs. 2 cells} = 0.86, D_{1 vs. 3 cells} = 0.50, P_{1 vs. 3 cells} = 0.066, D_{2 vs. 3 cells} = 0.46, P_{2 vs. 3 cells} = 0.11; Supplementary Fig. 11b, D_{1 vs. 2 cells} = 0.21, P_{1 vs. 2 cells} = 0.62, D_{1 vs. 3 cells} = 0.25, P_{1 vs. 3 cells} = 0.79, D_{2 vs. 3 cells} = 0.78, P_{2 vs. 3 cells} = 0.29; Supplementary Fig. 11c, D_{1 vs. 2 cells} = 0.46, P_{1 vs. 2 cells} = 0.0082, D_{1 vs. 3 cells} = 0.33, P_{1 vs. 3 cells} = 0.43, D_{2 vs. 3 cells} = 0.50, P_{2 vs. 3 cells} = 0.066; two-sample Kolmogorov‒Smirnov test, n = 24, 24, and 8 datasets for 1, 2, and 3 cells, respectively). To examine the relationships among LFPs and Vms in frequency bands other than θ, we calculated the cross-correlograms between pairs of bandpass-filtered LFPs, the correlation coefficients between LFP and Vm powers of single cells, and the correlation coefficients between LFPs and the mean Vm power of three simultaneously recorded cells for all three frequency bands. Overall, the correlations among LFPs and Vms were comparable to those in the θ frequency band (Supplementary Fig. 12a–i). However, the average power spectra of the LFPs and Vms over the entire recording period showed that θ power dominated in all other frequency bands (Supplementary Fig. 12j, k). Therefore, the predictability of LFP traces from Vm traces was applicable only for physiologically dominant oscillations, suggesting that the DNN could extract biologically prominent signals.

If the θ_LFP dynamics reflected the simple summation of multiple θ_Vms, the linear summations of the θ_Vm traces were expected to become more similar to the θ_LFP traces as the number of cells increased. As shown in Supplementary Fig. 13a, we analyzed the correlation between the θ_LFP traces and the mean θ_Vm traces of 1, 2, or 3 cells for each 1-s segment used in the θ_LFP prediction. However, contrary to expectations, the correlation coefficients decreased as the number of cells increased (D_{1 vs. 2 cells} = 0.029, P_{1 vs. 2 cells} = 6.5 × 10⁻⁴², D_{1 vs. 3 cells} = 0.049, P_{1 vs. 3 cells} = 4.1 × 10⁻⁵⁹, D_{2 vs. 3 cells} = 0.021, P_{2 vs. 3 cells} = 1.3 × 10⁻¹², two-sample Kolmogorov‒Smirnov test, n = 112,740, 112,740, and 37,580 1-s segments from 1, 2, and 3 cells, respectively, in 8 mice). This result indicates that the mean θ_Vm traces of more cells were less similar to the θ_LFP trace. The θ_LFP and θ_Vm powers were also calculated for each 1-s segment, and the correlation between the dynamics of the θ_LFP power and the dynamics of the mean θ_Vm power of 1, 2, or 3 cells were analyzed in each dataset (Supplementary Fig. 13b). There were no significant differences among the three distributions, indicating that the similarity between the dynamics of the θ_LFP power and the mean θ_Vm power of multiple cells did not change significantly depending on the number of cells (D_{1 vs. 2 cells} = 0.17, P_{1 vs. 2 cells} = 0.86, D_{1 vs. 3 cells} = 0.25, P_{1 vs. 3 cells} = 0.79, D_{2 vs. 3 cells} = 0.17, P_{2 vs. 3 cells} = 0.99, two-sample Kolmogorov‒Smirnov test, n = 24, 24, and 8 datasets from 1, 2, and 3 cells, respectively, in 8 mice). These results suggest that the ability to predict θ_LFP traces from the θ_Vm traces of three cells is not explained solely by the linear sum of multiple θ_Vms. Taken together, the DNN could predict θ_LFP waveforms from the θ_Vm dynamics of three cells based on their nonlinear relationships.

Discussion

We investigated the temporal correlations in extracellular and intracellular θ oscillations by directly comparing LFPs with the Vms of multiple CA1 pyramidal cells in vivo. We found that in terms of θ powers and frequencies, the θ_Vms of hippocampal CA1 pyramidal cells were loosely correlated with each other and with θ_LFP. These correlations were not explained by the anatomical locations and likely arose due to functionally coherent network activity. Consistent with this idea, we demonstrated, using a machine learning technique, that the θ_LFP waveforms could be predicted from the θ_Vm waveforms of only three pyramidal cells. Given that LFPs usually reflect the activity of considerably more than three neurons, our results suggest that many neurons simultaneously emit partially correlated θ_Vms and that this loose simultaneity constitutes hippocampal θ states and is experimentally captured as θ_LFP.

We first demonstrated that the temporal evolution of θ_LFP power was similar across our target area in the dorsal CA1 region. Previous studies have reported that θ_LFP travel along the longitudinal axis of the hippocampus^11,31,32 and that θ_LFP phase shifts monotonically as a function of the distance along the longitudinal axis, reaching ~180° between the septal and temporal poles³¹. Consistent with a previous report¹¹, mediolateral propagation of the θ_LFP was observed in our study instead of anteroposterior propagation, despite the different animal conditions, i.e., awake and anesthetized conditions in the previous and present study, respectively. Therefore, in the present study, we considered the phase shift when analyzing the phase difference between θ_LFP and θ_Vm (Fig. 3h), and the overall transition of the θ_LFP power was considered synchronous within our target area. The difference in the type of θ_LFP between awake and anesthetized animals should also be noted in considering the functional significance of our findings. The θ_LFP we recorded from urethane-anesthetized mice were atropine-sensitive type 2 θ_LFP, which usually have frequencies in the 4–7 Hz range; note that type 1 θ_LFP is resistant to atropine, have higher frequencies of ~8 Hz, and occur mainly during active locomotion and rapid eye movement sleep^13,14. We also recorded θ_LFP in awake mice. Although we did not examine the effect of muscarinic receptor antagonists, the θ_LFP were also likely type 2 because the mice were immobile under head-fixed conditions, and their θ_LFP frequencies did not differ from those of anesthetized mice. Under anesthesia, the CA1 region may receive less input from the entorhinal cortex, but in both urethane-anesthetized and awake mice, cholinergic and GABAergic inputs from the medial septum are essential to generate θ oscillations^{30,33,34,35,36,37}. Although type 1 and 2 θ_LFPs have different atropine sensitivities and θ frequency ranges, they share many common features; for example, both types depend on medial septal afferents and have similar θ phase distributions in the dorsal hippocampus^33,37,38. Therefore, we believe that the mechanisms underlying the observed cell-to-LFP or cell-to-cell correlations could be partially shared by type 1 θ_LFP, at least within the local hippocampal circuit. Supporting this theory, pairwise θ_Vm coherences during type 1 θ_LFP in awake, behaving mice have been reported to range from 0 to 0.8, regardless of the cell-to-cell distance³⁹, which is consistent with our findings on type 2 θ_LFP. However, the anesthetized condition causes distinct activity in the medial septum⁴⁰ and the entorhinal cortex^41,42. As a result, instructive signals for learning-dependent neuronal activity are lacking, as observed during type 1 θ_LFP in the hippocampus^43,44,45,46. Future experiments recording intracellular activity from multiple hippocampal neurons in awake behaving animals should clarify the subthreshold coordination of behavior-relevant cell assemblies in θ_LFP state.

LFPs are shaped by collecting a myriad of electrical currents arising from neural events, such as synaptic inputs and action potentials. Therefore, intuitively, the relationship between LFPs and Vms might be influenced by the physical distance from the cell body. However, we did not find that the cell-to-LFP correlations in the θ power or frequency changed with the cell-to-LFP distance, at least within a radius of ~1,000 µm. One possible explanation for this discrepancy is that synaptic inputs are received by dendrites distal from the cell bodies. The dendrites of many neurons intersect, generating spatially overlapping synaptic currents. The complexity of individual current sources may blur the dependency for cell-to-LFP distances. Another but more plausible possibility is that cell-to-cell coherence arises from intrinsic cell assembly dynamics. We recorded from only three cells out of numerous neurons in the dorsal hippocampus. Even though these cells were selected in a pseudorandom and blinded manner, their θ_Vms were partially correlated, enough for our machine learning model to predict θ_LFP. Therefore, we believe that the θ_LFP-to-θ_Vm correlations observed in the present study did not arise from a direct causal relationship produced by the neurons we recorded but rather from the activity of other neurons located closer to the LFP recording site that behaved in a similar manner to the recorded neurons.

The coordination of θ_LFP and θ_Vms could be achieved by the interplay of inhibitory inputs from various types of interneurons^47,48,49 and excitatory inputs mainly from CA3 pyramidal cells under our anesthetized condition^46,50,51, each of which phase-locks to a specific θ_LFP phase. Among the various types of hippocampal CA1 interneurons, soma-targeting parvalbumin-positive basket cells (PV-BCs) and cholecystokinin-positive basket cells (CCK-BCs) effectively regulate θ_Vm^37,46,52. Considering that PV- and CCK-BCs differentially innervate CA1 pyramidal cells in the deep and superficial layers⁵¹, i.e., PV-BCs and CCK-BCs preferentially project onto deep and superficial cells, respectively, the phase relationships between θ_LFP and θ_Vm may differ for deep and superficial cells⁵³. However, Supplementary Fig. 5h indicates that deep and superficial cells showed similar θ_LFP phase preferences⁵³. Because deep cells receive more inputs from the medial entorhinal cortex than superficial cells, this discrepancy might indicate that excitatory inputs from the medial entorhinal cortex, which are weakened under anesthesia, contribute to the shifted phase preference of deep cells. In addition, the variable holding Vm may have affected the phase lag between the peaks of θ_LFP and θ_Vm⁴⁶, while the overall phase lags were consistent with those in previous intracellular studies^37,54. Although we did not note any anatomical bias in the relationship between θ_LFP and θ_Vm, presumably due to the anesthesia and the large distance between the LFP and Vm recording sites (φ < 1,000 µm), the temporally precise and partially shared excitatory and inhibitory inputs among CA1 pyramidal cells may organize multicellular coordination in the θ_LFP state.

Using a DNN, we predicted the θ_LFP traces from the θ_Vm traces of three CA1 pyramidal neurons. Previous in silico studies have simulated LFPs based on modeled neuronal activity in the neocortex^55,56,57. However, no studies to date have attempted to predict real LFPs based on the membrane potentials of multiple neurons in vivo. This lack of data is partly due to the lack of simultaneous recordings of LFPs and Vms from multiple neurons, which is technically difficult to accomplish, especially in the hippocampus. Therefore, the present study provides the first evidence that θ_LFP dynamics are predictable from the raw θ_Vm traces of three neurons in the hippocampus in vivo. It remains unclear why the predictability increased in a nonlinear manner when the number of cells used for θ_LFP prediction was increased from two to three. One possible explanation is composite factors among the θ_Vms of multiple neurons, as implied in our triple-patching datasets (Fig. 4); possible combinations among these factors could increase in a nonlinear manner as the number of cells increases. Further investigations are needed to elucidate latent factors shared across θ_Vms that collectively predict θ_LFP dynamics.

One limitation of this study is that our prediction approach did not reflect the diversity of pyramidal cells embedded in anatomically and physiologically nonuniform hippocampal circuits^51,58,59. While our study did not observe any anatomical or physiological biases within our recorded cells (Supplementary Fig. 5), the θ_Vms of individual pyramidal cells should show distinct relationships with θ_LFP according to different input patterns and intrinsic properties in awake behaving animals^53,60. The DNN used to predict θ_LFP from θ_Vms may be improved by considering these biased innervation and intrinsic properties. Furthermore, the prediction could benefit by including not only the θ_Vms of pyramidal cells but also the activity of PV- and CCK-BCs^37,46,52 as the inputs to the DNN. On the other hand, the fact that the DNN significantly predicted θ_LFP from θ_Vms of as few as three pseudorandomly selected pyramidal cells might suggest that the DNN could accommodate the spatiotemporally biased circuit structure, confirming the potential ability of the DNN to process higher-order information. Future studies should combine cell-type-specific recordings of excitatory and inhibitory neurons with computational approaches such as deep learning-based analyses to better understand the circuit mechanisms involved in coordinating network activity at the single-cell level.

Methods

Animal ethics

Animal experiments were performed with the approval of the animal experiment ethics committee at the University of Tokyo (approval numbers: P29-9) and in accordance with the University of Tokyo guidelines for the care and use of laboratory animals. These experimental protocols were conducted in accordance with the Fundamental Guidelines for the Proper Conduct of Animal Experiments and Related Activities in Academic Research Institutions (Ministry of Education, Culture, Sports, Science and Technology, Notice No. 71 of 2006), the Standards for Breeding and Housing of and Pain Alleviation for Experimental Animals (Ministry of the Environment, Notice No. 88 of 2006) and the Guidelines on the Method of Animal Disposal (Prime Minister’s Office, Notice No. 40 of 1995).

Surgery and animal preparation

Whole-cell recordings through the hippocampal window were obtained from male ICR mice (Japan SLC, Shizuoka, Japan) that were 28–45 days old⁶¹. Mice were anesthetized with urethane (2.25 g/kg, intraperitoneal [i.p.]). Anesthesia was confirmed by the absence of paw withdrawal, whisker movement, and eyeblink reflexes. The skin was subsequently removed from the head, and the animal was implanted with a metal head-fixation plate. A craniotomy (2.5 × 2.0 mm²) was performed, centered at 2.0 mm posterior to the bregma and 2.5 mm ventrolateral to the sagittal suture, and neocortical tissues above the hippocampus were aspirated^62,63,64,65. The exposed hippocampal window was covered with 1.7% agar at a thickness of 1.5 mm. To obtain recordings from unanesthetized mice, mice were implanted with metal head-holding plates under short-term anesthesia with 2–3% isoflurane. After full recovery, the mice received head-fixation training on a custom-made stereotaxic fixture for 1–2 h per day. The training continued for up to 5 days until the mice learned to remain calm.

In vivo electrophysiology

Patch-clamp recordings were obtained from neurons in the dorsal CA1 stratum pyramidale (AP: -2.0 mm; ML: 2.0 mm; DV: 1.1–1.3 mm) using borosilicate glass electrodes (4–7 MΩ). Pyramidal cells were identified by their regular spiking properties and post hoc intracellular visualization. For current-clamp recordings, the intrapipette solution consisted of the following reagents (in mM): 120 K-gluconate, 10 KCl, 10 HEPES, 10 creatine phosphate, 4 MgATP, 0.3 Na₂GTP, 0.2 EGTA (pH 7.3), and 0.2% biocytin. Liquid junctions were corrected offline. Cells were discarded when the mean resting potential exceeded −50 mV or the action potentials did not exceed -20 mV. LFPs were obtained from the CA1 stratum pyramidale using tungsten electrodes (UEWMGCSEKNNM, FHC, USA) coated with 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine (DiI). The tungsten electrode location was detected by post hoc observation of fluorescent DiI tracks. Simultaneous quadruple LFP recordings were obtained by using four glass electrodes (0.5-2.5 MΩ) filled with artificial cerebrospinal fluid (aCSF), including DiI (4% w/v), Evans Blue (2%), or Trypan Blue (2%), for post hoc identification of the electrode locations (Fig. 1). The electrode locations estimated during the stereotaxic experiments were approximately the same as the post hoc visualized positions. Only the LFPs recorded in the pyramidal cell layer were included in the analyses. The signals from the four glass electrodes were amplified using a MultiClamp 700B amplifier, whereas the signals from the tungsten electrode were amplified using a DAM80 AC differential amplifier (World Precision Instruments). All signals were digitized at a sampling rate of 20 kHz using a Digidata 1440 A digitizer (Molecular Devices) that was controlled by pCLAMP 10.3 software (Molecular Devices). To confirm the type of θ_LFP (Supplementary Fig. 1), atropine was intraperitoneally injected at a dose of 50 mg/kg at least 120 s after the beginning of the LFP recordings. The effect of atropine was examined 960–1,080 s after the injection (a 120-s period).

Histology

Following each experiment, the electrode was carefully withdrawn from the hippocampus. The mice were transcardially perfused with 4% paraformaldehyde followed by overnight postfixation. The brains were sagittally sectioned at a thickness of 100 μm using a vibratome. The sections were incubated with 2 μg/ml streptavidin-Alexa Fluor 594 conjugate and 0.2% Triton X-100 for 4 h, followed by incubation with 0.4% NeuroTrace 435/455 blue fluorescent Nissl stain (Thermo Fisher Scientific; N21479) for 4 h. The tracks of the LFP electrodes were also detectable via DiI fluorescence. Fluorescence images were acquired using an FV1200 confocal microscope (Olympus, Tokyo, Japan) and subsequently merged. The depth of the soma and the tips of the tungsten electrodes were estimated in the Z-scan series of an FV1200 confocal microscope. More specifically, the CA1 area was roughly divided into three subareas along the proximodistal axis, and the locations of the soma and the tips of tungsten electrodes were visually classified as one of the following five positions: CA1a, the border between CA1a and b, CA1b, the border between CA1b and c, or CA1c. Then, the XYZ coordinates of the soma and the tips of tungsten electrodes in the brain were determined based on the origin located at the bregma, with the X- and Y-axes representing the mediolateral and anteroposterior axes, respectively.

Statistics and reproducibility

Data analyses were performed using MATLAB (R2017b, Natick, Massachusetts, USA), and the summarized data are reported as the mean ± SD unless otherwise specified. P < 0.05 was considered statistically significant. Sample size (the number of triple-patching datasets and single whole-cell recordings in awake condition) was determined by referencing previous publications (Jouhanneau et al., 2018, 2019). No statistical methods were used to predetermine the sample size. All conclusions of this study are based on recordings of populations of cells.

Data analysis

To detect periods with θ_LFP, wavelet transformations were first conducted for each LFP recording, the sampling rate of which was reduced to 500 Hz. Any period was defined as a θ_LFP period if the mean absolute value of its wavelet coefficients between 3‒10 Hz exceeded the mean ± 2 SDs of the values between 1–100 Hz. When the duration of θ_LFP or non-θ_LFP periods was <1 s, we regarded the duration as a non-θ_LFP or θ_LFP period, respectively. The 2 SD threshold for detecting the θ_LFP period was determined after ascertaining that the similarity of θ_LFP periods in the four simultaneously recorded LFPs at this threshold was most distinguishable from the surrogate data (Supplementary Fig. 2). θ_Vm periods were also detected using the same threshold. The similarity of θ_LFP periods in simultaneously recorded LFP pairs was quantified using the Dice similarity coefficient, the double union of two independent sets divided by the sum of the two sets. The surrogate data were created by randomly shuffling the timings of the individual θ_LFP periods without changing the duration of each period. The peak frequency was calculated based on the wavelet power as the absolute value of the wavelet coefficient. The wavelet power at each frequency was averaged across the target period, and the frequency at which the mean wavelet power reached its maximum value was calculated. The Z score powers of θ_LFP and θ_Vm were also calculated based on the wavelet power. We averaged the wavelet power for each frequency across 1-s bins. The maximum power for each bin and the Z scores of all bins were subsequently calculated.

Prediction of LFPs from Vms

A custom DNN model was constructed to predict LFPs from up to three simultaneously recorded Vms using Python. Our DNN had an encoder-decoder structure. The encoder compressed the input (i.e., 1, 2, or 3 Vms) to a lower dimensional representation and extracted features from the input, whereas the decoder reconstructed the final output (i.e., LFP) from the compressed vector. In our study, the Vms of 1, 2, or 3 cells over 1-s windows (size 500, 2-ms bins) were first passed through a convolutional layer. In this operation, the input was transformed into a feature matrix of reduced size through convolution by kernel matrices. This kernel processing enabled the extraction of meaningful features from the input into a smaller number of parameters⁶⁶. Then, the layer output was flattened to a one-dimensional vector (size 32,000). The one-dimensional vector was passed through four fully connected layers and finally compressed to a size of 100. This lower dimensional representation was reconstructed to a size of 500 via three fully connected layers. Our DNN was implemented using the Python deep learning library Keras and the TensorFlow backend. The network was optimized by adaptive moment estimation (Adam) with a learning rate of 0.001. The parameters for the optimizer Adam were as follows: β1 (an exponential decay rate for the first moment estimates) = 0.9, β2 (an exponential decay rate for the second moment estimates) = 0.999, ε = 10⁻⁷, and decay = 0.0001; the default values were used for the other parameters. Because our focus was θ oscillations, raw LFP and Vm traces (20,000 Hz) were downsampled to 500 Hz and bandpass filtered between 3 and 10 Hz in Fig. 5. In Supplementary Fig. 7, the downsampled traces were bandpass filtered at 60–100 Hz, 25–55 Hz, and 0.5–1 Hz for high gamma, low gamma, and slow oscillations, respectively. Datasets with recording durations >3 min were used for prediction (n = 8). Our DNN model was trained to produce 1-s θ-filtered LFPs (500 bins) from up to three Vms of the corresponding time bins. To assess the model performance on the entire dataset, 10-fold cross-validations were used. Each dataset was equally divided into 10 subsets, and during each training session, one subset was used as test data, while the remaining 9 subsets were used as training data. To obtain sufficient numbers of training data, 1-s segments (500 bins) were extracted by shifting a 1-s time window at a step of 2 ms (1 bin) across the training data. For test data, 1-s segments were extracted by shifting a 1-s time window at a step of 100 ms. For each cross-validation, the training lasted 50 epochs with a batch size of 256, and the RMSEs were calculated to assess how well the model predicted new data that had not been used for training. As a randomized control, surrogate data were produced by shuffling the combinations of three Vms; that is, the time labels for segments were exchanged within each cell. The DNN was also trained using the shuffled data, and RMSEs were calculated. To evaluate the significance for prediction, the RMSEs of all 1-s segments in all 10 subsets were pooled for either original or shuffled data in each dataset, and a two-sample Kolmogorov‒Smirnov test was used to calculate the D-values and P-values for each dataset.

Model and parameter tuning

The model architecture and training parameters were optimized on a different dataset before analyzing the main dataset. First, we compared four model structures with distinct characteristics (Supplementary Fig. 9a). In Model 1, which became our final model, the input is first passed to a convolutional layer and then to a series of fully connected layers. The structure of Model 2 is similar to that of Model 1, but without the first convolutional layer. Model 3 has only one fully connected layer. Finally, Model 4 has a convolutional layer and fully connected layers but does not have an encoder-decoder structure.

All models were trained on data that were specially prepared for model tuning (tuning datasets). Model 1, which was chosen as the final architecture in this work, showed the lowest RMSE value among all models (Supplementary Fig. 9b, c). In our model, the convolutional layer learns filters in the temporal dimension. Since convolutional layers are used to extract meaningful local structures, it is possible that convolutional layers successfully extracted local oscillations in the input Vms, which were important for predicting LFPs. The convolutional layer was followed by a series of deep layers. It is important to note that these fully connected layers have encoding and decoding architecture. By implementing this feature, the model is forced to extract and learn only the important features for predicting LFPs.

After the model architecture was selected, the model parameters were optimized based on the performance of the tuning data. As representative data, the results from four sets of parameters are shown in Supplementary Fig. 9d, e. Dropout rate of the dropout layers and learning rate were also optimized to 0.5 and 0.01 so that the RMSE takes the minimum value; the RMSE was 0.0203, 0.0229, 0.0205 when dropout rate was 0.5, 0.7, 0.9, and it was 0.0194, 0.112, 0.0201 when learning rate was 0.01, 0.001, 0.1. The optimal number of epochs was determined similarly based on the learning curve. The average of all traces shows that the RMSE value of the validation data hit the lowest at 5 epochs. After that, overfitting was observed as the RMSE of the validation data began to increase while the value of the training data continued to decrease.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

Source data for the presented figures are provided as Supplementary Data with this paper. The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

All offline computational analyses except Fig. 5 and Supplementary Fig. 9 were performed using MATLAB R2017b. The DNN based analyses in Fig. 5 and Supplementary Fig. 9 were performed using Python 3.9.1. Each analysis procedure is described in necessary detail in the Method section for others to execute. Any analysis code and analyzed data are available by sending a request to the corresponding author.

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Acknowledgements

This work was supported by JST ERATO (JPMJER1801), the Institute for AI and Beyond of the University of Tokyo, and JSPS Grants-in-Aid for Scientific Research (18H05525, 20K15926).

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Authors and Affiliations

Graduate School of Pharmaceutical Sciences, The University of Tokyo, Tokyo, 113-0033, Japan
Asako Noguchi, Kotaro Yamashiro, Nobuyoshi Matsumoto & Yuji Ikegaya
Institute for AI and Beyond, The University of Tokyo, Tokyo, 113-0033, Japan
Nobuyoshi Matsumoto & Yuji Ikegaya
Center for Information and Neural Networks, National Institute of Information and Communications Technology, Suita City, Osaka, 565-0871, Japan
Yuji Ikegaya

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Asako Noguchi
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Kotaro Yamashiro
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Nobuyoshi Matsumoto
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Yuji Ikegaya
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A.N. and Y.I. conceptualized the study; A.N., K.Y. and N.M. performed the experiments and data analyses; A.N. and Y.I. wrote the original draft; and A.N., K.Y., N.M., and Y.I. reviewed and edited the final manuscript.

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Correspondence to Asako Noguchi.

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Communications Biology thanks Michael Brecht, Liset de La Prida and Thomas McHugh for their contribution to the peer review of this work. Primary Handling Editor: Joao Valente. Peer reviewer reports are available.

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Noguchi, A., Yamashiro, K., Matsumoto, N. et al. Theta oscillations represent collective dynamics of multineuronal membrane potentials of murine hippocampal pyramidal cells. Commun Biol 6, 398 (2023). https://doi.org/10.1038/s42003-023-04719-z

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Received: 21 September 2022
Accepted: 16 March 2023
Published: 12 April 2023
DOI: https://doi.org/10.1038/s42003-023-04719-z

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