Dynamic Gamma Modulation of Hippocampal Place Cells Predominates Development of Theta Sequences

Reviewer #1 (Public Review):

Hippocampal place cells display a sequence of firing activities when the animal travels through a spatial trajectory at a behavioral time scale of seconds to tens of seconds. Interestingly, parts of the firing sequence also occur at a much shorter time scale: ~120 ms within individual cycles of theta oscillation. These so-called theta sequences are originally thought to naturally result from the phenomenon of theta phase precession. However, there is evidence that theta sequences do not always occur even when theta phase precession is present, for example, during the early experience of a novel maze. The question is then how they emerge with experience (theta sequence development). This study presents evidence that a special group of place cells, those tuned to fast-gamma oscillations, may play a key role in theta sequence development.

The authors analyzed place cells, LFPs, and theta sequences as rats traveled a circular maze in repeated laps. They found that a group of place cells were significantly tuned to a particular phase of fast-gamma (FG-cells), in contrast to others that did not show such tunning (NFG-cells). The authors then omitted FG-cells or the same number of NFG-cells, in their algorithm of theta sequence detection and found that the quality of theta sequences, quantified by a weighted correlation, was worse with the FG-cell omission, compared to that with the NFG-cell omission, during later laps, but not during early laps. What made the FG-cells special for theta sequences? The authors found that FG-cells, but not NFG-cells, displayed phase recession to slow-gamma (25 - 45 Hz) oscillations (within theta cycles) during early laps (both FG- and NFG-cells showed slow-gamma phase precession during later laps). Overall, the authors conclude that FG-cells contribute to theta sequence development through slow-gamma phase precession during early laps.

How theta sequences are formed and developed during experience is an important question, because these sequences have been implicated in several cognitive functions of place cells, including memory-guided spatial navigation. The identification of FG-cells in this study is straightforward. Evidence is also presented for the role of these cells in theta sequence development. However, given several concerns elaborated below, whether the evidence is sufficiently strong for the conclusion needs further clarification, perhaps, in future studies.

(1) The results in Figure 3 and Figure 8 seems contradictory. In Figure 8, all theta sequences displayed a seemingly significant weighted correlation (above 0) even in early laps, which was mostly due to FG-cell sequences but not NFG-cell sequences (correlation for NFG-sequences appeared below 0). However, in Figure 3H, omitting FG-cells and omitting NFG-cells did not produce significant differences in the correlation. Conversely, FG-cell and NFG-cell sequences were similar in later laps in Figure 8 (NFG-cell sequences appeared even better than FG-cell sequences), yet omitting NFG-cells produced a better correlation than omitting FG-cells. This confusion may be related to how "FG-cell-dominant sequences" were defined, which is unclear in the manuscript. Nevertheless, the different results are not easy to understand.

(2) The different contributions between FG-cells and NFG-cells to theta sequences are supposed not to be caused by their different firing properties (Figure 5). However, Figure 5D and E showed a large effect size (Cohen's D = 07, 0.8), although not significant (P = 0.09, 0.06). But the seemingly non-significant P values could be simply due to smaller N's (~20). In other parts of the manuscript, the effect sizes were comparable or even smaller (e.g. D = 0.5 in Figure 7B), but interpreted as positive results: P values were significant with large N's (~480 in Fig. 7B). Drawing a conclusion purely based on a P value while N is large often renders the conclusion only statistical, with unclear physical meaning. Although this is common in neuroscience publications, it makes more sense to at least make multiple inferences using similar sample sizes in the same study.

(3) In supplementary Figure 2 - S2, FG-cells displayed stronger theta phase precession than NFG-cells, which could be a major reason why FG-cells impacted theta sequences more than NFG cells. Although factors other than theta phase precession may contribute to or interfere with theta sequences, stronger theta phase precession itself (without the interference of other factors), by definition, can lead to stronger theta sequences.

(4) The slow-gamma phase precession of FG-cells during early laps is supposed to mediate or contribute to the emergence of theta sequences during late laps (Figure 1). The logic of this model is unclear. The slow-gamma phase precession was present in both early and late laps for FG-cells, but only present in late laps for NFG-cells. It seems more straightforward to hypothesize that the difference in theta sequences between early and later laps is due to the difference in slow-gamma phase precession of NFG cells between early and late laps. Although this is not necessarily the case, the argument presented in the manuscript is not easy to follow.

(5) There are several questions on the description of methods, which could be addressed to clarify or strengthen the conclusions.

(i) Were the identified fast- and slow-gamma episodes mutually exclusive?

(ii) Was the task novel when the data were acquired? How many days (from the 1st day of the task) were included in the analysis? When the development of the theta sequence was mentioned, did it mean the development in a novel environment, in a novel task, or purely in a sense of early laps (Lap 1, 2) on each day?

(iii) How were the animals' behavioral parameters equalized between early and later laps? For example, speed or head direction could potentially produce the differences in theta sequences.

Reviewer #2 (Public Review):

This manuscript addresses an important question that has not yet been solved in the field, what is the contribution of different gamma oscillatory inputs to the development of "theta sequences" in the hippocampal CA1 region? Theta sequences have received much attention due to their proposed roles in encoding short-term behavioral predictions, mediating synaptic plasticity, and guiding flexible decision-making. Gamma oscillations in CA1 offer a readout of different inputs to this region and have been proposed to synchronize neuronal assemblies and modulate spike timing and temporal coding. However, the interactions between these two important phenomena have not been sufficiently investigated. The authors conducted place cell and local field potential (LFP) recordings in the CA1 region of rats running on a circular track. They then analyzed the phase locking of place cell spikes to slow and fast gamma rhythms, the evolution of theta sequences during behavior, and the interaction between these two phenomena. They found that place cells with the strongest modulation by fast gamma oscillations were the most important contributors to the early development of theta sequences and that they also displayed a faster form of phase precession within slow gamma cycles nested with theta. The results reported are interesting and support the main conclusions of the authors. However, the manuscript needs significant improvement in several aspects regarding data analysis, description of both experimental and analytical methods, and alternative interpretations, as I detail below.

• The experimental paradigm and recordings should be explained at the beginning of the Results section. Right now, there is no description whatsoever which makes it harder to understand the design of the study.

• An important issue that needs to be addressed is the very small fraction of CA1 cells phased-locked to slow gamma rhythms (3.7%). This fraction is much lower than in many previous studies, that typically report it in the range of 20-50 %. However, this discrepancy is not discussed by the authors. This needs to be explained and additional analysis considered. One analysis that I would suggest, although there are also other valid approaches, is to, instead of just analyzing the phase locking in two discrete frequency bands, compute the phase locking will all LFP frequencies from 25-100 Hz. This will offer a more comprehensive and unbiased view of the gamma modulation of place cell firing. Alternative metrics to mean vector length that is less sensitive to firing rates, such as pairwise phase consistency index (Vinck et a., Neuroimage, 2010), could be implemented. This may reveal whether the low fraction of phase-locked cells could be due to a low number of spikes entering the analysis.

• From the methods, it is not clear to me whether the reference LFP channel was consistently selected to be a different one that where the spikes analyzed were taken. This is the better practice to reduce the contribution of spike leakage that could substantially inflate the coupling with faster gamma frequencies. These analyses need to be described in more detail.

• The initial framework of the authors of classifying cells into fast gamma and not fast gamma modulated implies a bimodality that may be artificial. The authors should discuss the nuances and limitations of this framework. For example, several previous work has shown that the same place cell can couple to different gamma oscillations (e.g., Lastoczni et al., Neuron, 2016; Fernandez-Ruiz et al., Neuron, 2017; Sharif et al., Neuron,2021).

• It would be useful to provide a more thorough characterization of the physiological properties of FG and NFG cells, as this distinction is the basis of the paper. Only very little characterization of some place cell properties is provided in Figure 5. Important characteristics that should be very feasible to compare include average firing rate, burstiness, estimated location within the layer (i.e., deep vs superficial sublayers) and along the transverse axis (i.e., proximal vs distal), theta oscillation frequency, phase precession metrics (given their fundamental relationship with theta sequences), etc.

• It is not clear to me how the analysis in Figure 6 was performed. In Figure 6B I would think that the grey line should connect with the bottom white dot in the third panel, which would be the interpretation of the results.

Reviewer #3 (Public Review):

[Editors' note: This review contains many criticisms that apply to the whole sub-field of slow/fast gamma oscillations in the hippocampus, as opposed to this particular paper. In the editors' view, these comments are beyond the scope of any single paper. However, they represent a view that, if true, should contextualise the interpretation of this paper and all papers in the sub-field. In doing so, they highlight an ongoing debate within the broader field.]

Summary:

The authors aimed to elucidate the role of dynamic gamma modulation in the development of hippocampal theta sequences, utilizing the traditional framework of "two gammas," a slow and a fast rhythm. This framework is currently being challenged, necessitating further analyses to establish and secure the assumed premises before substantiating the claims made in the present article.

The results are too preliminary and need to integrate contemporary literature. New analyses are required to address these concerns. However, by addressing these issues, it may be possible to produce an impactful manuscript.

I. Introduction
Within the introduction, multiple broad assertions are conveyed that serve as the premise for the research. However, equally important citations that are not mentioned potentially contradict the ideas that serve as the foundation. Instances of these are described below:

(1) Are there multiple gammas? The authors launched the study on the premise that two different gamma bands are communicated from CA3 and the entorhinal cortex. However, recent literature suggests otherwise, offering that the slow gamma component may be related to theta harmonics:

From a review by Etter, Carmichael and Williams (2023)
"Gamma-based coherence has been a prominent model for communication across the hippocampal-entorhinal circuit and has classically focused on slow and fast gamma oscillations originating in CA3 and medial entorhinal cortex, respectively. These two distinct gammas are then hypothesized to be integrated into hippocampal CA1 with theta oscillations on a cycle-to-cycle basis (Colgin et al., 2009; Schomburg et al., 2014). This would suggest that theta oscillations in CA1 could serve to partition temporal windows that enable the integration of inputs from these upstream regions using alternating gamma waves (Vinck et al., 2023). However, these models have largely been based on correlations between shifting CA3 and medial entorhinal cortex to CA1 coherence in theta and gamma bands. In vivo, excitatory inputs from the entorhinal cortex to the dentate gyrus are most coherent in the theta band, while gamma oscillations would be generated locally from presumed local inhibitory inputs (Pernía-Andrade and Jonas, 2014). This predominance of theta over gamma coherence has also been reported between hippocampal CA1 and the medial entorhinal cortex (Zhou et al., 2022). Another potential pitfall in the communication-through-coherence hypothesis is that theta oscillations harmonics could overlap with higher frequency bands (Czurkó et al., 1999; Terrazas et al., 2005), including slow gamma (Petersen and Buzsáki, 2020). The asymmetry of theta oscillations (Belluscio et al., 2012) can lead to harmonics that extend into the slow gamma range (Scheffer-Teixeira and Tort, 2016), which may lead to a misattribution as to the origin of slow-gamma coherence and the degree of spike modulation in the gamma range during movement (Zhou et al., 2019)."

And from Benjamin Griffiths and Ole Jensen (2023)
"That said, in both rodent and human studies, measurements of 'slow' gamma oscillations may be susceptible to distortion by theta harmonics [53], meaning open questions remain about what can be attributed to 'slow' gamma oscillations and what is attributable to theta."

This second statement should be heavily considered as it is from one of the original authors who reported the existence of slow gamma.

Yet another instance from Schomburg, Fernández-Ruiz, Mizuseki, Berényi, Anastassiou, Christof Koch, and Buzsáki (2014):
"Note that modulation from 20-30 Hz may not be related to gamma activity but, instead, reflect timing relationships with non-sinusoidal features of theta waves (Belluscio et al., 2012) and/or the 3rd theta harmonic."

One of this manuscript's authors is Fernández-Ruiz, a contemporary proponent of the multiple gamma theory. Thus, the modulation to slow gamma offered in the present manuscript may actually be related to theta harmonics.

With the above emphasis from proponents of the slow/fast gamma theory on disambiguating harmonics from slow gamma, our first suggestion to the authors is that they A) address these statements (citing the work of these authors in their manuscript) and B) demonstrably quantify theta harmonics in relation to slow gamma prior to making assertions of phase relationships (methodological suggestions below). As the frequency of theta harmonics can extend as high as 56 Hz (PMID: 32297752), overlapping with the slow gamma range defined here (25-45 Hz), it will be important to establish an approach that decouples the two phenomena using an approach other than an arbitrary frequency boundary.

(2) Can gammas be segregated into different lamina of the hippocampus? This idea appears to be foundational in the premise of the research but is also undergoing revision.

As discussed by Etter et al. above, the initial theory of gamma routing was launched on coherence values. However, the values reported by Colgin et al. (2009) lean more towards incoherence (a value of 0) rather than coherence (1), suggesting a weak to negligible interaction. Nevertheless, this theory is coupled with the idea that the different gamma frequencies are exclusive to the specific lamina of the hippocampus.

Recently, Deschamps et al. (2024) suggested a broader, more nuanced understanding of gamma oscillations than previously thought, emphasizing their wide range and variability across hippocampal layers. This perspective challenges the traditional dichotomy of gamma sub-bands (e.g., slow vs. medium gamma) and their associated cognitive functions based on a more rigid classification according to frequency and phase relative to the theta rhythm. Moreover, they observed all frequencies across all layers.

Similarly, the current source density plots from Belluscio et al. (2012) suggest that SG and FG can be observed in both the radiatum and lacunosum-moleculare.

Therefore, if the initial coherence values are weak to negligible and both slow and fast gamma are observed in all layers of the hippocampus, can the different gammas be exclusively related to either anatomical inputs or psychological functions (as done in the present manuscript)? Do these observations challenge the authors' premise of their research? At the least, please discuss.

(3) Do place cells, phase precession, and theta sequences require input from afferent regions? It is offered in the introduction that "Fast gamma (~65-100Hz), associated with the input from the medial entorhinal cortex, is thought to rapidly encode ongoing novel information in the context (Fernandez-Ruiz et al., 2021; Kemere, Carr, Karlsson, & Frank, 2013; Zheng et al., 2016)".

CA1 place fields remain fairly intact following MEC inactivation include Ipshita Zutshi, Manuel Valero, Antonio Fernández-Ruiz , and György Buzsáki (2022)- "CA1 place cells and assemblies persist despite combined mEC and CA3 silencing" and from Hadas E Sloin, Lidor Spivak, Amir Levi, Roni Gattegno, Shirly Someck, Eran Stark (2024) - "These findings are incompatible with precession models based on inheritance, dual-input, spreading activation, inhibition-excitation summation, or somato-dendritic competition. Thus, a precession generator resides locally within CA1."

These publications, at the least, challenge the inheritance model by which the afferent input controls CA1 place field spike timing. The research premise offered by the authors is couched in the logic of inheritance, when the effect that the authors are observing could be governed by local intrinsic activity (e.g., phase precession and gamma are locally generated, and the attribution to routed input is perhaps erroneous). Certainly, it is worth discussing these manuscripts in the context of the present manuscript.

II. Results

(1) Figure 2-
a. There is a bit of a puzzle here that should be discussed. If slow and fast frequencies modulate 25% of neurons, how can these rhythms serve as mechanisms of communication/support psychological functions? For instance, if fast gamma is engaged in rapid encoding (line 72) and slow gamma is related to the integration processing of learned information (line 84), and these are functions of the hippocampus, then why do these rhythms modulate so few cells? Is this to say 75% of CA1 neurons do not listen to CA3 or MEC input?

b. Figure 2. It is hard to know if the mean vector lengths presented are large or small. Moreover, one can expect to find significance due to chance. For instance, it is challenging to find a frequency in which modulation strength is zero (please see Figure 4 of PMID: 30428340 or Figure 7 of PMID: 31324673).

i. Please construct the histograms of Mean Vector Length as in the above papers, using 1 Hz filter steps from 1-120Hz and include it as part of Figure 2 (i.e., calculate the mean vector length for the filtered LFP in steps of 1-2 Hz, 2-3 Hz, 3-4 Hz,... etc). This should help the authors portray the amount of modulation these neurons have relative to the theta rhythm and other frequencies. If the theta mean vector length is higher, should it be considered the primary modulatory influence of these neurons (with slow and fast gammas as a minor influence)?

ii. It is possible to infer a neuron's degree of oscillatory modulation without using the LFP. For instance, one can create an ISI histogram as done in Figure 1 here (https://www.biorxiv.org/content/10.1101/2021.09.20.461152v3.full.pdf+html; "Distinct ground state and activated state modes of firing in forebrain neurons"). The reciprocal of the ISI values would be "instantaneous spike frequency". In favor of the Douchamps et al. (2024) results, the figure of the BioRXiV paper implies that there is a single gamma frequency modulate as there is only a single bump in the ISIs in the 10^-1.5 to 10^-2 range. Therefore, to vet the slow gamma results and the premise of two gammas offered in the introduction, it would be worth including this analysis as part of Figure 2.

c. There are some things generally concerning about Figure 2.

i. First, the raw trace does not seem to have clear theta epochs (it is challenging to ascertain the start and end of a theta cycle). Certainly, it would be worth highlighting the relationship between theta and the gammas and picking a nice theta epoch.

ii. Also, in panel A, there looks to be a declining amplitude relationship between the raw, fast, and slow gamma traces, assuming that the scale bars represent 100uV in all three traces. The raw trace is significantly larger than the fast gamma. However, this relationship does not seem to be the case in panel B (in which both the raw and unfiltered examples of slow and fast gamma appear to be equal; the right panels of B suggest that fast gamma is larger than slow, appearing to contradict the A= 1/f organization of the power spectral density). Please explain as to why this occurs. Including the power spectral density (see below) should resolve some of this.

iii. Within the example of spiking to phase in the left side of Panel B (fast gamma example)- the neuron appears to fire near the trough twice, near the peak twice, and somewhere in between once. A similar relationship is observed for the slow gamma epoch. One would conclude from these plots that the interaction of the neuron with the two rhythms is the same. However, the mean vector lengths and histograms below these plots suggest a different story in which the neuron is modulated by FG but not SG. Please reconcile this.

iv. For calculating the MVL, it seems that the number of spikes that the neuron fires would play a significant role. Working towards our next point, there may be a bias of finding a relationship if there are too few spikes (spurious clustering due to sparse data) and/or higher coupling values for higher firing rate cells (cells with higher firing rates will clearly show a relationship), forming a sort of inverse Yerkes-Dodson curve. Also, without understanding the magnitude of the MVL relative to other frequencies, it may be that these values are indeed larger than zero, but not biologically significant.

- Please provide a scatter plot of Neuron MVL versus the Neuron's Firing Rate for 1) theta (7-9 Hz), 2) slow gamma, and 3) fast gamma, along with their line of best fit.

- Please run a shuffle control where the LFP trace is shifted by random values between 125-1000ms and recalculate the MVL for theta, slow, and fast gamma. Often, these shuffle controls are done between 100-1000 times (see cross-correlation analyses of Fujisawa, Buzsaki et al.).

- To establish that firing rate does not play a role in uncovering modulation, it would be worth conducting a spike number control, reducing the number of spikes per cell so that they are all equal before calculating the phase plots/MVL.

(2) Something that I anticipated to see addressed in the manuscript was the study from Grosmark and Buzsaki (2016): "Cell assembly sequences during learning are "replayed" during hippocampal ripples and contribute to the consolidation of episodic memories. However, neuronal sequences may also reflect preexisting dynamics. We report that sequences of place-cell firing in a novel environment are formed from a combination of the contributions of a rigid, predominantly fast-firing subset of pyramidal neurons with low spatial specificity and limited change across sleep-experience-sleep and a slow-firing plastic subset. Slow-firing cells, rather than fast-firing cells, gained high place specificity during exploration, elevated their association with ripples, and showed increased bursting and temporal coactivation during postexperience sleep. Thus, slow- and fast-firing neurons, although forming a continuous distribution, have different coding and plastic properties."

My concern is that much of the reported results in the present manuscript appear to recapitulate the observations of Grosmark and Buzsaki, but without accounting for differences in firing rate. A parsimonious alternative explanation for what is observed in the present manuscript is that high firing rate neurons, more integrated into the local network and orchestrating local gamma activity (PING), exhibit more coupling to theta and gamma. In this alternative perspective, it's not something special about how the neurons are entrained to the routed fast gamma, but that the higher firing rate neurons are better able to engage and entrain their local interneurons and, thus modulate local gamma. However, this interpretation challenges the discussion around the importance of fast gamma routed from the MEC.

a. Please integrate the Grosmark & Buzsaki paper into the discussion.

b. Also, please provide data that refutes or supports the alternative hypothesis in which the high firing rate cells are just more gamma modulated as they orchestrate local gamma activity through monosynaptic connections with local interneurons (e.g., Marshall et al., 2002, Hippocampal pyramidal cell-interneuron spike transmission is frequency dependent and responsible for place modulation of interneuron discharge). Otherwise, the attribution to a MEC routed fast gamma routing seems tenuous.
c. It is mentioned that fast-spiking interneurons were removed from the analysis. It would be worth including these cells, calculating the MVL in 1 Hz increments as well as the reciprocal of their ISIs (described above).

(3) Methods - Spectral decomposition and Theta Harmonics.

a. It is challenging to interpret the exact parameters that the authors used for their multi-taper analysis in the methods (lines 516-526). Tallon-Baudry et al., (1997; Oscillatory γ-Band (30-70 Hz) Activity Induced by a Visual Search Task in Humans) discuss a time-frequency trade-off where frequency resolution changes with different temporal windows of analysis. This trade-off between time and frequency resolution is well known as the uncertainty principle of signal analysis, transcending all decomposition methods. It is not only a function of wavelet or FFT, and multi-tapers do not directly address this. (The multitaper method, by using multiple specially designed tapers -like the Slepian sequences- smooths the spectrum. This smoothing doesn't eliminate leakage but distributes its impact across multiple estimates). Given the brevity of methods and the issues of theta harmonics as offered above, it is worth including some benchmark trace testing for the multi-taper as part of the supplemental figures.

i. Please spectrally decompose an asymmetric 8 Hz sawtooth wave showing the trace and the related power spectral density using the multiple taper method discussed in the methods.

ii. Please also do the same for an elliptical oscillation (perfectly symmetrical waves, but also capable of casting harmonics). Matlab code on how to generate this time series is provided below:
A = 1; % Amplitude
T = 1/8; % Period corresponding to 8 Hz frequency
omega = 2*pi/T; % Angular frequency
C = 1; % Wave speed
m = 0.9; % Modulus for the elliptic function (0
x = linspace(0, 2*pi, 1000); % temporal domain
t = 0; % Time instant

% Calculate B based on frequency and speed
B = sqrt(omega/C);

% Cnoidal wave equation using the Jacobi elliptic function
u = A .* ellipj(B.*(x - C*t), m).^2;

% Plotting the cnoidal wave
figure;
plot(x./max(x), u);
title('8 Hz Cnoidal Wave');
xlabel('time (x)');
ylabel('Wave amplitude (u)');
grid on;

The Symbolic Math Toolbox needs to be installed and accessible in your MATLAB environment to use ellipj. Otherwise, I trust that, rather than plotting a periodic orbit around a circle (sin wave) the authors can trace the movement around an ellipse with significant eccentricity (the distance between the two foci should be twice the distance between the co-vertices).

iii. Line 522: "The power spectra across running speeds and absolute power spectrum (both results were not shown)...". Given the potential complications of multi-taper discussed above, and as each convolution further removes one from the raw data, it would be the most transparent, simple, and straightforward to provide power spectra using the simple fft.m code in Matlab (We imagine that the authors will agree that the results should be robust against different spectral decomposition methods. Otherwise, it is concerning that the results depend on the algorithm implemented and should be discussed. If gamma transience is a concern, the authors should trigger to 2-second epochs in which slow/fast gamma exceeds 3-7 std. dev. above the mean, comparing those resulting power spectra to 2-second epochs with ripples - also a transient event). The time series should be at least 2 seconds in length (to avoid spectral leakage issues and the issues discussed in Talon-Baudry et al., 1997 above).

Please show the unmolested power spectra (Y-axis units in mV2/Hz, X-axis units as Hz) as a function of running speed (increments of 5 cm/s) for each animal. I imagine three of these PSDs for 3 of the animals will appear in supplemental methods while one will serve as a nice manuscript figure. With this plot, please highlight the regions that the authors are describing as theta, slow, and fast gamma. Also, any issues should be addressed should there be notable differences in power across animals or tetrodes (issues with locations along proximal-distal CA1 in terms of MEC/LEC input and using a local reference electrode are discussed below).

iv. Schomberg and colleagues (2014) suggested that the modulation of neurons in the slow gamma range could be related to theta harmonics (see above). Harmonics can often extend in a near infinite as they regress into the 1/f background (contributing to power, but without a peak above the power spectral density slope), making arbitrary frequency limits inappropriate. Therefore, in order to support the analyses and assertions regarding slow gamma, it seems necessary to calculate a "theta harmonic/slow gamma ratio". Aru et al. (2015; Untangling cross-frequency coupling in neuroscience) offer that: " The presence of harmonics in the signal should be tested by a bicoherence analysis and its contribution to CFC should be discussed." Please test both the synthetic signals above and the raw LFP, using temporal windows of greater than 4 seconds (again, the large window optimizes for frequency resolution in the time-frequency trade-off) to calculate the bicoherence. As harmonics are integers of theta coupled to itself and slow gamma is also coupled to theta, a nice illustration and contribution to the field would be a method that uses the bispectrum to isolate and create a "slow gamma/harmonic" ratio.

(4) I appreciate the inclusion of the histology for the 4 animals. Knerim and colleagues describe a difference in MEC projection along the proximal-distal axis of the CA1 region (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3866456/)- "There are also differences in their direct projections along the transverse axis of CA1, as the LEC innervates the region of CA1 closer to the subiculum (distal CA1), whereas the MEC innervates the region of CA1 closer to CA2 and CA3 (proximal CA1)" From the histology, it looks like some of the electrodes are in the part of CA1 that would be dominated by LEC input while a few are closer to where the MEC would project.

a. How do the authors control for these differences in projections? Wouldn't this change whether or not fast gamma is observed in CA1?

b. I am only aware of one manuscript that describes slow gamma in the LEC which appeared in contrast to fast gamma from the MEC (https://www.science.org/doi/10.1126/science.abf3119). One would surmise that the authors in the present manuscript would have varying levels of fast gamma in their CA1 recordings depending on the location of the electrodes in the Proximal-distal axis, to the extent that some of the more medial tetrodes may need to be excluded (as they should not have fast gamma, rather they should be exclusively dominated by slow gamma). Alternatively, the authors may find that there is equal fast gamma power across the entire proximal-distal axis. However, this would pose a significant challenge to the LEC/slow gamma and MEC/fast gamma routing story of Fernandez-Ruiz et al. and require reconciliation/discussion.

c. Is there a difference in neuron modulation to these frequencies based on electrode location in CA1?

(5) Given a comment in the discussion (see below), it will be worth exploring changes in theta, theta harmonic, slow gamma, and fast gamma power with running speed as no changes were observed with theta sequences or lap number versus. Notably, Czurko et al., report an increase in theta and harmonic power with running speed (1999) while Ahmed and Mehta (2012) report a similar effect for gamma.

a. Please determine if the oscillations change in power and frequency of the rhythms discussed above change with running speed using the same parameters applied in the present manuscript. The specific concern is that how the authors calculate running speed is not sensitive enough to evaluate changes.

b. It is astounding that animals ran as fast as they did in what appears to be the first lap (Figure 3F), especially as rats' natural proclivity is thigmotaxis and inquisitive exploration in novel environments. Can the authors expand on why they believe their rats ran so quickly on the first lap in a novel environment and how to replicate this? Also, please include the individual values for each animal on the same plot.

c. Can the authors explain how the statistics on line 169 (F(4,44)) work? Specifically, it is challenging to determine how the degrees of freedom were calculated in this case and throughout if there were only 4 animals (reported in methods) over 5 laps (depicted in Figure 3F. Given line 439, it looks like trials and laps are used synonymously). Four animals over 5 laps should have a DOF of 16.

(6) Throughout the manuscript, I am concerned about an inflation of statistical power. For example on line 162, F(2,4844). The large degrees of freedom indicate that the sample size was theta sequences or a number of cells. Since multiple observations were obtained from the same animal, the statistical assumption of independence is violated. Therefore, the stats need to be conducted using a nested model as described in Aarts et al. (2014; https://pubmed.ncbi.nlm.nih.gov/24671065/). A statistical consult may be warranted.

(7) It is stated that one tetrode served as a quiet recording reference. The "quiet" part is an assumption when often, theta and gamma can be volume conducted to the cortex (e.g., Sirota et al., 2008; This is often why laboratories that study hippocampal rhythms use the cerebellum for the differential recording electrode and not an electrode in the corpus callosum). Generally, high frequencies propagate as well as low frequencies in the extracellular milieu (https://www.eneuro.org/content/4/1/ENEURO.0291-16.2016). For transparency, the authors should include a limitation paragraph in their discussion that describes how their local tetrode reference may be inadvertently diminishing and/or distorting the signal that they are trying to isolate. Otherwise, it would be worth hearing an explanation as to how the author's approach avoids this issue.

Apologetically, this review is already getting long. Moreover, I have substantial concerns that should be resolved prior to delving into the remainder of the analyses. e.g., the analyses related to Figure 3-5 assert that FG cells are important for sequences. However, the relationship to gamma may be secondary to either their relationship to theta or, based on the Grosmark and Buzsaki paper, it may just be a phenomenon coupled to the fast-firing cells (fast-firing cells showing higher gamma modulation due to a local PING dynamic). Moreover, the observation of slow gamma is being challenged as theta harmonics, even by the major proponents of the slow/fast gamma theory. Therefore, the report of slow gamma precession would come as an unsurprising extension should they be revealed to be theta harmonics (however, no control for harmonics was implemented; suggestions were made above). Following these amendments, I would be grateful for the opportunity to provide further feedback.

III. Discussion.

a. Line 330- it was offered that fast gamma encodes information while slow gamma integrates in the introduction. However, in a task such as circular track running (from the methods, it appears that there is no new information to be acquired within a trial), one would guess that after the first few laps, slow gamma would be the dominant rhythm. Therefore, one must wonder why there are so few neurons modulated by slow gamma (~3.7%).

b. Line 375: The authors contend that: "...slow gamma, related to information compression, was also required to modulate fast gamma phase-locked cells during sequence development. We replicated the results of slow gamma phase precession at the ensemble level (Zheng et al., 2016), and furthermore observed it at late development, but not early development, of theta sequences." In relation to the idea that slow gamma may be coupled to - if not a distorted representation of - theta harmonics, it has been observed that there are changes in theta relative to novelty.

i. A. Jeewajee, C. Lever, S. Burton, J. O'Keefe, and N. Burgess (2008) report a decrease in theta frequency in novel circumstances that disappears with increasing familiarity.

ii. One could surmise that this change in frequency is associated with alterations in theta harmonics (observed here as slow gamma), challenging the author's interpretation.

iii. Therefore, the authors have a compelling opportunity to replicate the results of Jeewajee et al., characterizing changes of theta along with the development of slow gamma precession, as the environment becomes familiar. It will become important to demonstrate, using bicoherence as offered by Aru et al., how slow gamma can be disambiguated from theta harmonics. Specifically, we anticipate that the authors will be able to quantify A) theta harmonics (the number, and their respective frequencies and amplitudes), B) the frequency and amplitude of slow gamma, and C) how they can be quantitatively decoupled. Through this, their discussion of oscillatory changes with novelty-familiarity will garner a significant impact.

c. Broadly, it is interesting that the authors emphasize the gamma frequency throughout the discussion. Given that the power spectral density of the Local Field Potential (LFP) exhibits a log-log relationship between amplitude and frequency, as described by Buzsáki (2005) in "Rhythms of the Brain," and considering that the LFP is primarily generated through synaptic transmembrane currents (Buzsáki et al., 2012), it seems parsimonious to consider that the bulk of synaptic activity occurs at lower frequencies (e.g., theta). Since synaptic transmission represents the most direct form of inter-regional communication, one might wonder why gamma (characterized by lower amplitude rhythms) is esteemed so highly compared to the higher amplitude theta rhythm. Why isn't the theta rhythm, instead, regarded as the primary mode of communication across brain regions? A discussion exploring this question would be beneficial.