A Theory of Hippocampal Theta Correlations: Extrinsic and Intrinsic Sequences

Reviewer #1 (Public Review):

In the manuscript entitled "A theory of hippocampal theta correlations", the authors propose a new mechanism for phase precession and theta-time scale generation, as well as their interpretation in terms of navigation and neural coding. The authors propose the existence of extrinsic and intrinsic sequences during exploration, which may have complementary functions. These two types of sequences depend on external input and network interactions, but differ on the extent to which they depend on movement direction. Moreover, the authors propose a novel interpretation for intrinsic sequences, namely to signal a landmark cue that is independent of direction of traversal. Finally, a readout neuron can be trained to distinguish extrinsic from intrinsic sequences.

The study puts forward novel computational ideas related to neural coding, partly based on previous work from the authors, including published (Leibold, 2020, Yiu et al., 2022) and unpublished (Ahmedi et al., 2022. bioRxiv) work. The manuscript will contribute to the understanding of the mechanisms behind phase precession, as well as to how we interpret hippocampal temporal coding for navigation and memory.

Reviewer #2 (Public Review):

Place cells fire sequentially during hippocampal theta oscillations, forming a spatial representation of behavioral experiences in a temporally-compressed manner. The firing sequences during theta cycles are widely considered as essential assemblies for learning, memory, and planning. Many theoretical studies have investigated the mechanism of hippocampal theta firing sequences; however, they are either entirely extrinsic or intrinsic. In other words, they attribute the theta sequences to external sensorimotor drives or focus exclusively on the inherent firing patterns facilitated by the recurrent network architectures. Both types of theories are inadequate for explaining the complexity of the phenomena, particularly considering the observations in a previous paper by the authors: theta sequences independent of animal movement trajectories may occur simultaneously with sensorimotor inputs (Yiu et al., 2022).

In this manuscript, the authors concentrate on the CA3 area of the hippocampus and develop a model that accounts for both mechanisms. Specifically, the model generates extrinsic sequences through the short-term facilitation of CA3 cell activities, and intrinsic sequences via recurrent projections from the dentate gyrus. The model demonstrates how the phase precession of place cells in theta sequences is modulated by running direction and the recurrent DG-CA3 network architecture. To evaluate the extent to which firing sequences are induced by sensorimotor inputs and recurrent network architecture, the authors use the Pearson correlation coefficient to measure the "intrinsicity" and "extrinsicity" of spike pairs in their simulations.

I find this research topic to be both important and interesting, and I appreciate the clarity of the paper. The idea of combining intrinsic and extrinsic mechanisms for theta sequences is novel, and the model effectively incorporates two crucial phenomena: phase precession and directionality of theta sequences. I particularly commend the authors' efforts to integrate previous theories into their model and conduct a systematic comparison. This is exactly what our community needs: not only the development of new models, but also understanding the critical relationships between different models.

Author Response

The following is the authors’ response to the original reviews.

We would like to thank the Reviewers for their careful reading and the many thoughtful suggestions to improve our manuscript, as well as both the Editors and Reviewers for the generally positive evaluations and encouraging statements.

Editorial assessment:

This important work presents an interesting perspective for the generation and interpretation of phase precession in the hippocampal formation. Through numerical simula- tions and comparison to experiments, the study provides solid evidence for the role of the DG-CA3 loop in generating theta-time scale correlations and sequences, which would be reinforced through the clarification of the concepts introduced in the study, in particular the notion of intrinsic and extrinsic sequences. This study will be of interest for the hippocampus and neural coding fields.

We appreciate that our work has been considered important. In our revision we made a considerable effort to improve on the presentation of our results and the justification of our model assumptions. Particularly we aimed to clarify the meaning of intrinsic and extrinsic sequences by ad- ditional figure panels as well as fleshing out their definition via spike-timing correlations being independent or dependent on the direction of the running trajectory, respectively. To address all the requests, we added 3 new Fig- ures, multiple new Figure panels and simulated a new model variant.

Reviewer #1 in their public review assessed ”The manuscript has the potential to contribute to the way we interpret hippocampal temporal coding for navigation and memory.”

They criticized

• The findings generally relate to network models of phase precession (re- viewed in e.g., Maurer and McNaughton, 2007, Jaramillo and Kempter, 2017). An important drawback of these models with respect to explaining specific experimentally observed features of phase precession, is that they cannot straightforwardly explain phase precession upon first exposure onto a novel track. This is because, specific connectivity in network models may re- quire experience-dependent plasticity, which would not be possible upon first exposure. This is essential, given that the manuscript addresses the possible origin of phase precession in terms of network models and at minimum, this weakness should be discussed.

We agree with Reviewer # 1 (and also with Reviewer # 2, who brought up a similar point) that models based on recurrence struggle to ex- plain how the recurrent connectivity matrix should come about. While we feel that a full model of how the 2-d topology in the recurrent weights can be learned goes far beyond the scope of this paper (and to our knowledge has not been solved so far in any existing model), we added a new model variant (new Figure 6 and Supplementary Figure 1), which explains the ba- sic phenomenology of extrinsic and intrinsic sequences without the need of recurrent connections, only using feed-forward synaptic facilitation. Thus, assuming recurrent connection is not necessary for our main findings. How- ever, we would like to point out that this does not exclude the possibility that recurrent connections, if set up in an appropriate way, also contribute to phase precession and theta sequences.

• An important and perhaps essential component of the manuscript, is the distinction between extrinsic and intrinsic models. However, the main con- cepts on which this hinges, namely extrinsic and intrinsic sequences (and the related extrinsicity and intrinsicity) could be better explained and illustrated. Along these lines, the result suggested by the title, namely, hippocampal theta correlations, may be important yet incidental in light of the new concepts (e.g., extrinsicity, intrinsicity) and computational models (e.g., DG-CA3 recurrent loop) that are put forward.

We have added substantial new explanatory material to the figures, captions and text to more didactically introduce the concepts of in- trinsicity and extrinsicity. We have also completely rewritten the abstract and added a subtitle: ”extrinsic and intrinsic sequences”

• The study seems to put forward novel computational ideas related to neural coding. However, assessing novelty is challenging as this manuscript builds on previous work from the authors, including published (Leibold, 2020, Yiu et al., 2022) and unpublished (Ahmadi et al., 2022. bioRxiv) work. For example, the interpretation of intrinsic sequences in terms of landmarks had been introduced in Leibold, 2020.

We agree with the reviewer that this paper touches on many related ideas from previous papers (not only of our lab) and is supposed to tie loose ends. Thus, the novel contribution is a biologically plausible mechanistic model of how intrinsic sequences and 2-d place maps interact on the level of interconnected spiking neurons. Such a level of explanation has not yet been available in previous work. We have considerably extended the Discussion section in our revision detailing the bigger picture underlying this theory. Also our addition of the non-recurrent model variant (see above) adds considerable novelty, since it provides an account of phase precession and preplay in novel environments.

• The significance of the readout tempotron neuron could be expanded on. In particular, there is room for interpretation of the output signal of that neuron (e.g., what is the significance of other neurons downstream? Why is the rationale for this output to being theta-modulated?)

We have added an additional Figure 8 to better illustrate the inner workings of the tempotron. We also extended the discussion to better explain the potential use of the tempotron output (see above). In short, we consider the tempotron to signal a unique behaviorally important context that is independent of remapping induced by changes of sensory cues, which is a new prediction of the model. Since the context signal is resulting from DG loops it requires a stable code to also exits in the DG. Evidence for such long-term stability in DG has been found in Hainmu¨ller & Bartos (2018).

Reviewer #2 in their public review find ”this research topic to be both important and interesting” and appreciates ”the clarity of the paper.”, com- mending our ”efforts to integrate previous theories into their model and con- duct a systematic comparison”.

We are very happy about these positive remarks and sincerely would like to thank the reviewer!

Reviewer #1 made the following specific recommendations for changes:

The abstract is somewhat difficult to parse. I have identified some words and/or sections that could be improved.

• ’ ....inherently 1 dimensional’. This statement seems to be related to an a priori interpretation of the authors. On the other hand, if offline sequences are trivially 1 dimensional because they are sequences (i.e., they constitute a vector), then online sequences would be 1-dimensional as well. What is the key difference between offline and online? Is it the omnidirectional place fields in two dimensions? Perhaps more importantly, how relevant is this fact with respect to the main results of the manuscript, which concern ex- trinsic and intrinsic sequences?

We indeed meant that the sequences are trivially 1-dimensional. The main challenge that we would like to address in this paper is how a 2-d topology of place cells (and direction dependent theta sequences) and a 1-d sequence topology of intrinsic theta correlations and during (p)replay can be reconciled. We hope this has become clearer in the rewritten abstract.

• The language in lines 36-38 is overly technical. I suggest modifying the language, the language was less technical and more understandable in the body of the manuscript, which should be also reflected in the Abstract.

We would would like to apologize for making the abstract too technical. Also in response to Reviewer #2, we decided to rewrite the ab- stract entirely.

The authors use a mixture of conductance based models and Izhikevich neurons, presumably for the spiking generating mechanism. The conductance component can be readily interpreted in terms of the underlying biophysics. The Izhikhevich neuron model, however, is phenomenological. I suggest you address i) the rationale for using Izhikevich model, 2) its biophysical inter- pretation, 3) and its combination with conductance-based currents.

The reviewer is correct that spike generation is modelled using Izhikevich’s model whereas synaptic integration is included in a conductance- based manner. As suggested by the reviewer, we have added further expla- nation in the Methods part, explaining that the Izhikevich approach allows to adjust burst firing properties with only few parameters by efficiently em- ulating the bifurcation structure of spike generation in the full biophysical model (1&2) and otherwise has no effect on the integration of conductance- based synaptic currents in a subthreshold regime (3).

Line 126: when you say preferred angle, do you mean preferred (heading) direction? If so, please maintain consistency throughout.

We thank the reviewer for pointing out the inconsistency. We have added the word ”heading” throughout the manuscript whenever ap- propriate. To further improve the consistency, we have clarified the meanings of ”best” (or ”worst”) direction and reserved the use of it solely for cases when trajectory direction is compared with the preferred heading direction, namely, ”best” (”worst”) direction when trajectory is along (opposite) the preferred heading direction.

Line 174: When discussing cross-correlation, sometimes you mean a cross-correlation function between two place fields and sometimes to the his- togram of all such correlations? Please clarify.

We used histograms to empirically estimate the underlying cross-correlation function. For clarity, we have specified that it is a cross- correlation histogram in the revised manuscript whenever we refer to the empirical estimate.

Figure 3:

Understanding the difference between extrinsic and intrinsic sequences is fundamental for the manuscript. I suggest that in the section that refers to Figure 3 (or Figure 3 itself), you kindly provide an example depicting how extrinsic and intrinsic sequences can

1. coexist yet be distinctly identified

1. depend on trajectory

1. depend on DG input

By coexistence, we meant the heterogeneous population of ex- trinsic and intrinsic cell pairs and, hence, the extrinsic and intrinsic theta correlations, as shown in Figure 3J. To improve the clarity, we added the following sentence in the section that refers to Figure 3: ”In our simula- tion, extrinsically and intrinsically driven cell pairs are both present in the population (Figure 3J), indicating a coexistence of extrinsic and intrinsic sequences.”. To illustrate how extrinsic and intrinsic sequences depend on both tra- jectory and DG recurrence, we have also added annotations in Figure 3F to mark the extrinsic and intrinsic part of the sequence.

Moreover, the caption of Figure 3 refers to the directionality of the theta sequences. How does this again relate to the extrinsic/intrinsic distinction?

We hope the highlighting in panel F of Figure 3 has resolved this problem.

Figure 5:

• This is a crucial figure that should illustrate the differences between extrinsic and intrinsic sequences, as the figure caption suggests. Surprisingly, it is not at all clear where (i.e., in which panel) and how (i.e., methodologi- cally) should one distinguish one type of sequence from another. I suggest that at least one such panel is dedicated to illustrating the difference and/or detection of these sequences in time and/or from phase precession plots. Moreover, there is significant visual crowding that makes the interpretation challenging (e.g., insert a space between G and E)

We would like to apologize that in the previous version of the manuscript, we seemed to have evoked the impression that the difference between intrinsic and extrinsic sequences should be mainly illustrated in Figure 5. We hope that our revisions of Figures 1 and 3 have made it sufficiently clear to this point. The main purpose of Figure 5 was (and is) to illustrate how intrinsic sequences can lead to out-of-field firing. We have modified the figure caption (and text) accordingly. To address the visual crowding problem in Figure 5, we have inserted a space between panels and also removed repeated labels.

Tempotron neuron and Figure 6:

From the reviewer’s questions on Figure 6, we feel that our presentation caused considerable confusion about the motivation and inter- pretation of the tempotron simulations. We therefore rewrote parts of the associated text and Figure caption. We hope that the revised presentation clarifies the issues. We therefore only briefly respond to the reviewer’s points here, because we think they largely resulted from misunderstandings.

• Intuitively, and as the manuscript results suggest, late phases are asso- ciated to extrinsic mechanisms while early phases are associated to intrinsic. Why not construct a simpler classifier readout based on this fact? How does it compare to a tempotron?

Opposite to the reviewer’s comment, extrinsic mechanisms are visible at early phases (late in the field), intrinsic mechanisms at late phases (early in the field). In fact, what the tempotron does is learning to identify the intrinsic (late phase) part and to disregard the extrinsic (early phase) part.

• What is the significance of theta-modulated output of the tempotron (readout) neuron?

The theta modulation of the tempotron output is a trivial re- sult of the theta-modulation of the input, i.e., the detection of the intrinsic sequence pattern is done once every cycle.

Suggestion for Figure 6 related to Tempotron readout: Focus on ’with DG loop condition’, as the challenge and most important point here is to identify extrinsic and intrinsic sequences. The No-loop condition could be left as a supplementary figure or side panel.

The no-loop condition is the essential control showing that the tempotron only responds to the previously learned intrinsic pattern and can- not identify spatial location based on the extrinsic pattern.

Further work/predictions.

Lines 196-198. ”Since intrinsic sequences can also propagate outside the trajectory (Figure 5) and activate place cells non-locally, our model predicts direction-dependent expansion of place fields.” If remote activation is ’suffi- ciently’ remote, wouldn’t this predict two separate place fields instead of an expansion?

The reviewer is completely correct. Out of field spiking can be also affecting remote locations, if the intrinsic sequences link to remote place fields. This would lead to double fields, however, the intrinsic part would only be active at late theta phases. For simplicity, we have not added such a case in our paper, but we would like to thank the reviewer for this comment, since it leads to a nice prediction of the model, which can be experimentally tested and therefore was included to the discussion.

Lines 556-558. ”In our model, firing rate is determined by both low-phase spiking from sensory input and high-phase spike arrivals of DG-CA3 loops, both producing opposing effects on the phase distribution.” Is it possible to make a differential prediction based on lesions here, e.g., along the lines of reduced range phase precession, for either high phases or for low phases?

We thank the reviewer for this great suggestion. Lesion of DG in the model does indeed reduce the phase range and mean spike phase. This further corroborates the effect of DG-loop on theta compression and high-phase spiking. We have included a new panel D in Figure 4 and a corresponding mention in the result section.

Line 570. ”We speculate that the functional roles of intrinsic sequences may not be limited to spatial memories.”. Is there any relationship to re- play and/or sleep-dependent memory consolidation? Some speculation in the Discussion section would be welcome and appropriate.

We have added some further speculative ideas to the last section of the Discussion. We propose that replay and preplay reflects the intrinsic sequences that express the current expectation of the animal. We have not yet thought well enough about their relation to memory consolidation to phrase this in the manuscript, but would suggest that they could serve to signal multimodal context information to the neocortex where it can evoke retrieval of unimodal memory traces.

The description of the results, as stated in the public review, can be im- proved. A key component is the definition and identification of extrinsic and intrinsic sequences.

Some comments:

• I think that the words ’extrinsic’ and ’intrinsic’ are problematic as both types of sequences/models rely on external (spatial) input, hence both are in some sense ’extrinsic’. On the other hand, both are network mechanisms, thus in some sense ’intrinsic’, where the asymmetry is either programmed directly onto the weights or due to synaptic depression. To add to the con- fusion, ’intrinsic’ mechanisms very often refer to cellular mechanisms in neurophysiology. I kindly ask you to, ideally, reconsider the terminology, or at the very least, be very thorough and precise when describing the mech- anisms. For example, sometimes extrinsic (intrinsic) ’models’ are referred to, sometimes ’sequences’, sometimes ’factors’, sometimes ’pairs’, etc.

We understand and appreciate the reviewers argument, but would like to stick to the terminology, since it was already used in our prior publication. We have made considerable effort to improve the explanation and illustration of extrinsic vs. intrinsic pairs in the main text, Figure 1 and 3 to highlight our definition that is based on pair correlations: Extrin- sic pairs flip the correlation lag with reversal of running direction, intrinsic pairs don’t. This is simply a functional definition and should not be con- fused with potential microscopic mechanisms. One of those (DG-loops) is suggested in our paper.

• As discussed in the public review, network mechanisms may require experience-dependent plasticity and hence cannot easily explain phase pre- cession on the first pass. Please discuss why and/or how your model fits with this observation.

We agree that the two models under consideration both require the recurrent network be set up appropriately and there is no theory so far that would explain how. The reason we chose these two models is because they are well known in the community and relatively similar. We reasoned that comparison between an intrinsic model and an extrinsic model would make most sense if the two are a similar as possible. Nevertheless, we ex- tended the manuscript by a new set of simulations in which we do not use re- current CA3 connections and obtain phase precession solely be feed-forward synaptic facilitation (new Figure 6 and supplementary Figure S1). The new simulations show that the basic phenomenology can also be obtained with- out using recurrent CA3 connections, however, as expected when removing one mechanisms of phase precession, the range of phase range is somewhat reduced as compared to the full model.

Along a similar vein, phase precession in Figure 1E only has a range of pi/2, which is about half of the typical range of phase precession for single runs. This should be characterized as a weakness of the intrinsic model.

The precession range in spiking models is highly sensitive to a large number of parameters such that it is hard to make such definite claims (see also above response). In the original Tsodyks et al. 1996 paper the phase range went up to 270 degrees with a slightly different implementation to ours in terms of current vs. conductance-based synapses, an exponen- tial instead of a Gaussian recurrent weight function, and 1-d (original) vs 2-d (ours). We chose conductance-based synapses, and a Gaussian weight profile for better comparison with the Romani and Tsodyks (2015) model. In the original non-spiking implementation by Romani and Tsodyks (2015), the phase range was hardly 70 degrees. Our model implementation of the Romani and Tsodyks (2015) model fits the experimentally reported phase ranges of about 70 to 180 degrees in CA3 (Harris et al., 2001).

Lines 282-284: ”...since phase precession properties change in relation to running directions, nor are they solely intrinsic since reversal of correlation is still observed in most of the sequences (Huxter et al., 2008; Yiu et al., 2022).”. To which extent is this a consequence of the phase precession model (extrinsic vs intrinsic) or the fact that place fields are sometimes directional?

The reversal of sequences with reversed running direction is how we define extrinsic correlation. We hope our changes in relation to Figure 1 has clarified this point.

Figure 2: Is it i) directional input or ii) short-term facilitation that gives rise to lower phase? (or perhaps both?) Please clarify.

It’s both. This is now clarified in the revised version of the Re- sults sections related to Figure 2: higher depolarization always yields earlier phases in spiking models, however, pair correlations are not affected by ei- ther of the two mechanisms.

Line 320. ”...onset of phase precession”. Do you mean in CA3/CA1/DG?

Thank you for pointing this out. We have clarified that this statement refers to CA3.

Line 323. ”....at a different location”. Please add rationale why it has to be at a different location and a reference to the appropriate equation.

The sequence rationale as well as the equation number have been added.

Line 384. ” ... predicting that loss of DG inputs is compensated for by the increase of release probability in the spared afferent synapses from the MEC.”. It wasn’t clear whether this was a ’homeostasis prediction’, or and implementation in the model. Please clarify.

Since the model explained the experimental observations by implementing an increased probability of release, the model predicts that in animals with DG lesion the probability of release should be enhanced. We have modified the wording to avoid confusion.

Line 428 ”...and near future locations) is obvious, the potential role of the lesser expressed intrinsic sequence contributions is not straightforward.”. Similar to my comments above regarding terminology, please clarify what are both contributions and why are intrinsic sequences ’lesser expressed’.

We have rewritten this passage to avoid unclear wording.

Line 474. ”...we showed that the trajectory-independent sequences”. Do you mean ’intrinsic sequences’?

We thank the reviewer for careful reading! We have changed the wording ”intrinsic sequences” in the revision.

Line 482. ”...field pairs being extrinsic”. Please clarify, as the usage of extrinsic now refers to field pairs.

Thank you for pointing this out. We went through the whole manuscript and clarified the terms.

Line 245 (heading). Consider rewriting as ’Dependence of theta se- quences on heading directions’. Extrinsic and Intrinsic models have not yet been introduced.

Since the main purpose of the first Results section is to explain the difference between extrinsic and intrinsic sequences we kept these terms in the heading but modified it to ”Dependence of theta sequences on head- ing directions: Extrinsic and intrinsic sequences”. Additionally, we have put more emphasis on introducing the terms ”extrinsic” and ”intrinsic” in this section.

Figure 1.

• I suggest using the same font - C and D, and F and G are too close to each other, consider adding space. For example, the exponent, 10-2 makes reading cumbersome. Line 300. Phase tail means offset phase? Phase tail may be too informal. Line 325: DG loop. Do you mean CA3-DG projection?

We thank the reviewer for the suggestions. In the revised manuscript, we have ensured that the same font is used in all of the fig- ures. To improve the readability of Figure 1, we have added space between panels as suggested, removed repeated axis label and downsized the text ”10-2”. Furthermore, we have rewritten the referenced line without using the word ”tail”, and also, clarified the meaning of DG loop as the short form of CA3-DG projection.

Figure 4 caption: ”DG lesion reduces temporal correlations...”. It is more precise to say that the lesion reduces the slope of the fitted lag vs dis- tance. And how is this related to sequence compression?

In the paragraph referring to Figure 4, we have elaborated on the meaning of theta compression and its relation with the the lag-distance plot. However, we argue that ”reduces the slope of the fitted curve” is not comprehensive enough to express our summarized conclusion in a caption title. We have modified the wording to be ”DG lesion reduces theta compression”.

In addition, we have changed the slope unit to be radians per cm rather than radians per maximum pair distance, in conformity to unit standards.

General comment about terminology with regards to tuning and connec- tivity: it is not formally correct to compare connectivity with trajectories (e.g., lines 388-395, caption of Figure 5A, etc). Perhaps compare tuning to particular directions/preference or receptive field?

We have corrected the wording such that the direction of DG- loop projection is compared to the direction of trajectory.

Line 470. ’...fixed recursive loop.” Sentence is not clear, do you mean recurrent loops?

The reviewer is correct. We corrected the wording

Reviewer #2 had the following recommendations.

M1. The abstract focuses on the differences between online and offline hippocampal replays. However, the replay topic is not touched upon in the rest of the manuscript. I found this very confusing when I first read the pa- per. I suggest the authors reconsider the best way to approach the opening or at least discuss if and how their model would incorporate replay phenomena.

Also in response to reviewer #1 we have rewritten the abstract focusing on the problem of how to generate 2-d topology from 1-d sequences. In addition, also in response to Reviewer#1 we added a paragraph in the discussion detailing a hypothesis on how er think replay and intrinsic se- quences work together.

m2. On lines 89-91, the authors provide the selection of neuronal pa- rameters for excitatory pyramidal cells and inhibitory cells in the Izhikevich model. While the choice of model is reasonable, it would be helpful to clarify the source of these neuronal parameters, especially for readers who are not familiar with the model.

Again, also in response to reviewer # 1, we have added more motivation for the Izhikevich model.

M3. On lines 94-98, the model considers a 2D sheet of CA3 neurons. One of the most significant assumptions is that each 2x2 tile of place cells is considered a unit with four directional angles. What is the basis for this assumption? Is there any experimental result supporting this, or is it a completely artificial design for the model? This is important since the or- ganization of CA3 cells also affects the network architecture discussed later and impacts the realism of the model.

This comment is related to Reviewer #1’s concern on experience- dependent plasticity: How is this connectivity pattern established? We fully agree that this is an open problem for the Tsodyks et al.-type networks. The main reason for choosing them (as argued in our response to reviewer #1) is to have two published models, representing one type of sequence each, that are similar enough for comparison. In addition, we added new simulations (new Figure 6 and Supplementary Figure S1), showing that the basic phe- nomenology can also be obtained in a model without recurrent connections (see also response to Reviewer # 1)

m4. Similarly, on lines 111 and 140, the model uses 500 ms for the timescales of short facilitation and short-term synaptic depression. The choices of these two timescales are vital for producing directionality in extrin- sic and intrinsic sequences, yet their experimental sources are not clarified.

In the Methods section of the revised manuscript, we have in- cluded the sources of previous experimental data and modelling work to support our choice of the time constants.

M5. On line 126, the authors assume that the synaptic strengths be- tween CA3 cells, Wij, are given by the distances between neurons and the similarity between their directional preferences. While this assumption seems reasonable in the sensory cortex, I am unsure if this is also the case in the hippocampus, and the authors should clarify the basis for this assumption.

The distance dependence simply reflects the original Romani and Tsodyks 2015 model (see response to M3) and we share the concern of the reviewers. The increased connectivity for neurons with the same di- rectional preference was necessary to recover the direction dependent phase precession properties (Figure 2) in the realm of the Romani and Tsodyks 2015 model. Please also see our new Figure 6 showing simulations without the recurrent matrix.

More importantly, the existing connections within CA3 and DG cells completely determine the ”intrinsic” sequences. But wouldn’t this be fragile when place cells undergo global remapping, which can take place within only a few seconds? The author should comment on this in the discussion.

We would like to thank the reviewer for bringing up this inter- esting point. In our thinking, the DG-CA3 connectivity is fixed (multiple 1-d trajectories, not necessarily requiring 2-d topology), i.e., the same in- trinsic sequence should show up in multiple environments (and should not remap), although it may just not be active in some environments). This is a prediction of our model and we have added it to the Discussion.

M6. I found the setup of DG place cells unreasonable. DG place cells are found to be granule cells rather than pyramidal cells. Moreover, the model does not consider recurrent connections between DG cells (These setups are closer to CA1 place cells).

We agree with the reviewer, DG granule cells should rather be modelled as high-input resistance EIF neurons. However, the feedback loop via the dentate is not a direct one. It involves hilar mossy cells plus multiple hierarchies of feedback inhibition (this is probably what the reviewer means with recurrent connections between DG neurons, because granule cells are not recurrently connected in the non-pathological state). To our knowledge a biologically realistic model of the hilar-DG network does not exist and it would be far beyond the scope of this paper to develop one. We therefore see our DG feedback model rather as phenomenological. The discussion paragraph on the anatomy of the dentate gyrus touches on these points.

Therefore, a significant concern is: Why should it be the DG feedback projection to CA3 responsible for the ”intrinsic” sequences instead of pro- jections from other brain areas?

The reviewer is generally correct, any brain structure which im- plements fixed sequences via a loop would do. The reason why we suggest the DG to be the best candidate is purely empirical referring to papers with dentate lesions: Sasaki et al. 2018 and Ahmadi et a. 2022. We have added a similar argument to the discussion.

m7. On line 166, the authors claim that there are no connections between inhibitory cells at all. While I understand that this is for simplification of the model, the lack of recurrent inhibition between interneurons may have limited the model’s ability to produce gamma-band dynamics (referring to PING and ING mechanisms), which are robust rhythms produced in CA3. I am very curious if the model can incorporate theta-gamma coupling by in- troducing connections between CA3 inhibitory cells.

We have omitted the gamma oscillation for simplicity, because we do not have a hypothesis for a functional role in the context of dis- tinguishing extrinsic from intrinsic sequences (Occam’s razor) and, as the reviewer correctly anticipates, they unavoidably show up when inhibitory in- terneurons connect to each other (e.g. Thurley et al. 2013). Of course, one could envision situations in which gamma for intrinsic sequences my have different frequency than for extrinsic ones, by differentially manipulating the CA3 and DG basket cell networks, but, as long as there is no experimental data, it would be pure speculation and thus we have not included it in the model.

m8. The authors should clarify the source of parameters in Table 1, especially the synaptic strengths. These values are vital for extrinsic and intrinsic theta sequences.

The weight values have been chosen to allow for large theta phase precession range, coexistence of extrinsic and intrinsic sequences, and stability of the network activity. A similar statement has been added to the manuscript.

M9. I have another concern regarding the measurements of ”extrinsic- ity” and ”intrinsicity” defined on lines 185-196. Are they the best measures? To distinguish the cause of spike correlations, the ”extrinsicity” and ”intrin- sicity” of a pair of spikes should not be high at the same time. However, this is clearly not the case in the model, according to Figs 3 and 5. Moreover, in the data analysis carried out later, spike pairs are considered extrinsic or intrinsic merely by comparing the two measurements. I suggest the authors consider counterfactual methods in causal inference. For example, would a spike pair (cell1, cell2) still exist if we change the sensorimotor inputs or the DG-CA3 projections? If this is difficult to implement, the authors should at least discuss how different choices of measurements would impact the con- clusions of the paper.

The problem the reviewer has identified arises from the funda- mental symmetry of theta phase quantification: if spikes of a pair of place fields have a phase difference of 180◦ one cannot say which cell leads and which cell follows, hence, the phase difference is both intrinsic (because the peak doesn’t flip) and extrinsic (because the peak flips and ends up at the same phase). The fact that in some cases extrinsicity as well as intrinsicity are high simply means that the field pair has a correlation peak lag close to 180◦. Since in the experimental data set in (Yiu et al. 2022) only field pairs were available, we have not been able to use a different quantification then and decided to apply the same quantification in our model for comparison. Moreover, Figure 5F nicely shows that the measures are able to retrieve the ground-truth intrinsic DG-loop structure when considered on the population level.

In our model, though, we can go beyond 2-nd order statistics and derive sequence similarity measures including multiple cells, e.g., Chenani et al. 2019. However, since, we already know the ground truth by construction, we decided to not use these methods. We added a paragraph in the discus- sion elaborating on beyond 2nd order sequence quantification.

m10. The authors begin discussing ”intrinsic sequences” from line 316. However, it is not defined before that (and in the rest of the paper as well), causing confusion when reading the paper. The exact definitions of extrinsic and intrinsic sequences should come earlier.

We hope that our changes to the beginning of the results section (Figure 1), also asked for by Reviewer # 1 could clarify the confusion.

m11. On lines 345-347, the authors claim that ”the intrinsic sequences are played out backward as determined by the direction of fixed recurrence (Figure 3F),” which is vague. If such sequences are present in that panel, it should be more explicitly indicated graphically.

Also in response to Reviewer #1, we have graphically high- lighted the two types of sequences.

M12. On lines 309, 356, 484, 495, 515, and possibly other instances, the authors repeatedly claim that the model simulations are in ”quantitative agreement” with their previous experimental paper. However, no experimen- tal data or comparison with the simulations are presented in this paper. The authors should at least create one figure to demonstrate the degree of consistency between them, instead of merely asking the reader to refer back to their previous paper.

We agree with the reviewer that the experimental data of our previous paper should be presented in the manuscript. However, creating more panels or figures is likely to clutter the already crowded visuals and ob- scure our main message. We therefore decided to give numerical comparisons the previous findings in the main text whenever appropriate, specifically, in the sections referring to Figures 2, 3 and in the Discussion.