Robust variability of grid cell properties within individual grid modules enhances encoding of local space

Reviewer #1 (Public review):

Summary:

The present paper by Redman et al. investigated the variability of grid cell properties in the MEC by analyzing publicly available large-scale neural recording data. Although previous studies have proposed that grid spacing and orientation are homogeneous within the same grid module, the authors found a small but robust variability in grid spacing and orientation across grid cells in the same module. The authors also showed, through model simulations, that such variability is useful for decoding spatial position.

Strengths:

The results of this study provide novel and intriguing insights into how grid cells compose the cognitive map in the axis of the entorhinal cortex and hippocampus. This study analyzes large data sets in an appropriate manner and the results are solid.

Weaknesses:

A weakness of this paper is that the scope of the study may be somewhat narrow, as this study focused only on the variability of spacing and orientation across grid cells. I would suggest some additional analysis or discussion that might increase the value of the paper.

(1) Is the variability in grid spacing and orientation that the authors found intrinsically organized or is it shaped by experience? Previous research has shown that grid representations can be modified through experience (e.g., Boccara et al., Science 2019). To understand the dynamics of the network, it would be important to investigate whether robust variability exists from the beginning of the task period (recording period) or whether variability emerges in an experience-dependent manner within a session.

(2) It is important to consider the optimal variability size. The larger the variability, the better it is for decoding. On the other hand, as the authors state in the Discussion, it is assumed that variability does not exist in the continuous attractor model. Although this study describes that it does not address how such variability fits the attractor theory, it would be better if more detailed ideas and suggestions were provided as to what direction the study could take to clarify the optimal size of variability.

Reviewer #2 (Public review):

Summary:

This paper presents an interesting and useful analysis of grid cell heterogeneity, showing that the experimentally observed heterogeneity of spacing and orientation within a grid cell module can allow more accurate decoding of location from a single module.

Strengths:

I found the statistical analysis of the grid cell variability to be very systematic and convincing. I also found the evidence for enhanced decoding of location based on between-cell variability within a module to be convincing and important, supporting their conclusions.

Weaknesses:

(1) Even though theoreticians might have gotten the mistaken impression that grid cells are highly regular, this might be due to an overemphasis on regularity in a subset of papers. Most experimentalists working with grid cells know that many if not most grid cells show high variability of firing fields within a single neuron, though this analysis focuses on between neurons. In response to this comment, the reviewers should tone down and modify their statements about what are the current assumptions of the field (and if possible provide a short supplemental section with direct quotes from various papers that have made these assumptions).

(2) The authors state that "no characterization of the degree and robustness of variability in grid properties within individual modules has been performed." It is always dangerous to speak in absolute terms about what has been done in scientific studies. It is true that few studies have had the number of grid cells necessary to make comparisons within and between modules, but many studies have clearly shown the distribution of spacing in neuronal data (e.g. Hafting et al., 2005; Barry et al., 2007; Stensola et al., 2012; Hardcastle et al., 2015) so the variability has been visible in the data presentations. Also, most researchers in the field are well aware that highly consistent grid cells are much rarer than messy grid cells that have unevenly spaced firing fields. This doesn't hurt the importance of the paper, but they need to tone down their statements about the lack of previous awareness of variability (specific locations are noted in the specific comments).

(3) The methods section needs to have a separate subheading entitled: How grid cells were assigned to modules" that clearly describes how the grid cells were assigned to a module (i.e. was this done by Gardner et al., or done as part of this paper's post-processing?

Reviewer #3 (Public review):

Summary:

Redman and colleagues analyze grid cell data obtained from public databases. They show that there is significant variability in spacing and orientation within a module. They show that the difference in spacing and orientation for a pair of cells is larger than the one obtained for two independent maps of the same cell. They speculate that this variability could be useful to disambiguate the rat position if only information from a single module is used by a decoder.

Strengths:

The strengths of this work lie in its conciseness, clarity, and the potential significance of its findings for the grid cell community, which has largely overlooked this issue for the past two decades. Their hypothesis is well stated and the analyses are solid.

Weaknesses:

On the side of weaknesses, we identified two aspects of concern. First, alternative explanations for the main result exist that should be explored and ruled out. Second, the authors' speculation about the benefits of variability in angle and spacing for spatial coding is not particularly convincing, although this issue does not diminish the importance or impact of the results.

Major comments:

(1) One possible explanation of the dispersion in lambda (not in theta) could be variability in the typical width of the field. For a fixed spacing, wider fields might push the six fields around the center of the autocorrelogram toward the outside, depending on the details of how exactly the position of these fields is calculated. We recommend authors show that lambda does not correlate with field width, or at least that the variability explained by field width is smaller than the overall lambda variability.

(2) An alternative explanation could be related to what happens at the borders. The authors tackle this issue in Figure S2 but introduce a different way of measuring lambda based on three fields, which in our view is not optimal. We recommend showing that the dispersions in lambda and theta remain invariant as one removes the border-most part of the maps but estimating lambda through the autocorrelogram of the remaining part of the map. Of course, there is a limit to how much can be removed before measures of lambda and theta become very noisy.

(3) A third possibility is slightly more tricky. Some works (for example Kropff et al, 2015) have shown that fields anticipate the rat position, so every time the rat traverses them they appear slightly displaced opposite to the direction of movement. The amount of displacement depends on the velocity. Maps that we construct out of a whole session should be deformed in a perfectly symmetric way if rats traverse fields in all directions and speeds. However, if the cell is conjunctive, we would expect a deformation mainly along the cell's preferred head direction. Since conjunctive cells have all possible preferred directions, and many grid cells are not conjunctive at all, this phenomenon could create variability in theta and lambda that is not a legitimate one but rather associated with the way we pool data to construct maps. To rule away this possibility, we recommend the authors study the variability in theta and lambda of conjunctive vs non-conjunctive grid cells. If the authors suspect that this phenomenon could explain part of their results, they should also take into account the findings of Gerlei and colleagues (2020) from the Nolan lab, that add complexity to this issue.

(4) The results in Figure 6 are correct, but we are not convinced by the argument. The fact that grid cells fire in the same way in different parts of the environment and in different environments is what gives them their appeal as a platform for path integration since displacement can be calculated independently of the location of the animal. Losing this universal platform is, in our view, too much of a price to pay when the only gain is the possibility of decoding position from a single module (or non-adjacent modules) which, as the authors discuss, is probably never the case. Besides, similar disambiguation of positions within the environment would come for free by adding to the decoding algorithm spatial cells (non-hexagonal but spatially stable), which are ubiquitous across the entorhinal cortex. Thus, it seems to us that - at least along this line of argumentation - with variability the network is losing a lot but not gaining much.

(5) In Figure 4 one axis has markedly lower variability. Is this always the same axis? Can the authors comment more on this finding?

(6) The paper would gain in depth if maps coming out of different computational models could be analyzed in the same way.

(7) Similarly, it would be very interesting to expand the study with some other data to understand if between-cell delta_theta and delta_lambda are invariant across environments. In a related matter, is there a correlation between delta_theta (delta_lambda) for the first vs for the second half of the session? We expect there should be a significant correlation, it would be nice to show it.

Author response:

We thank the reviewers for their time and thoughtful comments. We are encouraged that all reviewers found our work novel and clear. We will submit a full revision to address all the points the reviewers made. Below, we briefly highlight a few clarifications and planned analyses to address major concerns; all other concerns raised by the reviewers will also be addressed in the revision.

Reviewers #1 and #3 asked whether the variability in grid properties emerged with experience/time in the environment. We agree that this is an interesting question, and we will re-analyze the data to explore whether between-cell variability increases with time within a session. However, we note that since the rats were already familiarized to the environment for 10-20 sessions prior to the recordings, there may be limited additional changes in between-cell variability between recording sessions. In one case, two sessions from the same rat were recorded on consecutive days (R11/R12 and R21/R22) - these sessions did not show any difference in variability.

Reviewer #2 noted that the variability in grid properties is known to experimentalists. We will tone down our discussion on the current assumptions in the field to accurately reflect this awareness in the community. However, we would like to emphasize that the lack of work carefully examining the robustness of this variability has prevented a firm understanding of whether this is an inherent property of grid cells or due to noise. The impact of this can be seen in theoretical neuroscience work where a considerable number of articles (including recent publications) start with the assumption that all grid cells within a module have identical properties, with the exception of phase shift and noise. In addition, since grid cells are assumed to be identical in the computational neuroscience community, there has been little work on quantifying how much variability a given model produces. This makes it challenging to understand how consistent different models are with our observations. We believe that making these limitations of previous work clear is important to properly conveying our work’s contribution.

Reviewer #3 asked whether the variability in grid properties could be driven by cells that were conjunctively tuned with head direction. We agree that this is an interesting hypothesis and will explore this by performing new analysis. We note that, as reported by Gardner et al. (2022), only 19 of the 168 cells in recording session R12 are conjunctive. Even if these cells are included in the same proportion as pure grid cells by our inclusion criteria (which appears unlikely, given that conjunctive cells may be less reliable across splits of the data), then approximately 9 out of the 82 cells we analyzed would be conjunctive. Therefore, we expect it to be unlikely that they are the main source of the variability we find. However, we will test this in our revised manuscript.

Reviewer #3 asked whether the “price” paid in having grid property variability was too high for the modest gain in ability to encode local space. We agree that losing the continuous attractor network (CAN) structure, and the ability to path integrate, would be a very large loss. However, we do not believe that the variability we observe necessarily destroys either CAN or path integration. We argue this for two reasons. First, the data we analyzed [from Gardner et al. (2022)] is exactly the data set that was found to have toroidal topology and therefore viewed to be in line with a major prediction of CANs. Thus, the amount of variability in grid properties does not rule out the underlying presence of a continuous attractor. Second, path integration may still be possible with grid cells that have variable properties. To illustrate this, and to address another comment from Reviewer #3, we have begun to analyze the distribution of grid properties in a recurrent neural network (RNN) model trained to perform path integration (Sorscher et al., 2019). This RNN model, in addition to others (Banino et al., 2018; Cueva and Wei, 2018), has been found to develop grid cells and there is evidence that it develops CANs as the underlying circuit mechanism (Sorscher et al., 2023). We find that the grid cells that emerge from this model exhibit variability in their grid spacings and orientations. This illustrates that path integration (the very task the RNN was trained to perform) is possible using grid cells with variable properties.