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Summary 

The medial entorhinal cortex (MEC) integrates both self-motion and landmark cues, an open question is whether its cells can flexibly adjust their computations depending on behavioral demands. In this paper, the authors investigate whether the MEC cells can dissociate from landmarks anchoring to encode reward distance. To do this, they use electrophysiology to record MEC cells during a virtual reality path-integration(PI) task in mice navigating a cue-rich belt. By comparing the firing properties of MEC cells in a 2D open field, a cue-rich PI task, and a cue-rich fixed reward task, the authors show that both grid cells and border cells remap to encode reward distance. Using computational modeling, they further conclude that the observed changes in grid cells’ properties can be explained by a combination of a continuous attractor model and a theta interference model in which grid cells received two diverged theta frequency inputs. These findings are valuable, as they support the emerging view that MEC cells are not statically anchored to environmental cues but can flexibly shift their reference frame depending on behavioral demands. Overall, the main experiments and modeling are compelling, but additional analyses are needed to support the main claim that MEC grid cells are encoding reward distance during the PI task in a cue-rich environment. 

Major comments: 

1. Quantification of reward-distance coding. The authors convincingly show that MEC cells remap across tasks, as illustrated by differences between belt-aligned and reward-aligned firing maps in Figure 2 and Supplementary Figure 1. However, it remains unclear to what extent reward-distance coding accounts for MEC activity in the PI task. Specifically, the proportion of MEC neurons that encode reward distance is not quantified. Several example cells (e.g., cells 18 and 23 in Figure 2a, and cells 12, 7, and 24 in Supplementary Figure 1) appear to encode running distance rather than reward distance. I recommend that the authors use a decoding or model-comparison approach (e.g., GLM-based encoding models) to quantify the contribution of reward distance across the MEC population. If a neuron encodes reward distance, removing reward-distance predictors from the model should significantly reduce model performance. Such quantification would help clarify the definition and prevalence of reward-distance coding in the PI task. Additionally, for the future experimental design, the authors could consider interleaved probe trials(no reward delivered) to investigate whether reward is necessary for the observed neural coding in the PI task. 

1. Interpretation of grid-scale reduction and additional population analysis. The authors conclude that grid scale decreases during the PI task based on reduced inter-field distances. However, inter-field distances measured along a 1D trajectory depend on the angle at which the trajectory intersects the 2D hexagonal lattice (Yoon et al., 2016, DOI: 10.1016/j.cell.2018.08.066 ). Because the authors also report trial-to-trial shifts in firing fields during the PI task, it is unclear whether the apparent grid-scale reduction reflects a change in mapping angle rather than a true change in grid spacing. As the authors already collected consecutive sessions(OF/PI/Cue), I would recommend considering the toroidal analysis(see example in Wen et al., 2024, DOI: 10.1038/s41586-024-08034-3) to compare how the mapping between movement trajectory and population activity of grid cells changes in different tasks. If the ‘reward resetting’ is true, we should see a fixed bump location in the 2D toroid neural space when the animal passes the reward location, and the revolution of the bump activity traveling in the neural toroid should correspond to the reward trials instead of the belt cycle. The toroidal analysis will allow quantification of the anchoring strength of reward relative to landmarks in different conditions. 

1. Clarification of reward delivery. The authors should consider elaborating on what aspect of reward delivery entrains the grid-cell pattern. It is possible that sensory cues associated with reward delivery serve as the most reliable landmark, with the mouse using running distance to estimate the reward location during the PI task. In the Methods section, it would be helpful to clarify how the reward is delivered—automatically upon entering a reward zone, or contingent on behavioral criteria such as slowing or anticipatory licking. Given the behavioral analyses referenced in Figures 3a and 3g, quantifying behavioral engagement (misses, earlier licking, etc) would also help clarify whether reward-distance coding depends on active path integration and whether animals switch between reference frames. 

Minor comments: 

1. In “Results—Identification of grid and border cells,” the term “trials” is used to refer to reward-to-reward journeys in the PI task. This is potentially confusing because “trials” is also used for belt cycles in the fixed-reward cue-rich task and again in Figure 2c (belt-aligned vs. reward-aligned trials). Using distinct terms—e.g., “belt cycles” and “reward-to-reward journeys”—would improve clarity. 

1. In Figure 3a, it would be helpful to annotate how the correlation matrix was computed and how comparisons were made across animals and sessions. It is also unclear whether the example matrix represents a single session or aggregated data. 

Competing interests

The authors declare that they have no competing interests.

Use of Artificial Intelligence (AI)

The authors declare that they did not use generative AI to come up with new ideas for their review.