This article is a well-written overview of the current state of knowledge of the recently discovered grid-cell phenomenon. I have only the following suggestions for improvement.
1) Figure 2 could use some more explanation in the caption. The general reader will not necessarily know that the left part is a histologically stained section of brain tissue and what the various components signify.
2) Figure 3 does not really show the intended point clearly. The individual grids portrayed by each color are hard to discern, and subsequently the phase offset is not easily seen. Figure 3a of Hafting et al. 2005 is a better illustration of the point. A reproduction of this figure, or another example more like it, would help.
3) I would suggest that the article mention briefly the broader aspects of O’Keefe and Nadel’s cognitive map theory in the history. That is, it is not only a theory of flexible navigation, but also more broadly a theory of how the cognitive map is used as a spatial framework used by the brain to organize the different aspects of experience for memory storage.
4) Some of the links to other articles are inappropriate. For example, the colloquial use of the words “attention” and “trajectory” are not relevant to the technical articles that are linked to those terms.
5) It might be worth mentioning the work of Sharp and colleagues on subiculum cells, which also appear to constitute a “universal map” that is different from the context-specific maps of the CA regions and which share direct projections with the entorhinal cortex.
We have revised the article on grid cells, following all suggestions of the reviewers.
1. Legend of fig 2 expanded. 2. Figure 3 replaced as suggested. 3. Broader aspects of 'cognitive map' theory mentioned (in the introduction; although details would be more appropriate for the separate entry on cognitive maps). 4. Sharp paper (plus Redish & Touretzky) referred in connection with universal map. 5. Introductory sentence about beginning of studies of spatial representation has been rephrased. 6. Other minor changes accepted.