Natural environments are represented by local maps of grid cells and place cells that are stitched together. The manner by which transitions between map fragments are generated is unknown. We recorded grid cells while rats were trained in two rectangular compartments, A and B (each 1 m × 2 m), separated by a wall. Once distinct grid maps were established in each environment, we removed the partition and allowed the rat to explore the merged environment (2 m × 2 m). The grid patterns were largely retained along the distal walls of the box. Nearer the former partition line, individual grid fields changed location, resulting almost immediately in local spatial periodicity and continuity between the two original maps. Grid cells belonging to the same grid module retained phase relationships during the transformation. Thus, when environments are merged, grid fields reorganize rapidly to establish spatial periodicity in the area where the environments meet.
We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a maximum entropy kinetic pairwise model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.
Highlights d Grid-cell patterns exhibit stereotypical spatial distortions d Distortions are strongest at edges of the environment d Grid patterns are both sheared and compressed near edges and walls d The distortions do not reflect moment-to-moment changes in running speed Authors Martin H€ agglund, Maria Mørreaunet, May-Britt Moser, Edvard I. Moser Correspondence martin.hagglund@ntnu.no (M.H.), edvard.moser@ntnu.no (E.I.M.) In Brief H € agglund et al. analyze local distortions in spatial firing patterns of grid cells. Distortions are stronger at the edges of the environment than on open surfaces. Edge distoritions and curvature of grid axes can be explained by a geometrical model in which the grid pattern is both sheared and compressed along the walls of the enclosure.
The firing pattern of grid cells in rats has been shown to exhibit elastic distortions that compresses and shears the pattern and suggests that the grid is locally anchored. Anchoring points may need to be learned to account for different environments. We recorded grid cells in animals encountering a novel environment. The grid pattern was not stable but moved between the first few sessions predicted by the animals running behavior. Using a learning continuous attractor network model, we show that learning distributed anchoring points may lead to such grid field movement as well as previously observed shearing and compression distortions. The model further predicted topological defects comprising a pentagonal/heptagonal break in the pattern. Grids recorded in large environments were shown to exhibit such topological defects. Taken together, the final pattern may be a compromise between local network attractor states driven by self-motion signals and distributed anchoring inputs from place cells.
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