Correlations and functional connections in a population of grid cells.

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.

Grid-Cell Distortion along Geometric Borders.

Grid cells fire in a triangular pattern that tessellates the environment [1]. The pattern displays a global distortion that is well described by a shearing transformation of an idealized grid [2]. However, in addition, distortions often differ across parts of the environment, suggesting that the grid interacts with the environment locally [2-5]. How this occurs is poorly understood. To further determine the nature of local distortions, we therefore analyzed the local spatial characteristics of the grid pattern. When rats ran in a large square enclosure, the grid pattern displayed several stereotypical distortions in relation to features of the environment. These distortions were stronger at edges than on open surfaces. Curved axis orientations and distortions of the grid pattern in the corners could be explained by a geometrical model where the pattern, in conjunction with being sheared, is compressed along the walls of the enclosure. The grid compression coincided with stereotypical running behavior where the animals moved faster in the areas where the grid had the most pronounced distortions. However, neither running direction nor speed influenced the distortions on a moment-to-moment basis, raising the possibility that the distortions are a learned feature.

Integration of grid maps in merged environments.

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.