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.

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.

The way mammals navigate in space is hypothesized to depend on neural structures in the temporal lobe including the hippocampus and medial entorhinal cortex (MEC). In particular, grid cells, neurons whose firing is mostly restricted to regions of space that form a hexagonal pattern, are believed to be an important part of this circuitry. Despite several years of work, not much is known about the correlated activity of neurons in the MEC and how grid cells are functionally coupled to each other. Here, we have taken a statistical approach to these questions and studied pairwise correlations and functional connections between simultaneously recorded grid cells. Through careful statistical analysis, we demonstrate that grid cells with nearby firing vertices tend to have positive effects on eliciting responses in each other, while those further apart tend to have inhibitory or no effects. Cells that respond similarly to manipulations of the environment are considered to belong to the same module. Cells belonging to a module have stronger interactions with each other than those in different modules. These results are consistent with and shed light on the population-based mechanisms suggested by models for the generation of grid cell firing.