A computational model that explores the effect of environmental geometries on grid cell representations

Grid cells are a special class of spatial cells found in the medial entorhinal cortex (MEC) characterized by their strikingly regular hexagonal firing fields. This spatially periodic firing pattern was originally considered to be invariant to the geometric properties of the environment. However, this notion was contested by examining the grid cell periodicity in environments with different polarity (Krupic et al 2015) and in connected environments (Carpenter et al 2015). Aforementioned experimental results demonstrated the dependence of grid cell activity on environmental geometry. Analysis of grid cell periodicity on practically infinite variations of environmental geometry imposes a limitation on the experimental study. Hence we analyze the grid cell periodicity from a computational point of view using a model that was successful in generating a wide range of spatial cells, including grid cells, place cells, head direction cells and border cells. We simulated the model in four types of environmental geometries such as: 1) connected environments, 2) convex shapes, 3) concave shapes and 4) regular polygons with varying number of sides. Simulation results point to a greater function for grid cells than what was believed hitherto. Grid cells in the model code not just for local position but also for more global information like the shape of the environment. The proposed model is interesting not only because it was able to capture the aforementioned experimental results but, more importantly, it was able to make many important predictions on the effect of the environmental geometry on the grid cell periodicity.