Representation of an environmental space by grid fields: A study with a computational model of the grid cell based on a column structure

Recent experimental findings on spatially periodic firing fields of "grid cells" in the medial entorhinal cortex (MEC) of rats make our reconsideration on the origin of hippocampal place fields, and provide aspects of further research of the mechanism of spatial computation in the brain. However, the mechanism behind their periodic firing fields is still an open question. In this paper we provide a simple, biologically plausible computational model based on a hypothesis (Yamaguchi et al. 2007) which assumes the generation of grid fields in EC superficial layers from deep layers. In our model, units in the deep layer of a column structure are assumed as a hexagonal direction system module for local path integration from head direction and running velocity. By integrating outputs of this module, three or more units in the superficial layer of the column exhibit grid cell properties. With computer simulation of this model applied in a simulated moving path of a rat, we show precise hexagonal grid fields that are generated from the superficial units of the hypothesized column structure. Simulation results show grid fields generated by this model with various size, spacing and orientation, not being distorted by randomness of running velocity and head direction signals. Overall, our results indicate the possibility of a significant contribution of grid cells to the origin of hippocampal place fields. Furthermore, we show that our grid cell model for a two dimensional environment can be naturally extended to representation of a three dimensional environment to predict the properties of grid cells in case of movement in 3D space, from a theoretical point of view.