The arrangement of grid cells’ spatial firing fields, equidistant from neighbors, led to a hypothesis that they encode some neural representation of Euclidean Space. Also hints at a mechanism for dynamic computation of relative/self position based on continous updates regarding direction/position.
Toroidal Topology of Grid Cells
It is theorized that Continuous Attractor Networks serve as a substrate of the grid pattern. However it is still unclear if they really show Continuous Attractor Dynamics.
When looking at grid cells in the medial Entorhinal Cortex fire at various locations, a distinct periodic hexogonal pattern emerges. However, when looking at the population activity(collective grid cell firing rate patterns), researchers ( (Gardner et al., 2022) ) found that 2d grid pattern could not extend to this case. Rather, it was constrained to the surface of a Torus. Certainly more to investigate regarding these cells when I get the time
Bibliography
- Gardner, R. J., Hermansen, E., Pachitariu, M., Burak, Y., Baas, N. A., Dunn, B. A., Moser, M.-B., & Moser, E. I. (2022). Toroidal Topology of Population Activity in Grid Cells. Nature, 602(7895), 123–128. https://doi.org/10.1038/s41586-021-04268-7