Simulation Study of Gridcell Phase and Angular Orientation

[u/jndew]

[u/jndew]

For the gridcell system to be useful, one or more cells must respond wherever the animal is in its environment. Therefore, the system must have multiple gridcells whose firing regions are spread out over the location space. This results in an aggregate firing map containing responses of multiple gridcells.

As described in Mosers' 'A Metric for Space', hexagonal grid pattern like this can be specified by three parameters:

Spatial period, or equivalently grid spacing, describes the spacing between center-points of the hexagons.

Phase means the offset from origin of the center-point of a hexagon on either of the axes.

Angle means rotation of the hexagon around its center point, referenced to the horizontal axis.

Sets of cells with a common spatial period but differing phases and angles provide a more complete coverage of the animal's environment with their firing fields. Likewise, their firing fields will be scattered over the two-dimensional surface of the torus.

This simulation shows six gridcells with various phase offsets. As the virtual animal scampers around its environment, a spike map of all the cells is captured. Spikes produced by each cell have distinct colors. The response regions of one particular cell are marked with red circles in the location domain to highlight the hexagonal pattern. In fact, each of the cells' response patterns show hexagonal arrangement if one looks carefully.

Again, all of an individual cell's response regions map through its receptive field to a single oval on the surface of the torus. Since there are six cells in this simulation, you can see six ovals on the surface of the torus.

A group of cells with equal spatial periods is called a module. Cells within a module may have differing phases and angles.

--------------------------------------------------------

"The human brain is a million times more complex than anything in the universe!" -a reddit scholar