Figure 3. Grid cells and grid-like representations.

(A) Key characteristics of grid cells comprise orientation ϕ, spacing, and phase offset from a reference location (R; adapted from [110]) as well as theta phase modulation (adapted from [94]). (B) Grid-like representations may emerge from firing of conjunctive grid by head-direction cells that exhibit increased firing when moving aligned as compared to misaligned with the grid axes (reprinted from [14]). (C) In a grid cell population with similar orientation and spacing (but with random phases), aligned movements lead to more frequent activation (shorter distance between firing fields) of a smaller number of different grid cells, whereas misaligned movements lead to less frequent activation (larger distance between firing fields) of a higher number of different grid cells. Aligned movements may thus lead to more pronounced repetition suppression (black arrow) at the level of spiking activity and/or LFP power and/or BOLD signal (fMRI adaptation), resulting in meso- and/or macroscopic gridlike representations. Shaded circles represent firing fields of different grid cells with similar orientation and spacing, but different phase offsets. Each color, one grid cell. Green arrow, aligned movement; red arrow, misaligned movement. (D) Since anatomically adjacent grid cells exhibit similar phase offsets (upper panels adapted from [113]; similar color indicates similar phase offset) in addition to similar orientation and spacing, recording from a limited number of grid cells with a nonrandom distribution of phase offsets leads to grid-like representations (lower panels adapted from [69]).