Modularization of grid cells constrained by the pyramidal patch lattice

Grid cells provide a metric representation of self-location. They are organized into modules, showing discretized scales of grid spacing, but the underlying mechanism remains elusive. In this modeling study, we propose that the hexagonal lattice of pyramidal cell patches may underlie the discretization of grid spacing and orientation. In the continuous attractor network composed of interneurons, stellate and pyramidal cells, the hexagonal lattice of bump attractors is specifically aligned to the patch lattice under 22 conditions determined by the geometry of the patch lattice, while pyramidal cells exhibit synchrony to diverse extents. Given the bump attractor lattice in each module originates from those 22 scenarios, the experimental data on the grid spacing ratio and orientation difference between modules can be reproduced. This work recapitulates the patterns of grid spacing versus orientation in individual animals and reveals the correlation between microstructures and firing fields, providing a systems-level mechanism for grid modularity.