A geometric attractor mechanism for self-organization of entorhinal grid modules

Abstract

Grid cells in the medial entorhinal cortex (mEC) respond when an animal occupies a periodic lattice of \"grid fields\" in the environment. The grids are organized in modules with spatial periods clustered around discrete values separated by constant ratios reported in the range 1.3-1.8. We propose a mechanism for dynamical self-organization in the mEC that can produce this modular structure. In attractor network models of grid formation, the period of a single module is set by the length scale of recurrent inhibition between neurons. We show that grid cells will instead form a hierarchy of discrete modules if a continuous increase in inhibition distance along the dorso-ventral axis of the mEC is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids, whose lattice constants are separated by [Formula], or other ratios. We discuss how the interactions required by our model might be tested experimentally and realized by circuits in the mEC.