Grid cells in the entorhinal cortex respond when an animal occupies spatial locations that lie on the vertices of a regular lattice. The grids are organized in a discrete hierarchy of modules so that cells in each share the same lattice structure and orientation, but with lattice constants that scale geometrically between modules. When an environment is stretched or compressed, the grids deform proportionally. A neural network model with attractor dynamics is known to produce a single grid module, but the dynamical origin of the hierarchy is unknown. In this talk, I will show that the grid system should be understood as a two-dimensional number system for location in space, and that efficiency criteria predict the modular structure and the experimentally measured scaling ratio between modules. Then I will demonstrate that learned interactions between grid cells and border cells (which fire near boundaries), can reproduce the stretching and squashing of grids when an environment is deformed. Finally, I will describe a new model of grid self-organization which robustly produces a discrete hierarchy of modules with geometric scaling ratios in the experimental range. The model exploits an analogy between the structure of coupled neural networks with different inhibition length scales and the Frenkel-Kontorova model of condensed matter physics to achieve robust self-organization through geometric relations between the lattices produced in different modules. There is a rich phase structure, with these lattices showing commensurate, incommensurate, discommensurate and even quasi-crystalline organization depending on the relative strength of the excitatory and inhibitory couplings in the neural network.
Spatial localization in the brain via dynamical self-organization of grid cells
Monday, October 23, 2017 - 12:00pm
Joseph Henry Room, Jadwin Hall
CUNY-Princeton Biophysics Seminar
Physics and Lewis-Sigler Institute