Specific evidence of low-dimensional continuous attractor dynamics in grid cells

We examine simultaneously recorded spikes from multiple grid cells, to elucidate mechanisms underlying their activity. We demonstrate that grid cell population activity, among cells with similar spatial periods, is confined to lie close to a 2-dimensional manifold: grid cells differ only along two dimensions of their responses and are otherwise nearly identical. The relationships between cell pairs are conserved despite extensive deformations of single-neuron responses. Results from novel environments suggest such structure is not inherited from hippocampal or external sensory inputs. Across conditions, cell-cell relationships are better conserved than the responses of single cells. Finally, the system is continually subject to perturbations that were the 2-d manifold not attractive, would drive the system to inhabit a different region of state-space than observed. Together, these findings have strong implications for theories of grid cell activity, and provide compelling support for the general hypothesis that the brain computes using low-dimensional continuous attractors.