Modeled grid cells aligned by a flexible attractor

Abstract

ABSTRACTEntorhinal grid cells implement a spatial code with hexagonal periodicity, signaling the position of the animal within an environment. Grid maps of cells belonging to the same module share spacing and orientation, only differing in relative two-dimensional spatial phase, which could result from their participation in a two-dimensional attractor. Such an architecture, however, has the drawbacks of being complex to construct and rigid, allowing no degrees of freedom for grid cells to deviate from the hexagonal pattern, as happens under a variety of experimental manipulations. Here we show that a simpler one-dimensional architecture is enough to align grid cells equally well. Using topological data analysis, we show that the resulting population activity is a sample of a torus, while the ensemble of maps preserves features of the network architecture. The flexibility of this low dimensional attractor allows it to negotiate with the feedforward inputs the geometry of the representation manifold, rather than imposing it, finding a number of equally viable configurations. Our results represent a proof of principle against the intuition that the architecture and the representation manifold of an attractor are the same topological object, with implications to the study of attractor networks across the brain.