To navigate a novel environment, we must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks.
How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such maps? We demonstrate analytically that a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network. Moreover, we verify several experimentally testable predictions of our model in an extended collaboration with Dr. Giocomo’s lab at Stanford. Our predictions include: (1) systematic deformations in the firing fields of grid cells in irregular environments, akin to elastic deformations of solids forced into irregular containers, (2) systematic path-dependent shifts in the firing fields of grid cells towards the most recently encountered landmark, even in a fully learned environment, (3) a dynamical phase transition separating two operating regimes in which grid cells either entrain to or break away from the landmark reference frame, when the consistency between self-motion and landmarks is altered in a virtual reality environment, and (4) the creation of topological defects in grid cell firing patterns through precise environmental manipulations. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.