Emergent elasticity in the neural code for space

Significance We develop a theoretical model, grounded in known properties of neural dynamics and synaptic plasticity, that can fuse information gathered from the past history of velocity and sequence of encountered landmarks during exploratory behavior, to construct a self-consistent internal representation of space. Moreover, through model reduction techniques, we obtain conceptual insights into how consistent internal spatial representations naturally emerge through an elastic relaxation process in an effective spring–particle system. We verify several experimentally testable predictions of our model involving the spatial behavior of grid cells in the medial entorhinal cortex, as well as suggest additional experiments. Upon encountering a novel environment, an animal must construct a consistent environmental map, as well as an internal estimate of its position within that map, by combining information from two distinct sources: self-motion cues and sensory landmark cues. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to accomplish this feat? Here we show analytically how a neural attractor model that combines path integration of self-motion cues 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, our model makes several experimentally testable predictions, including (i) systematic path-dependent shifts in the firing fields of grid cells toward the most recently encountered landmark, even in a fully learned environment; (ii) systematic deformations in the firing fields of grid cells in irregular environments, akin to elastic deformations of solids forced into irregular containers; and (iii) the creation of topological defects in grid cell firing patterns through specific environmental manipulations. Taken together, our results conceptually link known 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.