Continuous Attractor Network Model for Conjunctive Position-by-Velocity Tuning of Grid Cells

The spatial responses of many of the cells recorded in layer II of rodent medial entorhinal cortex (MEC) show a triangular grid pattern, which appears to provide an accurate population code for animal spatial position. In layer III, V and VI of the rat MEC, grid cells are also selective to head-direction and are modulated by the speed of the animal. Several putative mechanisms of grid-like maps were proposed, including attractor network dynamics, interactions with theta oscillations or single-unit mechanisms such as firing rate adaptation. In this paper, we present a new attractor network model that accounts for the conjunctive position-by-velocity selectivity of grid cells. Our network model is able to perform robust path integration even when the recurrent connections are subject to random perturbations.Author Summary: How do animals self-localize when they explore the environments with variable velocities? One mechanism is dead reckoning or path-integration. Recent experiments on rodents show that such computation may be performed by grid cells in medial entorhinal cortex. Each grid cell fires strongly when the animal enters locations that define the vertices of a triangular grid. Some of the grid cells show grid firing patterns only when the animal runs along particular directions. Here, we propose that grid cells collectively represent arbitrary conjunctions of positions and movements of the animal. Due to asymmetric recurrent connections, the network has grid patterns as states that are able to move intrinsically with all possible directions and speeds. A velocity-tuned input will activate a subset of the population that prefers similar movements, and the pattern in the network moves with a velocity proportional to the movement of the animal in physical space, up to a fixed rotation. Thus the network ‘imagines’ the movement of the animal, and produces single cell grid firing responses in space with different degree of head-direction selectivity. We propose testable predictions for new experiments to verify our model.