Accurate Path Integration in Continuous Attractor Network Models ofGrid Cells

摘要

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range ofparameters and the inclusion of spike variability, our model networks canaccurately integrate velocity inputs over a maximum of ∼10–100meters and ∼1–10 minutes. These findings form aproof-of-concept that continuous attractor dynamics may underlie velocityintegration in the dorsolateral medial entorhinal cortex. The simulations alsogenerate pertinent upper bounds on the accuracy of integration that may beachieved by continuous attractor dynamics in the grid cell network. We suggestexperiments to test the continuous attractor model and differentiate it frommodels in which single cells establish their responses independently of eachother.