Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Grid cells in the rat entorhinal cortex display strikingly regular firingresponses to the animal''s position in 2-D space and have beenhypothesized to form the neural substrate for dead-reckoning. However, errorsaccumulate rapidly when velocity inputs are integrated in existing models ofgrid cell activity. To produce grid-cell-like responses, these models wouldrequire frequent resets triggered by external sensory cues. Such inadequacies,shared by various models, cast doubt on the dead-reckoning potential of the gridcell system. Here we focus on the question of accurate path integration,specifically in continuous attractor models of grid cell activity. We show, incontrast to previous models, that continuous attractor models can generateregular triangular grid responses, based on inputs that encode only therat''s velocity and heading direction. We consider the role of thenetwork boundary in the integration performance of the network and show thatboth periodic and aperiodic networks are capable of accurate path integration,despite important differences in their attractor manifolds. We quantify the rateat which errors in the velocity integration accumulate as a function of networksize 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.