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Grid cells in the rodent entorhinal cortex display strikingly regular firingresponses to the animal's position in 2-D space, and have been hypothesized toform the neural substrate for dead-reckoning. However, in previous modelssuggested for grid cell activity, errors accumulate rapidly in the integrationof velocity inputs. To produce grid-cell like responses, these models wouldrequire frequent resets triggered by external sensory cues, casting doubt onthe dead-reckoning potential of the grid cell system. Here we focus on theaccuracy of path integration in continuous attractor models of grid cellactivity. We show, in contrast to previous models, that continuous attractormodels can generate regular triangular grid responses, based on inputs thatencode only the rat's velocity and heading. We consider the role of the networkboundary in integration performance, and show that both periodic and aperiodicnetworks are capable of accurate path integration, despite importantdifferences in their attractor manifolds. We show that the rate at which errorsaccumulate in the integration of velocity depends on the network's organizationand size, and on the intrinsic noise within the network. With a plausible rangeof parameters and the inclusion of spike variability, our model can accuratelyintegrate velocity inputs over a maximum of ~10-100 m and ~1-10 minutes. Thesefindings form a proof-of-concept that continuous attractor dynamics mayunderlie velocity integration in dMEC. The simulations also generate pertinentupper bounds on the accuracy of integration that may be achieved by continuousattractor dynamics in the grid cell network. We suggest experiments to test thecontinuous attractor model and differentiate it from models in which singlecells establish their responses independently of each other.

Accurate path integration in continuous attractor network models of grid cells